• Syllabus

Topic 1 - Number and algebra

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Sub sections and their related questions

1.0

• 10M.1.sl.TZ1.14b.i: Find the value of a.
• 11N.1.sl.TZ0.1a: Find the exact value of \(z\).
• 10M.2.sl.TZ1.4f: To calculate the cost of air conditioning, engineers must estimate the weight of air in the...
• 10M.2.sl.TZ1.5A.b: Determine Daniel’s best investment option.
• 11N.1.sl.TZ0.8b: On his return, George had \(160\) EUR to change back into USD. There was \(4.5\% \) commission...
• 10N.1.sl.TZ0.1b: Write down the smallest of these numbers.
• 10N.1.sl.TZ0.1c: Write down the value of q + s.
• 10N.1.sl.TZ0.3b: Joaquin estimates the volume of one cube to be 500 cm3. He uses this value to estimate the number...
• 10N.1.sl.TZ0.5b: Estimate the number of students who achieved a mark greater than 32.
• 10N.1.sl.TZ0.9a.i: List the elements of the following set. A
• 10N.1.sl.TZ0.9b: Write down one element of \((A \cup B)'\).
• 10N.1.sl.TZ0.9c: One of the statements in the table below is false. Indicate with an X which statement is false....
• 10N.1.sl.TZ0.14a: Write down an expression for A in terms of x.
• 10N.1.sl.TZ0.14c: The owner of the garden puts a fence around the shaded region. Find the length of this fence.
• 11N.1.sl.TZ0.13a: (i) Find the value of \(k\) . (ii) Calculate the \(y\)-coordinate of this minimum point.
• 10N.2.sl.TZ0.1A.c: Write down the percentage of students who had fruit for breakfast.
• 10N.2.sl.TZ0.3c: Village D is halfway between A and B. A new road perpendicular to AB and passing through D is...
• 10N.2.sl.TZ0.5d: (i) Use f '(x) to find the x-coordinate of M and of N. (ii) Hence or otherwise write down the...
• 11N.1.sl.TZ0.15b: The graph passes through the point (2, 48) . Find the value of \(c\) .
• 12N.2.sl.TZ0.2g: The students are asked to collect money for charity. In the first month, the students collect x...
• 12N.2.sl.TZ0.3e: He next marks a fourth point, D, on the ground at a distance of 6 m from B , such that angle BDC...
• 12M.1.sl.TZ1.3a: Calculate the exact time, in hours, for the spacecraft to reach the star Ross.
• 12M.1.sl.TZ1.14b: Write down the value of r .
• 12M.1.sl.TZ1.14c: Find the value of s .
• 12M.2.sl.TZ1.5b: Find the value of f (−1).
• 12M.2.sl.TZ1.5e: Show that \(f'( - 1) =  - \frac{{16}}{3}\).
• 12M.1.sl.TZ2.1a: Write down the value of r = c × d.  
• 12M.1.sl.TZ2.1c: Consider the following statements about c, d and r. Only three of these statements are...
• 12M.1.sl.TZ2.6a: Write down the boiling point of water at sea level.
• 12M.1.sl.TZ2.6b: Use the model to calculate the boiling point of water at a height of 1.37 km above sea level.
• 12M.1.sl.TZ2.6c: Water boils at the top of Mt. Everest at 70 °C. Use the model to calculate the height above sea...
• 12M.2.sl.TZ2.1a: Write down the total number of fish in the pond.
• 12M.2.sl.TZ2.2a: Write down the amount of the deposit.
• 12M.2.sl.TZ2.2b: Calculate the total cost of the loan under this repayment scheme.
• 12M.2.sl.TZ2.2e: Cedric’s mother decides to help him by giving him an interest free loan of €8000 to buy the car....
• 12M.2.sl.TZ2.5a: Show that y =12 − 3x .
• 12M.2.sl.TZ2.5b: Show that the volume V m3 of the container is given by V = 24x2 − 6x3
• 11N.2.sl.TZ0.4c: Show that \(f'(x)\) can be written as \(f'(x) = \frac{{2{x^3} - 2{x^2} - 9}}{{{x^2}}}\) .
• 11M.1.sl.TZ1.1a: Calculate the value of \(p\).
• 11M.1.sl.TZ1.1b: Barry first writes \(x\) , \(y\) and \(z\) correct to one significant figure and then uses these...
• 11M.1.sl.TZ1.2a: Find the value of \(q\) .
• 11M.1.sl.TZ1.15b: The point \((2{\text{, }}1)\) lies on the graph of \(y = f(x)\) . Calculate the value of \(a\) .
• 09M.2.sl.TZ1.4c: It is known that 1 cm3 of this chocolate weighs 1.5 g. Calculate the weight of the chocolate bar.
• 09M.2.sl.TZ1.4e: The weight of this chocolate bar is 500 g. Find its length.
• 11M.2.sl.TZ1.3d: Find \(f'(2)\) .
• 11M.2.sl.TZ1.5b: The fence costs \(17\) USD per metre to build. Calculate the cost of building the fence. Give...
• 11M.2.sl.TZ1.5e: She sells the land for \(120\) USD per square metre. Calculate the value of the land that...
• 09M.2.sl.TZ2.3d: The farmer wants to build a fence around ABD. The farmer pays 802.50 USD for the fence. Find the...
• 11M.1.sl.TZ2.7a: Write down an equation in \(x\) and \(y\) .
• 11M.1.sl.TZ2.7b: The cost of an adult ticket was \(12\) Australian dollars (AUD). The cost of a child ticket was...
• 11M.1.sl.TZ2.7c: The total cost of tickets sold for the sports match was \(108800{\text{ AUD}}\). Write down a...
• 11M.1.sl.TZ2.12a: Find the number of statues that are non-defective.
• 11M.1.sl.TZ2.15a: Write down and simplify a quadratic equation in \(x\) which links the three sides of the triangle.
• 13M.1.sl.TZ1.1a: Find the value of z when x = 12.5, a = 0.572 and b = 0.447. Write down your full calculator display.
• 13M.1.sl.TZ1.6d: Write down a value of \(x\) for which \(\neg p \vee q\) is false.
• 13M.1.sl.TZ1.9d: Write down \(f (x)\) in the form \(f (x) = −(x − p) (x + q)\).
• 13M.1.sl.TZ1.12b: The tenth term of the sequence is double the seventh term. (i) Write down an equation in u1 and...
• 13M.1.sl.TZ1.15b: Write down the value of \(f ′(0)\).
• 13M.1.sl.TZ1.15c: The function has a local maximum at x = −2. Calculate the value of a.
• 13M.2.sl.TZ1.3a: Write down the decrease in the temperature of the coffee (i) during the first minute (between t...
• 13M.2.sl.TZ1.3b: Assuming the pattern in the answers to part (a) continues, show that \(k = 19\).
• 13M.2.sl.TZ1.5g: The cost of one square metre of glass used to construct the greenhouse is 4.80 USD. Calculate...
• 11M.2.sl.TZ2.3B.b: The sum of the first \(n\) terms of this sequence is \(\frac{n}{2}(3n - 1)\). (i)     Find the...
• 13M.1.sl.TZ2.9b: Write down the value of y.
• 13M.1.sl.TZ2.9c: The areas of regions A, B, and C are equal. Write down the area of region A.
• 13M.1.sl.TZ2.9d: Using your answers to parts (b) and (c), find the value of x.
• SPM.1.sl.TZ0.13c: Use the model to predict the temperature of the liquid \(60{\text{ seconds}}\) after the start of...
• SPM.2.sl.TZ0.6d: Show that the total external surface area, \(A\) , of the bin is...
• SPM.2.sl.TZ0.6f: (i)     Find the value of \(r\) that minimizes the total external surface area of the wastepaper...
• 07N.1.sl.TZ0.1a: Calculate \(\frac{{77.2 \times {3^3}}}{{3.60 \times {2^2}}}\).
• 07N.1.sl.TZ0.10a: Solve the following equation for x \(3(2x +1) − 2(3 − x)=13\).
• 07N.1.sl.TZ0.10b: Factorize the expression \(x^2 + 2x − 3\).
• 08N.1.sl.TZ0.1a: Calculate the exact value of \(h\) when \(\ell  = 0.03625\) and \(d = 0.05\) .
• 08N.1.sl.TZ0.13a: Factorise the expression \({x^2} - kx\) .
• 08M.1.sl.TZ1.1a: Calculate exactly \(\frac{{{{(3 \times 2.1)}^3}}}{{7 \times 1.2}}\).
• 08M.2.sl.TZ1.5i.a: Factorise \(3{x^2} + 13x - 10\).
• 08M.2.sl.TZ1.5ii.b: Find an expression for \(y\) in terms of \(x\).
• 08M.1.sl.TZ2.10a: Factorise the expression \({x^2} - 3x - 10\).
• 10M.1.sl.TZ1.14b.ii: Find the value of b.
• 10M.2.sl.TZ2.4a.iii: Find how many bricks are required to pave the total area.
• 10M.2.sl.TZ2.4b.iv: Find the percentage of the rectangular area which is to be lawn.
• 10N.1.sl.TZ0.9a.ii: List the elements of the following set. \(A \cap B'\)
• 14M.1.sl.TZ2.1c: Today is Anna’s 17th birthday. Calculate the total distance that Anna has travelled around the...
• 14M.1.sl.TZ2.4b: Write down the volume of 20 chocolates.
• 14M.1.sl.TZ2.6c: The area of the carpet is \({\text{10 }}{{\text{m}}^2}\). Hence, write down the value of the...
• 14M.2.sl.TZ2.2d: The distance from \({\text{B}}\) to \({\text{C}}\) is \(850\) metres. Running this part of the...
• 14M.2.sl.TZ2.4a: If Hugh chooses Option A, calculate the total value of his allowance at the end of the two year...
• 14M.2.sl.TZ2.4e: State which of the options, A, B, C or D, Hugh should choose to give him the greatest total value...
• 14M.2.sl.TZ2.5b: Show that \(l = \frac{{150}}{w}\).
• 14M.2.sl.TZ2.6g: The water tank is shown below. It is partially filled with water.   The water tank has a...
• 13N.1.sl.TZ0.2a: List the elements of \(A\).
• 13N.1.sl.TZ0.2b: List the elements of \(B\).
• 13N.1.sl.TZ0.9a: Expand the expression \(x(2{x^3} - 1)\).
• 13N.2.sl.TZ0.5b: Write down, in \({\text{GBP}}\), the amount of money Arthur saved by buying the car in Germany.
• 14M.1.sl.TZ1.5b: On arrival in Singapore, Dumisani changes 3000 USD to Singapore dollars (SGD) to pay for his...
• 14M.2.sl.TZ1.6c: The volume of the lobster trap is \(0.75{\text{ }}{{\text{m}}^{\text{3}}}\). Show that...
• 14N.1.sl.TZ0.4a: Calculate the amount that Albena receives in EUR.
• 14N.1.sl.TZ0.9d: An Olympic sized swimming pool is \(50\) m long and \(25\) m wide. Determine the area of the...
• 14N.2.sl.TZ0.3c: A company designs cone-shaped tents to resemble the traditional tepees. These cone-shaped tents...
• 14N.2.sl.TZ0.4b: The surveyor measures the size of angle \({\text{CDE}}\) to be twice that of angle...
• 14N.2.sl.TZ0.5a: Write down the distance, \({a_1}\), in metres that she has to run in order to collect the first...
• 15M.1.sl.TZ1.1a: Calculate the exact value of \(T\).
• 15M.1.sl.TZ1.5b: The volume of the Moon is \(2.1958 \times {10^{10}}\;{\text{k}}{{\text{m}}^3}\). Calculate how...
• 15M.1.sl.TZ1.12c: At 210°C the length of the iron bar is 181.5 mm. Hence, find the length of the iron bar at 40°C.
• 15M.1.sl.TZ1.15a: Find the value of \(a\).
• 15M.1.sl.TZ2.1a: Find the distance from \({\text{P}}(100,{\text{ }}200)\) to \({\text{A}}\). Give your answer...
• 15M.2.sl.TZ1.3i: It is proposed that the speed limit past the hospital gate is reduced to...
• 15M.2.sl.TZ1.4b: It is estimated that the fastest boat in the race can travel at an average speed of...
• 15M.2.sl.TZ1.5d: The graph of \(y = f(x)\) has a local minimum point at \(x = 4\). Find \(f'(2)\)
• 15M.2.sl.TZ2.1c: The number of customers that like only mangoes is equal to the number of customers that like only...
• 15M.2.sl.TZ2.2d: Temi covers the perfume bottles with a paint that costs 3 South African rand (ZAR) per...
• 15M.2.sl.TZ2.3e: The \({n^{{\text{th}}}}\) term of the arithmetic sequence is given by \({u_n}\). Find the lowest...
• 15M.2.sl.TZ2.4d: Daniel assumes that the diameters of all of the apples from his harvest are normally distributed...
• 15M.2.sl.TZ2.6e: All the bicycles that are produced are sold. The bicycles are sold for 304 USD each. (i)    ...

1.1

• 10M.1.sl.TZ1.2: The sets \(P\), \(Q\) and \(U\) are defined as U = {Real Numbers} ,  P = {Positive Numbers} and...
• 12M.1.sl.TZ2.1c: Consider the following statements about c, d and r. Only three of these statements are...
• 09N.1.sl.TZ0.2: The Venn diagram shows the number sets \(\mathbb{N}\), \(\mathbb{Z}\), \(\mathbb{Q}\) and...
• 13M.1.sl.TZ2.3: Consider the numbers 3, −5 , \(\sqrt{7}\), \(2^{−3}\) and 1.75. Complete the table below,...
• 11M.1.sl.TZ2.1b: List the elements of \(B\) .
• 13M.1.sl.TZ1.2a: List the elements of (i) U ; (ii) B .
• 07M.1.sl.TZ0.1b: Calculate \(\sqrt {{{3.87}^5} - {{8.73}^{ - 0.5}}} \), giving your answer (i) correct to the...
• 07M.1.sl.TZ0.6c: State which of the numbers in part (a) is irrational.
• 08M.1.sl.TZ1.11a: Consider the numbers \(2\), \(\sqrt 3 \), \( - \frac{2}{3}\) and the sets \(\mathbb{N}\),...
• 08M.1.sl.TZ2.4: Consider the numbers \(\sqrt 3 \), \(6\), \(2\frac{1}{2}\), \(\pi \), \( - 5\), and the sets...
• 14M.1.sl.TZ2.3a: 4
• 14M.1.sl.TZ2.3b: \(\frac{1}{3}\)
• 14M.1.sl.TZ2.3c: \(\pi \)
• 14M.1.sl.TZ2.3d: \(0.38\)
• 14M.1.sl.TZ2.3e: \(\sqrt 5 \)
• 14M.1.sl.TZ2.3f: \(-0.25\)
• 16M.1.sl.TZ1.5a: Consider the following statements \(z\,:\,x\) is an integer\(q\,:\,x\) is a rational...
• 16M.1.sl.TZ1.5b: Write the following argument in symbolic form:“If \(x\) is a real number and \(x\) is not a...
• 16M.1.sl.TZ1.5c: Phoebe states that the argument in part (b) can be shown to be valid, without the need of a truth...
• 16M.1.sl.TZ2.2: Consider the numbers \( - 1,\,\,4,\,\,\frac{2}{3},\,\,\sqrt 2 ,\,\,0.35\) and \( -...
• 18M.1.sl.TZ2.4a: Complete the second column of the table by giving one example of a number from each set.
• 18M.1.sl.TZ2.4b: Josh states: “Every integer is a natural number”. Write down whether Josh’s statement is...

1.2

• 10M.1.sl.TZ1.1b: Jim estimates the dimensions of the container as 15 m, 2 m and 3 m and uses these to estimate the...
• 10M.1.sl.TZ1.5a: Calculate the volume of the sphere. Give your answer correct to two decimal places.
• 10M.1.sl.TZ1.5b: Write down your answer to (a) correct to the nearest integer.
• 10M.1.sl.TZ2.1c: José estimates the angle between the horizontal and the top of the cliff as 28.3° and uses it to...
• 10M.1.sl.TZ2.10a: Find the interest Astrid has earned during the five years of her investment. Give your answer...
• 10M.1.sl.TZ2.12c: Determine the length of time it would take for 150 teenagers to have heard the rumour. Give your...
• 11N.1.sl.TZ0.1b.i: Write your answer to part (a) correct to 2 decimal places.
• 11N.1.sl.TZ0.1b.ii: Write your answer to part (a) correct to three significant figures.
• 11N.1.sl.TZ0.1b.iii: Write your answer to part (a) in the form \(a \times {10^k}\), where 1 ≤ a < 10,...
• 10N.1.sl.TZ0.3c: The actual number of cubes in the box is 350. Find the percentage error in Joaquin’s estimated...
• 12N.1.sl.TZ0.3c: Marian calculates the mean length and finds it to be 105 cm. Calculate the percentage error made...
• 12M.1.sl.TZ1.3b: Give your answer to part (a) in years. (Assume 1 year = 365 days)
• 10M.2.sl.TZ2.2e: Using your graph, estimate the time when Alex and Kris pass the 85 km distance marker. Give your...
• 12M.2.sl.TZ1.1f: The population of Beartown is 120 000. The local radio station claimed that 34 000 of the town’s...
• 12M.2.sl.TZ1.3b: Show that the volume of the metal used in the cylinder is 402 cm3, given correct to three...
• 09N.1.sl.TZ0.3b: Helen’s estimate of the area of the rectangle is \(1\,600\,000{\text{ }}{{\text{m}}^2}\). Find...
• 09N.1.sl.TZ0.8a: Find the exchange rate between GBP and EUR in the form 1 GBP = k EUR, where k is a constant. Give...
• 09N.1.sl.TZ0.8b: Isabella changes 400 USD into Euros and is charged 2 % commission. Calculate how many Euros she...
• 09N.1.sl.TZ0.15b: Mr Black invested 5000 CHF in Bank B at a nominal annual interest rate of 3.6 %, compounded...
• 11M.1.sl.TZ1.1b: Barry first writes \(x\) , \(y\) and \(z\) correct to one significant figure and then uses these...
• 11M.1.sl.TZ1.1c: Calculate the percentage error in Barry’s estimate of the value of \(p\) .
• 11M.1.sl.TZ1.5b: Calculate the distance travelled by the satellite in one orbit of the Earth. Give your answer...
• 09M.1.sl.TZ1.10b: Nadia makes an accurate drawing of triangle ABC. She measures angle BAC and finds it to be...
• 11M.2.sl.TZ1.5b: The fence costs \(17\) USD per metre to build. Calculate the cost of building the fence. Give...
• 11M.2.sl.TZ1.5e: She sells the land for \(120\) USD per square metre. Calculate the value of the land that...
• 09M.1.sl.TZ2.1b: Find the area of the rectangle, giving your answer correct to the nearest thousand square...
• 11M.1.sl.TZ2.6c: A local newspaper claims that the mean number of goals scored per match is two. Calculate the...
• 13M.1.sl.TZ1.1b: Write down your answer to part (a) (i) correct to the nearest 1000 ; (ii) correct to three...
• 13M.1.sl.TZ1.11b: Calculate the number of American dollars (USD) Neung takes home. Give your answer correct to 2...
• 13M.1.sl.TZ1.11c: At the airport in Vietnam, Neung changes 150 USD into Vietnamese dong (VND) to pay for her...
• 13M.2.sl.TZ1.3i: Find the percentage error in this estimate of the temperature of the coffee at t = 3.
• 13M.2.sl.TZ1.5g: The cost of one square metre of glass used to construct the greenhouse is 4.80 USD. Calculate...
• 13M.1.sl.TZ2.1b: Write your answer to part (a) correct to (i) one decimal place; (ii) three significant figures.
• 13M.1.sl.TZ2.12b: Yoshi spends 426.70 EUR in Italy. In an American bank he changes the remaining amount, into US...
• 13M.1.sl.TZ2.15a: Calculate the total amount of interest Marcus would earn, in AUD, over the three years. Give your...
• 07M.1.sl.TZ0.1a: (i) Find the mean of the contractor’s measurements. (ii) Calculate the percentage error between...
• 07M.1.sl.TZ0.1b: Calculate \(\sqrt {{{3.87}^5} - {{8.73}^{ - 0.5}}} \), giving your answer (i) correct to the...
• 07M.1.sl.TZ0.3a: 1 Brazilian Real (BRL) = 2.607 South African Rand (ZAR). Giving answers correct to two decimal...
• SPM.1.sl.TZ0.11a: Find the value of the investment after 3 years.
• SPM.1.sl.TZ0.11b: Find the difference in the final value of the investment if the interest was compounded quarterly...
• SPM.2.sl.TZ0.1e: Sam estimated the value of the mean of the measured lengths to be \(43{\text{ cm}}\). Find the...
• SPM.2.sl.TZ0.3e: The selling price, in US dollars (USD), of each size is shown in the table below.The probability...
• 07M.2.sl.TZ0.2i.a: Calculate the volume of the cylinder in cm3. Give your answer correct to two decimal places.
• 07M.2.sl.TZ0.4ii.d: Explain why the sum of the first 1000 terms of G2 will give the same answer as the sum of the...
• 07M.2.sl.TZ0.4ii.e: Using your results from parts (a) to (c), or otherwise, calculate the sum of the first 10 terms...
• 07N.1.sl.TZ0.1c: Juan estimates the length of a carpet to be 12 metres and the width to be 8 metres. He then...
• 07N.1.sl.TZ0.6b: Calculate the value of Ben’s investment at the end of 6 years. Give your answer correct to 2...
• 07N.2.sl.TZ0.3ii.a: Calculate correct to 2 decimal places the amount of euros he receives.
• 07N.2.sl.TZ0.3ii.b: He buys 1 kilogram of Belgian chocolates at 1.35 euros per 100 g. Calculate the cost of his...
• 07N.2.sl.TZ0.4ii.c: Find the expected frequency for the number of females who had ‘Comedy’ as their most-watched...
• 08N.1.sl.TZ0.1b: Write down the answer to part (a) correct to three decimal places.
• 08N.1.sl.TZ0.1c: Write down the answer to part (a) correct to three significant figures.
• 08N.1.sl.TZ0.5a: Kwai Fan changes \({\text{S\$ }}500\) to Indian rupees. Calculate the number of Indian rupees...
• 08N.1.sl.TZ0.5c: On her return to Singapore, Kwai Fan has \(2500\) Indian rupees left from her trip. She wishes to...
• 08M.1.sl.TZ1.1b: Write the answer to part (a) correct to 2 significant figures.
• 08M.1.sl.TZ1.1c: Calculate the percentage error when the answer to part (a) is written correct to 2 significant...
• 08M.2.sl.TZ1.1d: Using your graphical display calculator write down the coordinates of one of the points of...
• 08M.1.sl.TZ2.11a: Minbin has \(1250\) Japanese Yen which she wishes to exchange for Chinese Yuan. Calculate how...
• 08M.1.sl.TZ2.11b: Rupert has \(855\) Canadian Dollars which he wishes to exchange for Japanese Yen. Calculate how...
• 08M.1.sl.TZ2.11c: Find how many Norwegian Kroner there are to the Euro. Give your answer correct to 2 decimal places.
• 14M.2.sl.TZ2.2a: Using ‘distance = speed \( \times \) time’, show that the distance...
• 13N.2.sl.TZ0.1h: The actual price of the return ticket is \(\$80\). Using your answer to part (f), calculate the...
• 14M.1.sl.TZ1.1a: Calculate the value of \(p\) when \(x = 45^\circ \), \(y = 8192\) and \(z = 64\). Write down your...
• 14M.1.sl.TZ1.1b: Write down your answer to part (a) (i)     correct to two decimal places; (ii)     correct to...
• 14M.1.sl.TZ1.12c: Ludmila estimates that she will have to repay \({\text{360}}\,{\text{000}}\) BRL at the end of...
• 14N.1.sl.TZ0.6a: Find the amount of the interest that Mandzur must pay. Give your answer correct to the nearest...
• 14N.2.sl.TZ0.1h: A cricket makes 20 chirps in 15 seconds. For this chirp rate (i)     calculate an estimate for...
• 14N.2.sl.TZ0.4a: (i)     Find the size of angle \({\rm{ACB}}\). (ii)     Show that the size of angle...
• 15M.1.sl.TZ1.1b: Give your answer to \(T\) correct to (i)     two significant figures; (ii)     three decimal...
• 15M.1.sl.TZ1.1c: Pyotr estimates the value of \(T\) to be \(0.002\). Calculate the percentage error in Pyotr’s...
• 15M.1.sl.TZ1.5b: The volume of the Moon is \(2.1958 \times {10^{10}}\;{\text{k}}{{\text{m}}^3}\). Calculate how...
• 15M.1.sl.TZ1.10a: Calculate the value of Pierre’s investment at the end of this time. Give your answer correct to...
• 15M.1.sl.TZ2.1a: Find the distance from \({\text{P}}(100,{\text{ }}200)\) to \({\text{A}}\). Give your answer...
• 15M.1.sl.TZ2.1b: Write down your answer to part (a) correct to three significant figures.
• 15M.1.sl.TZ2.2c: Fabián estimates that the distance from the base of the building to the car is 150 metres....
• 15M.1.sl.TZ2.10a: Find the amount of money that Minta will have in the bank after 3 years. Give your answer correct...
• 15M.2.sl.TZ2.2d: Temi covers the perfume bottles with a paint that costs 3 South African rand (ZAR) per...
• 15M.2.sl.TZ2.2e: Temi sells her perfume bottles in a craft fair for 325 ZAR each. Dominique from France buys one...
• 15M.2.sl.TZ2.6c: Estimate the total cost, to the nearest USD, of producing \(13\) bicycles on a particular day.
• 16M.1.sl.TZ1.6a: One of the locations in the \(2016\) Olympic Games is an amphitheatre. The number of seats in the...
• 16M.1.sl.TZ1.6b: There are \(20\) rows in the amphitheatre. Find the total number of seats in the amphitheatre.
• 16M.1.sl.TZ1.6c: Anisha visits the amphitheatre. She estimates that the amphitheatre has \(6500\)...
• 16N.1.sl.TZ0.1a: Calculate the value of \(p\). Write down your full calculator display.
• 16N.1.sl.TZ0.1b: Write your answer to part (a) (i)     correct to two decimal places; (ii)     correct to three...
• 16N.1.sl.TZ0.1c: Write your answer to part (b)(ii) in the form \(a \times {10^k}\), where...
• 16N.1.sl.TZ0.8a: Use the above information to write down an equation in \(x\) and \(y\).
• 16N.1.sl.TZ0.8b: Use the information about the cost of tickets to write down a second equation in \(x\) and \(y\).
• 16N.1.sl.TZ0.8c: Find the value of \(x\) and the value of \(y\).
• 16N.1.sl.TZ0.8d: Find the percentage error.
• 16N.2.sl.TZ0.3a: Show that A lies on \({L_1}\).
• 16N.2.sl.TZ0.3b: Find the coordinates of M.
• 16N.2.sl.TZ0.3c: Find the length of AC.
• 16N.2.sl.TZ0.3d: Show that the equation of \({L_2}\) is \(2y + x - 19 = 0\).
• 16N.2.sl.TZ0.3e: Find the coordinates of D.
• 16N.2.sl.TZ0.3f: Write down the length of MD correct to five significant figures.
• 16N.2.sl.TZ0.3g: Find the area of ABCD.
• 17M.1.sl.TZ2.6a: Write down the median length of these leaves.
• 17M.1.sl.TZ2.6b: Write down the number of leaves with a length less than or equal to 8 cm.
• 17M.1.sl.TZ2.6c.i: Use the graph to find the value of \(k\).
• 17M.1.sl.TZ2.6c.ii: Before measuring, the researcher estimated \(k\) to be approximately 9.5 cm. Find the percentage...
• 17M.2.sl.TZ1.1a: Find the range of the average body weights for these seven species of mammal.
• 17M.2.sl.TZ1.1b.i: For the data from these seven species calculate \(r\), the Pearson’s product–moment correlation...
• 17M.2.sl.TZ1.1b.ii: For the data from these seven species describe the correlation between the average body weight...
• 17M.2.sl.TZ1.1c: Write down the equation of the regression line \(y\) on \(x\), in the form \(y = mx + c\).
• 17M.2.sl.TZ1.1d: Use your regression line to estimate the average weight of the brain of grey wolves.
• 17M.2.sl.TZ1.1e: Find the percentage error in your estimate in part (d).
• 17M.2.sl.TZ1.1f: State whether it is valid to use the regression line to estimate the average weight of the brain...
• 17N.2.sl.TZ0.3a: Show that \({\text{BD}} = 93{\text{ m}}\) correct to the nearest metre.
• 17N.2.sl.TZ0.3b: Calculate angle \({\rm{B\hat CD}}\).
• 17N.2.sl.TZ0.3c: Find the area of ABCD.
• 17N.2.sl.TZ0.3d.i: Calculate Abdallah’s estimate for the area.
• 17N.2.sl.TZ0.3d.ii: Find the percentage error in Abdallah’s estimate.
• 18M.1.sl.TZ1.1a: Based on the owner’s claim, calculate the total attendance for the games at Peterson United’s...
• 18M.1.sl.TZ1.1b: Calculate the percentage error in the owner’s claim.
• 18M.1.sl.TZ1.1c: Write down your answer to part (b) in the form a × 10k where 1 ≤ a < 10, \(k \in \mathbb{Z}\).
• 18M.2.sl.TZ2.5a.i: Use Giovanni’s diagram to show that angle ABC, the angle at which the Tower is leaning relative...
• 18M.2.sl.TZ2.5a.ii: Use Giovanni's diagram to calculate the length of AX.
• 18M.2.sl.TZ2.5a.iii: Use Giovanni's diagram to find the length of BX, the horizontal displacement of the Tower.
• 18M.2.sl.TZ2.5b: Find the percentage error on Giovanni’s diagram.
• 18M.2.sl.TZ2.5c: Giovanni adds a point D to his diagram, such that BD = 45 m, and another triangle is...

1.3

• 10M.1.sl.TZ1.5c: Write down your answer to (b) in the form \(a \times {10^n}\), where \(1 \leqslant a < 10\)...
• 11N.1.sl.TZ0.1b.iii: Write your answer to part (a) in the form \(a \times {10^k}\), where 1 ≤ a < 10,...
• 10N.1.sl.TZ0.1a: One of these numbers is written in the form \(a \times {10^k}\) where \(1 \leqslant a < 10\)...
• 10N.1.sl.TZ0.1c: Write down the value of q + s.
• 10N.1.sl.TZ0.1d: Give your answer to part (c) in the form \(a \times {10^k}\) where \(1 \leqslant a < 10\) and...
• 12N.1.sl.TZ0.3b: Write your answer to part (a) in the form a × 10k where 1 ≤ a < 10 and \(k \in \mathbb{Z}\).
• 12M.1.sl.TZ1.3c: Give your answer to part (b) in the form a×10k, where 1 ≤ a < 10 and \(k \in \mathbb{Z}\).
• 12M.1.sl.TZ2.1b: Write down your value of r in the form a × 10k, where 1 ≤ a < 10 and \(k \in \mathbb{Z}\).
• 09N.1.sl.TZ0.3a: Write down the area of the rectangle in the form a × 10k, where 1 ≤ a < 10, k ∈ \(\mathbb{Z}\).
• 11M.1.sl.TZ1.5c: Write down your answer to (b) in the form \(a \times {10^k}\) , where...
• 11M.1.sl.TZ2.4b: Give your answer to part (a) in the form \(a \times {10^k}\) where \(1 \leqslant a \leqslant 10\)...
• 09M.1.sl.TZ2.1a: Find the perimeter of the rectangle, giving your answer in the form \(a \times {10^k}\), where...
• 13M.1.sl.TZ1.1c: Write your answer to part (b)(ii) in the form a × 10k, where 1 ≤ a < 10, \(k \in \mathbb{Z}\).
• 13M.1.sl.TZ2.1c: Write your answer to part (b)(ii) in the form \(a \times 10^k\), where...
• 07M.1.sl.TZ0.1b: Calculate \(\sqrt {{{3.87}^5} - {{8.73}^{ - 0.5}}} \), giving your answer (i) correct to the...
• 07M.1.sl.TZ0.6a: Write down the following numbers in increasing order. \(3.5\), \(1.6 \times 10^{−19}\),...
• 07N.1.sl.TZ0.1b: Express your answer to part (a) in the form \(a \times 10^k\), where \(1 \leqslant a < 10\)...
• 08N.1.sl.TZ0.1d: Write down the answer to part (a) in the form \(a \times {10^k}\) , where...
• 08M.1.sl.TZ1.1d: Write your answer to part (c) in the form \(a \times {10^k}\) where...
• 14M.1.sl.TZ2.1a: Write down this radius, in kilometres, in the form \(a \times {10^k}\), where...
• 14M.1.sl.TZ2.1c: Today is Anna’s 17th birthday. Calculate the total distance that Anna has travelled around the...
• 13N.2.sl.TZ0.2d: Write \({\text{13}}\,{\text{400}}\,{\text{000}}\) in the form \(a \times {10^k}\) where...
• 14M.1.sl.TZ1.1b: Write down your answer to part (a) (i)     correct to two decimal places; (ii)     correct to...
• 14N.1.sl.TZ0.6b: Write down your answer to part (a) in the form...
• 15M.1.sl.TZ1.5a: Calculate the volume of the Earth in \({\text{k}}{{\text{m}}^3}\). Give your answer in the form...
• 15M.1.sl.TZ1.5b: The volume of the Moon is \(2.1958 \times {10^{10}}\;{\text{k}}{{\text{m}}^3}\). Calculate how...
• 15M.1.sl.TZ2.1c: Write down your answer to part (b) in the form \(a \times {10^k}\), where...
• 16M.2.sl.TZ1.4a: The Great Pyramid of Giza in Egypt is a right pyramid with a square base. The pyramid is made of...
• 16M.2.sl.TZ1.4b: Calculate the height of the pyramid, \({\text{VO}}\) .
• 16M.2.sl.TZ1.4c: Find the volume of the pyramid.
• 16M.2.sl.TZ1.4d: Write down your answer to part (c) in the form \(a \times {10^k}\)  where...
• 16M.2.sl.TZ1.4e: Ahmad is a tour guide at the Great Pyramid of Giza. He claims that the amount of stone used to...
• 16M.2.sl.TZ1.4f: Ahmad and his friends like to sit in the pyramid’s shadow, \({\text{ABW}}\), to cool down.At...
• 16N.1.sl.TZ0.1a: Calculate the value of \(p\). Write down your full calculator display.
• 16N.1.sl.TZ0.1b: Write your answer to part (a) (i)     correct to two decimal places; (ii)     correct to three...
• 16N.1.sl.TZ0.1c: Write your answer to part (b)(ii) in the form \(a \times {10^k}\), where...
• 16M.1.sl.TZ2.1a: Assume that the Earth is a sphere with a radius, \(r\) , of \(6.38 \times {10^3}\,{\text{km}}\)...
• 17M.1.sl.TZ1.2a: Calculate the percentage of the population of Ottawa that speak English but not French.
• 17M.1.sl.TZ1.2b: Calculate the number of people in Ottawa that speak both English and French.
• 17M.1.sl.TZ1.2c: Write down your answer to part (b) in the form \(a \times {10^k}\) where...
• 17M.1.sl.TZ2.1a: Calculate \(\sqrt[3]{{\frac{p}{q}}}\). Give your full calculator display.
• 17M.1.sl.TZ2.1b.i: Write down your answer to part (a) correct to two decimal places;
• 17M.1.sl.TZ2.1b.ii: Write down your answer to part (a) correct to three significant figures.
• 17M.1.sl.TZ2.1c: Write your answer to part (b)(ii) in the form \(a \times {10^k}\), where...
• 17N.1.sl.TZ0.3a: Calculate the time, in minutes, it takes for light from the Sun to reach the Earth.
• 17N.1.sl.TZ0.3b: Find the distance from the Earth to Polaris in millions of km. Give your answer in the form...
• 18M.1.sl.TZ1.1a: Based on the owner’s claim, calculate the total attendance for the games at Peterson United’s...
• 18M.1.sl.TZ1.1b: Calculate the percentage error in the owner’s claim.
• 18M.1.sl.TZ1.1c: Write down your answer to part (b) in the form a × 10k where 1 ≤ a < 10, \(k \in \mathbb{Z}\).
• 18M.2.sl.TZ1.1a: Calculate the area of triangle EAD.
• 18M.2.sl.TZ1.1b: Calculate the total volume of the barn.
• 18M.2.sl.TZ1.1c: Calculate the length of MN.
• 18M.2.sl.TZ1.1d: Calculate the length of AE.
• 18M.2.sl.TZ1.1e: Show that Farmer Brown is incorrect.
• 18M.2.sl.TZ1.1f: Calculate the total length of metal required for one support.
• 18M.2.sl.TZ1.6a: Write down the height of the cylinder.
• 18M.2.sl.TZ1.6b: Find the total volume of the trash can.
• 18M.2.sl.TZ1.6c: Find the height of the cylinder, h , of the new trash can, in terms of r.
• 18M.2.sl.TZ1.6d: Show that the volume, V cm3 , of the new trash can is given by \(V = 110\pi {r^3}\).
• 18M.2.sl.TZ1.6e: Using your graphic display calculator, find the value of r which maximizes the value of V.
• 18M.2.sl.TZ1.6f: The designer claims that the new trash can has a capacity that is at least 40% greater than the...
• 18M.1.sl.TZ2.3a: Find the length, in cm, of this line. Give your answer in the form a × 10k , where 1 ≤ a < 10...
• 18M.1.sl.TZ2.3b.i: Write down the length of the Amazon River in cm.
• 18M.1.sl.TZ2.3b.ii: Find the value of x.

1.4

• 10M.1.sl.TZ2.1a: Express this distance in metres.
• 10M.2.sl.TZ1.4f: To calculate the cost of air conditioning, engineers must estimate the weight of air in the...
• 10N.2.sl.TZ0.3f: The average speed of the bus while it is moving on the road is 70 km h–1. The bus stops for 5...
• 12M.1.sl.TZ1.3a: Calculate the exact time, in hours, for the spacecraft to reach the star Ross.
• 10M.2.sl.TZ2.4e: Find the number of kilograms of soil required for this garden bed.
• 11N.2.sl.TZ0.5b: In a revolution, C reaches points A and B , which are at the same height above the ground as the...
• 09M.2.sl.TZ2.3f: A layer of earth 3 cm thick is removed from ABD. Find the volume removed in cubic metres.
• 07M.2.sl.TZ0.2i.a: Calculate the volume of the cylinder in cm3. Give your answer correct to two decimal places.
• 07M.2.sl.TZ0.2i.b: The cylinder is used for storing tennis balls. Each ball has a radius of 3.25 cm. Calculate how...
• 07M.2.sl.TZ0.2i.c: (i) Jenny fills the cylinder with the number of balls found in part (b) and puts the lid on....
• 07N.2.sl.TZ0.2b: The glass weighs 9.3 grams per cm3. Calculate the weight of the pyramid.
• 08M.1.sl.TZ1.14b: Calculate how long Michael takes in seconds.
• 14M.2.sl.TZ2.2a: Using ‘distance = speed \( \times \) time’, show that the distance...
• 14M.2.sl.TZ2.2b: The distance from \({\text{B}}\) to \({\text{C}}\) is \(850\) metres. Running this part of the...
• 15M.2.sl.TZ1.4b: It is estimated that the fastest boat in the race can travel at an average speed of...
• 15M.2.sl.TZ2.2d: Temi covers the perfume bottles with a paint that costs 3 South African rand (ZAR) per...
• 16M.1.sl.TZ1.2a: Temi’s sailing boat has a sail in the shape of a right-angled triangle,...
• 16M.1.sl.TZ1.2b: William also has a sailing boat with a sail in the shape of a right-angled triangle,...
• 16M.2.sl.TZ1.1a: For an ecological study, Ernesto measured the average concentration \((y)\) of the fine...
• 16M.2.sl.TZ1.1b: Calculate i)      \({\bar x}\) , the mean distance from the power plant; ii)     \({\bar y}\) ,...
• 16M.2.sl.TZ1.1c: Write down the equation of the regression line \(y\) on \(x\) .
• 16M.2.sl.TZ1.1d: Ernesto’s school is located \(14\,{\text{km}}\) from the power plant. He uses the equation of...
• 16M.2.sl.TZ1.3a: A distress flare is fired into the air from a ship at sea. The height, \(h\) , in metres, of the...
• 16M.2.sl.TZ1.3b: Find the height of the flare \(15\) seconds after it was fired.
• 16M.2.sl.TZ1.3c: The flare fell into the sea \(k\) seconds after it was fired. Find the value of \(k\) .
• 16M.2.sl.TZ1.3d: Find \(h'\,(t)\,.\)
• 16M.2.sl.TZ1.3e: i)     Show that the flare reached its maximum height \(40\) seconds after being fired. ii)  ...
• 16M.2.sl.TZ1.3f: The nearest coastguard can see the flare when its height is more than \(40\) metres above sea...
• 16M.2.sl.TZ1.4a: The Great Pyramid of Giza in Egypt is a right pyramid with a square base. The pyramid is made of...
• 16M.2.sl.TZ1.4b: Calculate the height of the pyramid, \({\text{VO}}\) .
• 16M.2.sl.TZ1.4c: Find the volume of the pyramid.
• 16M.2.sl.TZ1.4d: Write down your answer to part (c) in the form \(a \times {10^k}\)  where...
• 16M.2.sl.TZ1.4e: Ahmad is a tour guide at the Great Pyramid of Giza. He claims that the amount of stone used to...
• 16M.2.sl.TZ1.4f: Ahmad and his friends like to sit in the pyramid’s shadow, \({\text{ABW}}\), to cool down.At...
• 16M.1.sl.TZ2.1b: The surface area of the Earth that is covered by water is approximately...
• 16M.1.sl.TZ2.3a: A ladder is standing on horizontal ground and leaning against a vertical wall. The length of the...
• 16M.1.sl.TZ2.3b: Calculate the distance between the top of the ladder and the base of the wall.
• 16M.1.sl.TZ2.3c: Calculate the obtuse angle made by the ladder with the ground.
• 16M.1.sl.TZ2.6a: When Bermuda \({\text{(B)}}\), Puerto Rico \({\text{(P)}}\), and Miami \({\text{(M)}}\) are...
• 16M.1.sl.TZ2.6b: Calculate the area of the Bermuda triangle.
• 16M.1.sl.TZ2.9a: Each day a supermarket records the midday temperature and how many cold drinks are sold on that...
• 16M.1.sl.TZ2.9b: Draw the line of best fit on the scatter diagram.
• 16M.1.sl.TZ2.9c: Use the line of best fit to estimate the number of cold drinks that are sold on a day when the...
• 16M.1.sl.TZ2.11a: A snack container has a cylindrical shape. The diameter of the base is \(7.84\,{\text{cm}}\). The...
• 16M.1.sl.TZ2.11b: Calculate the area of the base of the container.
• 16M.1.sl.TZ2.11c: Dan is going to paint the curved surface and the base of the snack container. Calculate the area...
• 16N.2.sl.TZ0.6a: Write down a formula for \(A\), the surface area to be coated.
• 16N.2.sl.TZ0.6b: Express this volume in \({\text{c}}{{\text{m}}^3}\).
• 16N.2.sl.TZ0.6c: Write down, in terms of \(r\) and \(h\), an equation for the volume of this water container.
• 16N.2.sl.TZ0.6e: Find \(\frac{{{\text{d}}A}}{{{\text{d}}r}}\).
• 16N.2.sl.TZ0.6f: Using your answer to part (e), find the value of \(r\) which minimizes \(A\).
• 16N.2.sl.TZ0.6g: Find the value of this minimum area.
• 16N.2.sl.TZ0.6h: Find the least number of cans of water-resistant material that will coat the area in part (g).
• 17M.1.sl.TZ1.9a: Find the radius, \(r\), of the circular base of the cone.
• 17M.1.sl.TZ1.9b: Find the slant height, \(l\), of the cone.
• 17M.1.sl.TZ1.9c: Find the curved surface area of the cone.
• 17M.2.sl.TZ1.1a: Find the range of the average body weights for these seven species of mammal.
• 17M.2.sl.TZ1.1b.i: For the data from these seven species calculate \(r\), the Pearson’s product–moment correlation...
• 17M.2.sl.TZ1.1b.ii: For the data from these seven species describe the correlation between the average body weight...
• 17M.2.sl.TZ1.1c: Write down the equation of the regression line \(y\) on \(x\), in the form \(y = mx + c\).
• 17M.2.sl.TZ1.1d: Use your regression line to estimate the average weight of the brain of grey wolves.
• 17M.2.sl.TZ1.1e: Find the percentage error in your estimate in part (d).
• 17M.2.sl.TZ1.1f: State whether it is valid to use the regression line to estimate the average weight of the brain...
• 17M.2.sl.TZ1.4a: Calculate the volume of this pan.
• 17M.2.sl.TZ1.4b: Find the radius of the sphere in cm, correct to one decimal place.
• 17M.2.sl.TZ1.4c: Find the value of \(a\).
• 17M.2.sl.TZ1.4d: Find the temperature that the pizza will be 5 minutes after it is taken out of the oven.
• 17M.2.sl.TZ1.4e: Calculate, to the nearest second, the time since the pizza was taken out of the oven until it can...
• 17M.2.sl.TZ1.4f: In the context of this model, state what the value of 19 represents.
• 17N.1.sl.TZ0.3a: Calculate the time, in minutes, it takes for light from the Sun to reach the Earth.
• 17N.1.sl.TZ0.3b: Find the distance from the Earth to Polaris in millions of km. Give your answer in the form...
• 18M.1.sl.TZ1.14a: Calculate the radius of the base of the cone which has been removed.
• 18M.1.sl.TZ1.14b: Calculate the curved surface area of the cone which has been removed.
• 18M.1.sl.TZ1.14c: Calculate the curved surface area of the remaining solid.
• 18M.1.sl.TZ2.8a: Calculate the length of side AC in km.
• 18M.1.sl.TZ2.8b: Calculate the area of the park.
• 18M.1.sl.TZ2.15a: Find an expression for the slant height of the cone in terms of r.
• 18M.1.sl.TZ2.15b: The total external surface area of the pencil case rounded to 3 significant figures is 570...
• 18M.2.sl.TZ2.5a.i: Use Giovanni’s diagram to show that angle ABC, the angle at which the Tower is leaning relative...
• 18M.2.sl.TZ2.5a.ii: Use Giovanni's diagram to calculate the length of AX.
• 18M.2.sl.TZ2.5a.iii: Use Giovanni's diagram to find the length of BX, the horizontal displacement of the Tower.
• 18M.2.sl.TZ2.5b: Find the percentage error on Giovanni’s diagram.
• 18M.2.sl.TZ2.5c: Giovanni adds a point D to his diagram, such that BD = 45 m, and another triangle is...
• 16N.2.sl.TZ0.6d: Show that \(A = \pi {r^2} + \frac{{1\,000\,000}}{r}\).

1.5

• 10M.1.sl.TZ1.12a: Calculate the number of Thai baht Susi buys. Give your answer correct to the nearest baht.
• 10M.1.sl.TZ1.12b: Calculate the total number of Indonesian rupiah Susi receives, correct to the nearest thousand...
• 10M.1.sl.TZ1.12c: Calculate Susi’s exchange rate between Singapore dollars and Indonesian rupiah. Give your answer...
• 11N.1.sl.TZ0.8a: Calculate the number of EUR George received.
• 11N.1.sl.TZ0.8b: On his return, George had \(160\) EUR to change back into USD. There was \(4.5\% \) commission...
• 11N.1.sl.TZ0.8c: On his return, George had \(160\) EUR to change back into USD. There was \(4.5\% \) commission...
• 10N.2.sl.TZ0.4A.a: Find, in BRL, the amount of money Estela has after commission.
• 10N.2.sl.TZ0.4A.b: Find, in GBP, the amount of money Estela receives.
• 10N.2.sl.TZ0.4A.c: After her trip to the United Kingdom Estela has 400 GBP left. At the airport she changes this...
• 10N.2.sl.TZ0.4A.d: Estela actually receives 1216.80 BRL after commission. Find, in BRL, the commission charged to...
• 10N.2.sl.TZ0.4A.e: The commission rate is t % . Find the value of t.
• 12N.1.sl.TZ0.7a: Calculate the amount of Euros Isabel receives.
• 12N.1.sl.TZ0.7b: Isabel then changes 750 EUR into Canadian dollars (CAD) and is charged 3.12 % commission. The...
• 12M.1.sl.TZ1.8a: Find the number of MXN that Sasha received.
• 12M.1.sl.TZ1.8b: Before her return to the USA, Sasha exchanged 2300 MXN back into USD. The bank charged a...
• 12M.1.sl.TZ1.8c: Before her return to the USA, Sasha exchanged 2300 MXN back into USD. The bank charged a...
• 10M.2.sl.TZ2.3e: Ruby moves from the USA to Italy. She transfers 6610 USD into an Italian bank which has an...
• 10M.2.sl.TZ2.3f: Ruby returns to the USA for a short holiday. She converts 800 Euros at a bank in Chicago and...
• 12M.1.sl.TZ2.9a: Calculate the amount of commission charged in SEK.
• 12M.1.sl.TZ2.9b: Write down the amount of money she receives from the bank after commission.
• 12M.1.sl.TZ2.9c: Chiara returns to Italy with 296 SEK. She changes this money back into euros at a bank and...
• 09N.1.sl.TZ0.8a: Find the exchange rate between GBP and EUR in the form 1 GBP = k EUR, where k is a constant. Give...
• 09N.1.sl.TZ0.8b: Isabella changes 400 USD into Euros and is charged 2 % commission. Calculate how many Euros she...
• 09M.1.sl.TZ2.12a, i: Enrico has 475 USD. How many euros is this worth?
• 09M.1.sl.TZ2.12b: Find the exchange rate from euros to yen.
• 11M.1.sl.TZ2.12b: The manufacturer sells each non-defective statue for \(5.25\) British pounds (GBP) to an American...
• 11M.1.sl.TZ2.12c: The American company sells one of the statues to an Australian customer for \(12{\text{ USD}}\)....
• 13M.1.sl.TZ1.11a: Calculate the amount of commission on the exchange in SGD.
• 13M.1.sl.TZ1.11b: Calculate the number of American dollars (USD) Neung takes home. Give your answer correct to 2...
• 13M.1.sl.TZ1.11c: At the airport in Vietnam, Neung changes 150 USD into Vietnamese dong (VND) to pay for her...
• 13M.1.sl.TZ2.12a: Calculate the amount Yoshi receives, in EUR.
• 13M.1.sl.TZ2.12b: Yoshi spends 426.70 EUR in Italy. In an American bank he changes the remaining amount, into US...
• 07M.1.sl.TZ0.3a: 1 Brazilian Real (BRL) = 2.607 South African Rand (ZAR). Giving answers correct to two decimal...
• 07N.2.sl.TZ0.3ii.a: Calculate correct to 2 decimal places the amount of euros he receives.
• 07N.2.sl.TZ0.3ii.b: He buys 1 kilogram of Belgian chocolates at 1.35 euros per 100 g. Calculate the cost of his...
• 08N.1.sl.TZ0.5a: Kwai Fan changes \({\text{S\$ }}500\) to Indian rupees. Calculate the number of Indian rupees...
• 08N.1.sl.TZ0.5b: On her return to Singapore, Kwai Fan has \(2500\) Indian rupees left from her trip. She wishes to...
• 08N.1.sl.TZ0.5c: On her return to Singapore, Kwai Fan has \(2500\) Indian rupees left from her trip. She wishes to...
• 08M.1.sl.TZ1.10a: Calculate the number of \({\text{USD}}\) Jane receives.
• 08M.1.sl.TZ1.10b: Jane spends \(1350{\text{ USD}}\) and then decides to convert the remainder back to...
• 08M.1.sl.TZ1.10c: If Jane had waited until she returned to Amsterdam she could have changed her \({\text{USD}}\) at...
• 08M.1.sl.TZ2.11a: Minbin has \(1250\) Japanese Yen which she wishes to exchange for Chinese Yuan. Calculate how...
• 08M.1.sl.TZ2.11b: Rupert has \(855\) Canadian Dollars which he wishes to exchange for Japanese Yen. Calculate how...
• 08M.1.sl.TZ2.11c: Find how many Norwegian Kroner there are to the Euro. Give your answer correct to 2 decimal places.
• 09M.1.sl.TZ2.12a, ii: Enrico has 475 USD. Enrico goes to a bank to exchange his dollars. The bank charges 3 %...
• 14M.1.sl.TZ2.9a: Fumie is going for a holiday to Great Britain. She changes \({\text{100}}\,{\text{000}}\)...
• 14M.1.sl.TZ2.9b: At the end of Fumie’s holiday in Great Britain she has 239 GBP. She converts this back to JPY at...
• 13N.2.sl.TZ0.5a: Calculate, in GBP, the price that Arthur paid for the car.
• 14M.1.sl.TZ1.5a: Calculate the number of USD that Dumisani must change to pay for his air fare.
• 14M.1.sl.TZ1.5c: The exchange rate is \(1{\text{ USD }} = 1.29903{\text{ SGD}}\). Calculate the number of SGD...
• 14N.1.sl.TZ0.4a: Calculate the amount that Albena receives in EUR.
• 14N.1.sl.TZ0.4b: At the airport shop, Albena buys chocolates that cost 34.50 BGN. She uses 20 EUR to pay for the...
• 15M.1.sl.TZ1.6a: Calculate the number of SGD Pietro receives.
• 15M.1.sl.TZ1.6b: Pietro also has 100 GBP that he wishes to change to USD for a trip to Cambodia. To perform this...
• 15M.2.sl.TZ2.2e: Temi sells her perfume bottles in a craft fair for 325 ZAR each. Dominique from France buys one...
• 16M.1.sl.TZ1.9a: In this question give all answers correct to the nearest whole number. Loic travelled from China...
• 16M.1.sl.TZ1.9b: When he returned to China, Loic changed his remaining \({\text{BRL}}\) at a bank. The exchange...
• 16N.1.sl.TZ0.4a: Calculate the amount of VEF that Javier receives.
• 16N.1.sl.TZ0.4b: Calculate the total amount, in USD, that Javier has remaining from his 5000 USD after his trip to...
• 16M.1.sl.TZ2.10a: Obi travels from Dubai to Pretoria and changes \(2000\) United Arab Emirates Dirham...
• 16M.1.sl.TZ2.10b: Obi decides to invest half of the money he receives, \(3080\,\,{\text{ZAR}}\), in an account...
• 17M.1.sl.TZ1.8a: Calculate the amount of PEN she receives.
• 17M.1.sl.TZ1.8b: Calculate the amount of USD she receives.
• 17M.1.sl.TZ2.8a: Find the amount of Euros that Claudia receives. Give your answer correct to two decimal places.
• 17M.1.sl.TZ2.8b: Find the value of \(r\).
• 17N.1.sl.TZ0.8a: Use this exchange rate to calculate the amount of ARS that is equal to 350 AUD.
• 17N.1.sl.TZ0.8b: Calculate the total amount of ARS Jose paid to get 350 AUD.
• 17N.1.sl.TZ0.8c: Find the value of \(x\).
• 18M.2.sl.TZ1.3a: Calculate the value of r.
• 18M.2.sl.TZ1.3b: Calculate 14 000 USD in INR.
• 18M.2.sl.TZ1.3c: Calculate the amount of this investment, in INR, in this account after five years.
• 18M.2.sl.TZ1.3d: Harinder chose option B. At the end of five years, Harinder converted this investment back to...
• 18M.1.sl.TZ2.5a.i: Calculate the amount of money he has in the account after 5 years.
• 18M.1.sl.TZ2.5a.ii: Write down the amount of interest he earned after 5 years.
• 18M.1.sl.TZ2.5b: Karl decides to donate this interest to a charity in France. The charity receives 170 euros...

1.6

• 10N.1.sl.TZ0.13b: Find the value of p and of q.
• 10N.1.sl.TZ0.14b: Find the value of x given that A = 109.25 m2.
• 10N.2.sl.TZ0.5f: Lines L1 and L2 are parallel, and they are tangents to the graph of f (x) at points A and B...
• 12N.1.sl.TZ0.15b: Find using your answer to part (a) the x-coordinate of (i) the local maximum point; (ii) the...
• 12N.2.sl.TZ0.2f: The students are asked to collect money for charity. In the first month, the students collect x...
• 12M.1.sl.TZ1.14a: Find the value of (i) p ; (ii) q .
• 12M.2.sl.TZ1.4A.b: Write down the value of (i) d ; (ii) u1 .
• 12M.1.sl.TZ2.7c: The area of triangle ABC is 360 cm2. Calculate the length of side AC. Express your answer in...
• 12M.2.sl.TZ2.2d: Cedric’s mother decides to help him by giving him an interest free loan of €8000 to buy the car....
• 09N.2.sl.TZ0.5B, c: The gradient of the curve \(y = p{x^2} + qx - 4\) at the point (2, –10) is 1. Solve the...
• 09M.1.sl.TZ1.5a: Factorise \(x^2 - 6x + 8\).
• 09M.1.sl.TZ1.5b: Hence, or otherwise, solve the equation \(x^2 - 6x + 8 = 0\).
• 09M.1.sl.TZ1.5c: Let \(g(x) = x + 3\). Write down the solutions to the equation \(f (x) = g(x)\).
• 09M.1.sl.TZ1.14b: Use the above information to calculate the value of p and of q ;
• 11M.1.sl.TZ2.7d: Write down the value of \(x\) and the value of \(y\) .
• 11M.1.sl.TZ2.15b: Solve the quadratic equation found in part (a).
• 13M.1.sl.TZ1.9d: Write down \(f (x)\) in the form \(f (x) = −(x − p) (x + q)\).
• 13M.2.sl.TZ1.3e: Solve the equations found in part (d) to find the value of p and the value of q.
• 11M.2.sl.TZ2.3B.b: The sum of the first \(n\) terms of this sequence is \(\frac{n}{2}(3n - 1)\). (i)     Find the...
• 13M.1.sl.TZ2.8d: Lines L1 and L2 intersect at point P. Using your graphic display calculator or otherwise, find...
• 07M.1.sl.TZ0.12a: Using simplest terms, write an equation in b and m for Thursday’s sales.
• 07M.1.sl.TZ0.12b: Find b and m.
• 07M.1.sl.TZ0.15c: The length of one side of a rectangle is 2 cm longer than its width. The perimeter of a square...
• SPM.1.sl.TZ0.13b: Using your graphic display calculator or otherwise, find the value of \(a\) and of \(b\) .
• 07N.1.sl.TZ0.10c: Find the positive solution of the equation \(x^2 + 2x − 6 = 0\).
• 08N.1.sl.TZ0.13b: Hence solve the equation \({x^2} - kx = 0\) .
• 08M.2.sl.TZ1.4i.a: Write down an equation showing this information, taking \(b\) to be the cost of one tin of beans...
• 08M.2.sl.TZ1.4i.b: Stephen thinks that Mal has not bought enough so he buys \(12\) more tins of beans and \(6\) more...
• 08M.2.sl.TZ1.4i.c: Stephen thinks that Mal has not bought enough so he buys \(12\) more tins of beans and \(6\) more...
• 08M.2.sl.TZ1.4i.d: (i)     Sketch the graphs of the two equations from parts (a) and (b). (ii)    Write down the...
• 08M.2.sl.TZ1.5i.b: Solve the equation \(3{x^2} + 13x - 10 = 0\).
• 08M.2.sl.TZ2.5d: The area of \({\text{OBCD}}\) is \(9.75\) square units. Write down a quadratic equation that...
• 08M.2.sl.TZ2.5e: (i) Using your graphic display calculator, or otherwise, find the two solutions to the quadratic...
• 14M.1.sl.TZ2.6b: The area of the carpet is \({\text{10 }}{{\text{m}}^2}\). Calculate the value of \(x\).
• 13N.1.sl.TZ0.12b: Solve the equations to find the value of (i)     \(a\); (ii)     \(b\).
• 13N.1.sl.TZ0.12c: Find the value of \(c\).
• 14M.1.sl.TZ1.13c: Find the value of \(a\) and of \(b\).
• 14N.2.sl.TZ0.5e: Peter also plays the game. When the signal is given for the end of the game he has run 940...
• 14N.2.sl.TZ0.6e: Calculate the value of \(a\).
• 15M.1.sl.TZ1.12c: At 210°C the length of the iron bar is 181.5 mm. Hence, find the length of the iron bar at 40°C.
• 15M.1.sl.TZ2.15b: Site T has the same area as site S, but a different width. Find the width of T.
• 15M.2.sl.TZ2.3f: The \({n^{{\text{th}}}}\) term of the arithmetic sequence is given by \({u_n}\). There is a...
• 16M.1.sl.TZ1.13a: The golden ratio, \(r\) , was considered by the Ancient Greeks to be the perfect ratio...
• 16M.1.sl.TZ1.13b: Phidias is designing rectangular windows with adjacent sides of length \(x\) metres...
• 16M.1.sl.TZ1.13c: Phidias designs the windows so that the ratio between the longer side, \(y\) , and the...
• 16M.1.sl.TZ1.13d: Find the value of \(x\) .
• 16N.2.sl.TZ0.6a: Write down a formula for \(A\), the surface area to be coated.
• 16N.2.sl.TZ0.6b: Express this volume in \({\text{c}}{{\text{m}}^3}\).
• 16N.2.sl.TZ0.6c: Write down, in terms of \(r\) and \(h\), an equation for the volume of this water container.
• 16N.2.sl.TZ0.6e: Find \(\frac{{{\text{d}}A}}{{{\text{d}}r}}\).
• 16N.2.sl.TZ0.6f: Using your answer to part (e), find the value of \(r\) which minimizes \(A\).
• 16N.2.sl.TZ0.6g: Find the value of this minimum area.
• 16N.2.sl.TZ0.6h: Find the least number of cans of water-resistant material that will coat the area in part (g).
• 17M.1.sl.TZ2.1a: Calculate \(\sqrt[3]{{\frac{p}{q}}}\). Give your full calculator display.
• 17M.1.sl.TZ2.1b.i: Write down your answer to part (a) correct to two decimal places;
• 17M.1.sl.TZ2.1b.ii: Write down your answer to part (a) correct to three significant figures.
• 17M.1.sl.TZ2.1c: Write your answer to part (b)(ii) in the form \(a \times {10^k}\), where...
• 17M.2.sl.TZ2.5a: Show that the width of the plot, in metres, is given by \(100 - x\).
• 17M.2.sl.TZ2.5b: Write down the area of the plot in terms of \(x\).
• 17M.2.sl.TZ2.5c: Find the value of \(x\) that maximizes the area of the plot.
• 17M.2.sl.TZ2.5d: Show that Violeta earns 5000 BGN from selling the flowers grown on the plot.
• 17M.2.sl.TZ2.5e.i: Find the amount of money that Violeta would have after 6 years. Give your answer correct to two...
• 17M.2.sl.TZ2.5f: Find the lowest possible value for \(r\).
• 17M.2.sl.TZ2.5e.ii: Find how long it would take for the interest earned to be 2000 BGN.
• 16N.2.sl.TZ0.6d: Show that \(A = \pi {r^2} + \frac{{1\,000\,000}}{r}\).

1.7

• 10M.1.sl.TZ2.7a: Find the common difference of this arithmetic sequence.
• 10M.1.sl.TZ2.7b: There are 10 rows in the choir and 11 singers in the first row. Find the total number of singers...
• 10M.2.sl.TZ1.5B.a: Calculate u1, the first term in the sequence.
• 10M.2.sl.TZ1.5B.b: Show that the common difference is 7.
• 10M.2.sl.TZ1.5B.c: Sn is the sum of the first n terms of the sequence. Find an expression for Sn. Give your answer...
• 11N.1.sl.TZ0.6a: Find the value of the common difference of this sequence.
• 11N.1.sl.TZ0.6b: Calculate the sum of the first 10 terms of this sequence.
• 11N.1.sl.TZ0.6c: Find the number of terms in this sequence.
• 10N.1.sl.TZ0.8a: Write down the second term of this sequence.
• 10N.1.sl.TZ0.8b: Write down the common difference of this sequence.
• 10N.1.sl.TZ0.8c: Write down the fourth term of this sequence.
• 10N.1.sl.TZ0.8d: The nth term is the first term in this sequence which is greater than 1000. Find the value of n.
• 12N.1.sl.TZ0.2a: Calculate the common difference;
• 12N.1.sl.TZ0.2b: Calculate the 95th term of the sequence;
• 12N.1.sl.TZ0.2c: Calculate the sum of the first 250 terms.
• 12N.2.sl.TZ0.2f: The students are asked to collect money for charity. In the first month, the students collect x...
• 10M.2.sl.TZ2.3a: Find the amount of money that Ruby will have in the bank after 3 years.
• 12M.2.sl.TZ1.4A.a: (i) Write an equation for u6 in terms of d and u1. (ii) Write an equation for u10 in terms of d...
• 12M.2.sl.TZ1.4A.c: Find the total number of seats in the amphitheatre.
• 12M.2.sl.TZ1.4A.d: A few years later, a second level was added to increase the amphitheatre’s capacity by another...
• 12M.1.sl.TZ2.5a: Find the first term of the sequence.
• 12M.1.sl.TZ2.5b: Find the 21st term of the sequence.
• 12M.1.sl.TZ2.5c: Find the sum of the first 30 terms of the sequence.
• 12M.2.sl.TZ2.2c: Cedric’s mother decides to help him by giving him an interest free loan of €8000 to buy the car....
• 09N.1.sl.TZ0.4a: Find the common difference.
• 09N.1.sl.TZ0.4b: Find the twelfth term.
• 09N.1.sl.TZ0.4c: Find the sum of the first 100 terms.
• 09M.1.sl.TZ1.3a: Calculate the number of leaves that the tree loses on the 21st October.
• 09M.1.sl.TZ1.3b: Find the total number of leaves that the tree loses in the 31 days of the month of October.
• 11M.1.sl.TZ1.8a: Calculate the annual salary for the fifth year of her employment.
• 11M.1.sl.TZ1.8b: She remains in this employment for 10 years. Calculate the total salary she earns in this...
• 09M.1.sl.TZ2.4a: Find the number of terms of the sequence.
• 09M.1.sl.TZ2.4b: Find the sum of the sequence.
• 13M.1.sl.TZ1.12a: Find the common difference, d.
• 13M.1.sl.TZ1.12b: The tenth term of the sequence is double the seventh term. (i) Write down an equation in u1 and...
• 11M.2.sl.TZ2.3B.b: The sum of the first \(n\) terms of this sequence is \(\frac{n}{2}(3n - 1)\). (i)     Find the...
• 11M.2.sl.TZ2.3B.a: Find the value of the eleventh term.
• 13M.2.sl.TZ2.4a: Find the time, in seconds, Paco takes to run his fifth lap.
• 13M.2.sl.TZ2.4b: Paco runs his last lap in 260 seconds. Find how many laps he has run on Monday.
• 13M.2.sl.TZ2.4c: Find the total time, in minutes, run by Paco on Monday.
• 07M.2.sl.TZ0.4i.a: State the values of u1 and d for this sequence.
• 07M.2.sl.TZ0.4i.b: Use an appropriate formula to show that the sum of the natural numbers from 1 to n is given by...
• 07M.2.sl.TZ0.4i.c: Calculate the sum of the natural numbers from 1 to 200.
• 07N.1.sl.TZ0.3a: (i) Find the common difference. (ii) Find the first term of the sequence.
• 07N.1.sl.TZ0.3b: Calculate the eighty-fourth term.
• 07N.1.sl.TZ0.3c: Calculate the sum of the first 200 terms.
• 08N.1.sl.TZ0.8a: Write down the common difference of the sequence.
• 08N.1.sl.TZ0.8b: Calculate the sum of the first \(50\) terms of the sequence.
• 08N.1.sl.TZ0.8c: \({u_k}\) is the first term in the sequence which is negative. Find the value of \(k\).
• 08N.2.sl.TZ0.1c: Grove School had \(110\) students in January 2000. Every full year, the number of students is...
• 08N.2.sl.TZ0.1d: Grove School had \(110\) students in January 2000. Every full year, the number of students is...
• 08N.2.sl.TZ0.1e: Each January, one of these two schools, the one that has more students, is given extra money to...
• 08M.1.sl.TZ1.8a: Find the value of the \({96^{{\text{th}}}}\) term of the sequence.
• 08M.1.sl.TZ1.8b: The first term of a geometric sequence is \(6\). The \({6^{{\text{th}}}}\) term of the geometric...
• 08M.2.sl.TZ2.1a: If Clara chooses option 1, (i) write down the values of the second and third installments; (ii)...
• 08M.2.sl.TZ2.1d: Clara knows that the total amount she would pay for the land is not the same for both options....
• 14M.2.sl.TZ2.4b: If Hugh chooses Option B, calculate (i)     the amount of money he will receive in the 17th...
• 13N.1.sl.TZ0.6a: Find the common difference of the sequence.
• 13N.1.sl.TZ0.6b: The \({n^{{\text{th}}}}\) term, \({u_n}\), of the sequence is \(–7\). Find the value of \(n\).
• 13N.1.sl.TZ0.6c: The \({n^{{\text{th}}}}\) term, \({u_n}\), of the sequence is \(–7\). Find \({S_{20}}\), the sum...
• 14M.2.sl.TZ1.3a: Find the value of \({u_{20}}\).
• 14M.2.sl.TZ1.3b: Find the sum of the first 10 terms of the sequence.
• 14M.2.sl.TZ1.3e: \(k\) is the smallest value of \(n\) for which \({v_n}\) is greater than \({u_n}\). Calculate...
• 14N.1.sl.TZ0.7a: Find the value of \(m\).
• 14N.1.sl.TZ0.7b: State what \(m\) represents in this context.
• 14N.1.sl.TZ0.7d: State what \(n\) represents in this context.
• 14N.2.sl.TZ0.5b: The distances she runs to collect each pumpkin form a sequence...
• 14N.2.sl.TZ0.5c: Write down the common difference, \(d\), of the sequence.
• 14N.2.sl.TZ0.5d: The final pumpkin Sirma collected was 24 metres from the start. (i)     Find the total number of...
• 14N.2.sl.TZ0.5e: Peter also plays the game. When the signal is given for the end of the game he has run 940...
• 14N.2.sl.TZ0.5f: Peter also plays the game. When the signal is given for the end of the game he has run 940...
• 15M.1.sl.TZ1.7a: Calculate (i)     the common difference of the sequence; (ii)     the first term of the sequence.
• 15M.1.sl.TZ1.7b: The first, second and fifth terms of this arithmetic sequence are the first three terms of a...
• 15M.1.sl.TZ2.9a: Only one of the following four sequences is arithmetic and only one of them is geometric.     ...
• 15M.2.sl.TZ2.3a: Write down the value of (i)     \({S_1}\); (ii)     \({S_2}\).
• 15M.2.sl.TZ2.3b: The \({n^{{\text{th}}}}\) term of the arithmetic sequence is given by \({u_n}\). Show that...
• 15M.2.sl.TZ2.3c: The \({n^{{\text{th}}}}\) term of the arithmetic sequence is given by \({u_n}\). Find the common...
• 15M.2.sl.TZ2.3d: The \({n^{{\text{th}}}}\) term of the arithmetic sequence is given by \({u_n}\). Find \({u_{10}}\).
• 15M.2.sl.TZ2.3e: The \({n^{{\text{th}}}}\) term of the arithmetic sequence is given by \({u_n}\). Find the lowest...
• 15M.2.sl.TZ2.3f: The \({n^{{\text{th}}}}\) term of the arithmetic sequence is given by \({u_n}\). There is a...
• 16M.1.sl.TZ1.6a: One of the locations in the \(2016\) Olympic Games is an amphitheatre. The number of seats in the...
• 16M.1.sl.TZ1.6b: There are \(20\) rows in the amphitheatre. Find the total number of seats in the amphitheatre.
• 16M.1.sl.TZ1.6c: Anisha visits the amphitheatre. She estimates that the amphitheatre has \(6500\)...
• 16M.2.sl.TZ1.5a: Antonio and Barbara start work at the same company on the same day. They each earn an annual...
• 16M.2.sl.TZ1.5b: Write down an expression for i)     Antonio’s annual salary during his \(n\) th year of...
• 16M.2.sl.TZ1.5c: Determine the number of years for which Antonio’s annual salary is greater than or equal to...
• 16M.2.sl.TZ1.5d: Both Antonio and Barbara plan to work at the company for a total of \(15\) years. i)  ...
• 16N.1.sl.TZ0.13a: Find the year in which the comet was seen from Earth for the fifth time.
• 16N.1.sl.TZ0.13b: Determine how many times the comet has been seen from Earth up to the year 2014.
• 16M.2.sl.TZ2.2a: Prachi is on vacation in the United States. She is visiting the Grand Canyon. When she reaches...
• 16M.2.sl.TZ2.2b: Calculate the distance the coin falls during the \(15{\text{th}}\) second.  
• 16M.2.sl.TZ2.2c: Calculate the total distance the coin falls in the first \(15\) seconds. Give your answer...
• 16M.2.sl.TZ2.2d: Prachi drops the coin from a height of \(1800\) metres above the ground. Calculate the time, to...
• 16M.2.sl.TZ2.2e: Prachi visits a tourist centre nearby. It opened at the start of \(2015\) and in the first...
• 16M.2.sl.TZ2.2f: Calculate the total number of people expected to visit the tourist centre during the first...
• 17M.1.sl.TZ1.5a: Find the distance from the base of this ladder to the top rung.
• 17M.1.sl.TZ1.5b: The company also makes a ladder that is 1050 cm long. Find the maximum number of rungs in this...
• 17M.1.sl.TZ2.5a: Diagram \(n\) is formed with 52 sticks. Find the value of \(n\).
• 17M.1.sl.TZ2.5b: Find the total number of sticks used by Tomás for all 24 diagrams.
• 17N.2.sl.TZ0.2a.i: Write down the distance Rosa runs in the third training session;
• 17N.2.sl.TZ0.2a.ii: Write down the distance Rosa runs in the \(n\)th training session.
• 17N.2.sl.TZ0.2b: Find the value of \(k\).
• 17N.2.sl.TZ0.2c: Calculate the total distance, in kilometres, Rosa runs in the first 50 training sessions.
• 17N.2.sl.TZ0.2d: Find the distance Carlos runs in the fifth month of training.
• 17N.2.sl.TZ0.2e: Calculate the total distance Carlos runs in the first year.
• 18M.1.sl.TZ1.7a.i: For that day find how much weight was added after each lift.
• 18M.1.sl.TZ1.7a.ii: For that day find the weight of Sergei’s first lift.
• 18M.1.sl.TZ1.7b: On that day, Sergei made 12 successive lifts. Find the total combined weight of these lifts.
• 18M.2.sl.TZ2.4a: Find the café’s profit during the 11th week.
• 18M.2.sl.TZ2.4b: Calculate the café’s total profit for the first 12 weeks.
• 18M.2.sl.TZ2.4c: Find the tea-shop’s profit during the 11th week.
• 18M.2.sl.TZ2.4d: Calculate the tea-shop’s total profit for the first 12 weeks.
• 18M.2.sl.TZ2.4e: In the mth week the tea-shop’s total profit exceeds the café’s total profit, for the first time...

1.8

• 10M.2.sl.TZ1.5B.d: The first term, v1, of a geometric sequence is 20 and its fourth term v4 is 67.5. Show that the...
• 10M.2.sl.TZ1.5B.e: Tn is the sum of the first n terms of the geometric sequence. Calculate T7, the sum of the first...
• 11N.1.sl.TZ0.12a: Calculate the exact value of the ninth term of the sequence.
• 11N.1.sl.TZ0.12b: Calculate the least number of terms required for the sum of the sequence to be greater than 682.6
• 10N.1.sl.TZ0.11a: Write down the common ratio.
• 10N.1.sl.TZ0.11b.i: Write down the value of a.
• 10N.1.sl.TZ0.11c: The sum of the first n terms is 31.9375. Find the value of n.
• 12N.1.sl.TZ0.6a: Calculate the common ratio of the sequence;
• 12N.1.sl.TZ0.6b: Calculate the eleventh term of the sequence;
• 12N.1.sl.TZ0.6c: Calculate the sum of the first 23 terms of the sequence.
• 12M.2.sl.TZ1.4B.a: Write down the next two terms of this geometric sequence.
• 12M.2.sl.TZ1.4B.b: Write down the common ratio of this geometric sequence.
• 12M.2.sl.TZ1.4B.c: Calculate the number of people who will receive the text message at 12:30.
• 12M.2.sl.TZ1.4B.d: Calculate the total number of people who will have received the text message by 12:30.
• 12M.2.sl.TZ1.4B.e: Calculate the exact time at which a total of 29 524 people will have received the text message.
• 12M.1.sl.TZ2.15a: Write down the distance he runs on the second day of training.
• 12M.1.sl.TZ2.15b: Calculate the total distance Javier runs in the first seven days of training.
• 12M.1.sl.TZ2.15c: Javier stops training on the day his total distance exceeds 100 km. Calculate the number of days...
• 09N.1.sl.TZ0.12a: Write down the population of big cats at the beginning of 2005.
• 09N.1.sl.TZ0.12b: Find the population of big cats at the beginning of 2010.
• 09N.1.sl.TZ0.12c: Find the number of years, from the beginning of 2004, it will take the population of big cats to...
• 09M.1.sl.TZ1.8a: Calculate the common ratio for the increasing sequence of fees.
• 09M.1.sl.TZ1.8b: Give your answer correct to 2 decimal places. The fees continue to increase in the same...
• 09M.1.sl.TZ1.8c: Give your answer correct to 2 decimal places. The fees continue to increase in the same...
• 11M.1.sl.TZ1.11a: Write down the common ratio of the sequence.
• 11M.1.sl.TZ1.11b: Find \({u_1}\) .
• 11M.1.sl.TZ1.11c: The sum of the first \(k\) terms in the sequence is \(118 096\) . Find the value of \(k\) .
• 09M.2.sl.TZ2.4i, a: Calculate the value of the common ratio.
• 09M.2.sl.TZ2.4i, b: Calculate the 10th term of this sequence.
• 09M.2.sl.TZ2.4i, c: The kth term is the first term which is greater than 2000. Find the value of k.
• 13M.1.sl.TZ1.7a: Find the common ratio of the sequence.
• 13M.1.sl.TZ1.7b: Find u1, the first term of the sequence.
• 13M.1.sl.TZ1.7c: Calculate the sum of the first 10 terms of the sequence.
• 11M.2.sl.TZ2.3A.a: Show that the common ratio is \(\frac{1}{2}\) .
• 11M.2.sl.TZ2.3A.b: Find the value of the eleventh term.
• 11M.2.sl.TZ2.3A.c: Find the sum of the first eight terms.
• 11M.2.sl.TZ2.3A.d: Find the number of terms in the sequence for which the sum first exceeds \(2047.968\).
• 13M.2.sl.TZ2.4d: On Wednesday Paco takes Lola to train. They both run the first lap of the track in 120 seconds....
• 13M.2.sl.TZ2.4e: Find the total time, in seconds, Lola takes to run her first four laps.
• 07M.2.sl.TZ0.4ii.a: The sum of the first n terms of G1 is 29 524. Find n.
• 07M.2.sl.TZ0.4ii.b: A second geometric progression G2 has the form \(1,\frac{1}{3},\frac{1}{9},\frac{1}{{27}}...\)
• 07M.2.sl.TZ0.4ii.c: Calculate the sum of the first 10 terms of G2.
• 07M.2.sl.TZ0.4ii.d: Explain why the sum of the first 1000 terms of G2 will give the same answer as the sum of the...
• 07M.2.sl.TZ0.4ii.e: Using your results from parts (a) to (c), or otherwise, calculate the sum of the first 10 terms...
• 08N.2.sl.TZ0.1a: Park School started in January 2000 with \(100\) students. Every full year, there is an increase...
• 08N.2.sl.TZ0.1b: Park School started in January 2000 with \(100\) students. Every full year, there is an increase...
• 08N.2.sl.TZ0.1e: Each January, one of these two schools, the one that has more students, is given extra money to...
• 08M.1.sl.TZ1.8b: The first term of a geometric sequence is \(6\). The \({6^{{\text{th}}}}\) term of the geometric...
• 08M.1.sl.TZ1.8c: The first term of a geometric sequence is \(6\). The \\({6^{{\text{th}}}}\) term of the geometric...
• 08M.2.sl.TZ2.1b: If Clara chooses option 2, (i) find the value of the second installment; (ii) show that the...
• 08M.2.sl.TZ2.1d: Clara knows that the total amount she would pay for the land is not the same for both options....
• 10N.1.sl.TZ0.11b.ii: Write down the value of b.
• 14M.2.sl.TZ2.4c: If Hugh chooses Option C, calculate (i)     the amount of money Hugh would receive in the 13th...
• 13N.1.sl.TZ0.11a: Find the number of competitors who play in round 6 of the tournament.
• 13N.1.sl.TZ0.11b: Find the total number of matches played in the tournament.
• 14M.2.sl.TZ1.3c: Now consider the sequence...
• 14M.2.sl.TZ1.3d: Now consider the sequence...
• 14M.2.sl.TZ1.3e: \(k\) is the smallest value of \(n\) for which \({v_n}\) is greater than \({u_n}\). Calculate...
• 15M.1.sl.TZ1.7b: The first, second and fifth terms of this arithmetic sequence are the first three terms of a...
• 15M.1.sl.TZ2.9a: Only one of the following four sequences is arithmetic and only one of them is geometric.     ...
• 15M.1.sl.TZ2.9b(i): For another geometric sequence...
• 15M.1.sl.TZ2.9b(ii): For another geometric sequence...
• 16M.2.sl.TZ1.5a: Antonio and Barbara start work at the same company on the same day. They each earn an annual...
• 16M.2.sl.TZ1.5b: Write down an expression for i)     Antonio’s annual salary during his \(n\) th year of...
• 16M.2.sl.TZ1.5c: Determine the number of years for which Antonio’s annual salary is greater than or equal to...
• 16M.2.sl.TZ1.5d: Both Antonio and Barbara plan to work at the company for a total of \(15\) years. i)  ...
• 16N.1.sl.TZ0.10a: Find the value of the common ratio for this sequence.
• 16N.1.sl.TZ0.10b: Find the distance that the post is driven into the ground by the eighth strike of the hammer.
• 16N.1.sl.TZ0.10c: Find the total depth that the post has been driven into the ground after 10 strikes of the hammer.
• 16M.2.sl.TZ2.2a: Prachi is on vacation in the United States. She is visiting the Grand Canyon. When she reaches...
• 16M.2.sl.TZ2.2b: Calculate the distance the coin falls during the \(15{\text{th}}\) second.  
• 16M.2.sl.TZ2.2c: Calculate the total distance the coin falls in the first \(15\) seconds. Give your answer...
• 16M.2.sl.TZ2.2d: Prachi drops the coin from a height of \(1800\) metres above the ground. Calculate the time, to...
• 16M.2.sl.TZ2.2e: Prachi visits a tourist centre nearby. It opened at the start of \(2015\) and in the first...
• 16M.2.sl.TZ2.2f: Calculate the total number of people expected to visit the tourist centre during the first...
• 17M.1.sl.TZ1.10a: Find the value of \(r\), the common ratio of the sequence.
• 17M.1.sl.TZ1.10b: Find the value of \(n\) for which \({u_n} = 2\).
• 17M.1.sl.TZ1.10c: Find the sum of the first 30 terms of the sequence.
• 17M.1.sl.TZ2.9a: Write down the common ratio of the sequence.
• 17M.1.sl.TZ2.9b: Find the value of \({u_5}\).
• 17M.1.sl.TZ2.9c: Find the smallest value of \(n\) for which \({u_n}\) is less than \({10^{ - 3}}\).
• 17N.2.sl.TZ0.2a.i: Write down the distance Rosa runs in the third training session;
• 17N.2.sl.TZ0.2a.ii: Write down the distance Rosa runs in the \(n\)th training session.
• 17N.2.sl.TZ0.2b: Find the value of \(k\).
• 17N.2.sl.TZ0.2c: Calculate the total distance, in kilometres, Rosa runs in the first 50 training sessions.
• 17N.2.sl.TZ0.2d: Find the distance Carlos runs in the fifth month of training.
• 17N.2.sl.TZ0.2e: Calculate the total distance Carlos runs in the first year.
• 18M.1.sl.TZ1.11a: Find the height of the smallest doll in this set.
• 18M.1.sl.TZ1.11b: Find the total height if all 51 dolls were placed one on top of another.
• 18M.2.sl.TZ2.4a: Find the café’s profit during the 11th week.
• 18M.2.sl.TZ2.4b: Calculate the café’s total profit for the first 12 weeks.
• 18M.2.sl.TZ2.4c: Find the tea-shop’s profit during the 11th week.
• 18M.2.sl.TZ2.4d: Calculate the tea-shop’s total profit for the first 12 weeks.
• 18M.2.sl.TZ2.4e: In the mth week the tea-shop’s total profit exceeds the café’s total profit, for the first time...

1.9

• 10M.1.sl.TZ2.10a: Find the interest Astrid has earned during the five years of her investment. Give your answer...
• 10M.2.sl.TZ1.5A.a: Calculate the value of his investment at the end of the third year for each investment option,...
• 11N.1.sl.TZ0.11b: Kunal borrows 200 000 Indian rupees (INR) from a money lender for 18 months at a nominal annual...
• 10N.2.sl.TZ0.4B.a: Show that after three years Daniel will have $1109.70 in his account, correct to two decimal places.
• 10N.2.sl.TZ0.4B.b: Write down the interest Daniel receives after three years.
• 12N.1.sl.TZ0.14b: Maddison invests 15 000 AUD in a bank that offers compound interest at a nominal annual interest...
• 12M.1.sl.TZ1.15b: Option 2 offers a nominal annual interest rate of 4 %, compounded monthly. Find the amount that...
• 10M.2.sl.TZ2.3b: Show that Ying will have 7545 USD in the bank at the end of 10 years.
• 10M.2.sl.TZ2.3c: Find the number of complete years it will take for Ying’s investment to first exceed 6500 USD.
• 12M.2.sl.TZ2.2f: Cedric decides to buy a cheaper car for €6000 and invests the remaining €2000 at his bank. The...
• 09N.1.sl.TZ0.15b: Mr Black invested 5000 CHF in Bank B at a nominal annual interest rate of 3.6 %, compounded...
• 09M.1.sl.TZ1.12b: 5000 AUD is invested at a nominal annual interest rate of 2.5 % compounded half...
• 11M.2.sl.TZ1.5f: Pauline invests \(300 000\) USD from the sale of the land in a bank that pays compound interest...
• 09M.1.sl.TZ2.8a: Bank 1 charges compound interest at a rate of 15 % per annum, compounded quarterly. Calculate...
• 11M.1.sl.TZ2.14a: Write down the value of the car when Shiyun bought it.
• 11M.1.sl.TZ2.14b: Calculate the value of the car three years after Shiyun bought it. Give your answer correct to...
• 11M.1.sl.TZ2.14c: Calculate the time for the car to depreciate to half of its value since Shiyun bought it.
• 13M.1.sl.TZ1.14b: Ramón invests $18 000 in a bank account that pays 3.4 % nominal annual interest, compounded...
• 11M.2.sl.TZ2.2d: On 1 January 2007, Daniel reinvested \(80\% \) of the money from the Regular Saver account in an...
• 11M.2.sl.TZ2.2c: On 1 January 2005, Rebecca invested \(30000{\text{ AUD}}\) in a Supersaver account at a nominal...
• 11M.2.sl.TZ2.2b: On 1 January 2005, Rebecca invested \(30000{\text{ AUD}}\) in a Supersaver account at a nominal...
• 13M.1.sl.TZ2.15a: Calculate the total amount of interest Marcus would earn, in AUD, over the three years. Give your...
• 13M.1.sl.TZ2.15b: Marcus would earn the same amount of interest, compounded annually, for three years if he...
• SPM.1.sl.TZ0.11a: Find the value of the investment after 3 years.
• SPM.1.sl.TZ0.11b: Find the difference in the final value of the investment if the interest was compounded quarterly...
• 07N.1.sl.TZ0.6b: Calculate the value of Ben’s investment at the end of 6 years. Give your answer correct to 2...
• 08N.1.sl.TZ0.10a: Eva invests \({\text{USD}}2000\) at a nominal annual interest rate of \(8\% \) compounded...
• 08N.1.sl.TZ0.10b: Toni invests \({\text{USD}}1500\) at an annual interest rate of \(7.8\% \) compounded...
• 08M.1.sl.TZ1.13b: Charles invests \(3000{\text{ USD}}\) in a bank that offers compound interest at a rate of...
• 08M.1.sl.TZ2.8a: Calculate the amount of money that Emma would have in her account after 15 years. Give your...
• 08M.1.sl.TZ2.8b: After a period of time she decides to withdraw the money from this bank. There is...
• 08M.2.sl.TZ2.1c: The price of the land is \(\$ 80000\). In option 1 her total repayments are \(\$ 88000\) over the...
• 14M.2.sl.TZ2.4d: If Hugh chooses Option D, calculate the total value of his allowance at the end of the two year...
• 14M.2.sl.TZ2.4f: Another bank guarantees Hugh an amount of \(\$1750\) after two years of investment if he invests...
• 13N.2.sl.TZ0.5d: Between \({1^{{\text{st}}}}\) August 2008 and \({1^{{\text{st}}}}\) August 2012 Arthur’s car...
• 13N.2.sl.TZ0.5e: Between \({1^{{\text{st}}}}\) August 2008 and \({1^{{\text{st}}}}\) August 2012 Arthur’s car...
• 14M.1.sl.TZ1.12a: Write down the number of times interest is added to the loan in the two years.
• 14M.1.sl.TZ1.12b: Calculate the exact amount of money that Ludmila must repay at the end of the two years.
• 14N.1.sl.TZ0.6a: Find the amount of the interest that Mandzur must pay. Give your answer correct to the nearest...
• 15M.1.sl.TZ1.10a: Calculate the value of Pierre’s investment at the end of this time. Give your answer correct to...
• 15M.1.sl.TZ1.10b: Carla has 7000 dollars to invest in a fixed deposit which is compounded annually. She aims to...
• 15M.1.sl.TZ2.10a: Find the amount of money that Minta will have in the bank after 3 years. Give your answer correct...
• 15M.1.sl.TZ2.10b: Minta will withdraw the money from her bank account when the interest earned is 300 euros. Find...
• 16M.1.sl.TZ1.12a: In this question give all answers correct to two decimal places. Diogo deposited \(8000\)...
• 16M.1.sl.TZ1.12b: Carmen also deposited \({\text{ARS}}\) in a bank account. Her account pays a nominal annual...
• 16N.1.sl.TZ0.15a: Write down, and simplify, an expression for the car’s value when Gabriella purchased it.
• 16N.1.sl.TZ0.15b: Find the value of \(k\).
• 16N.1.sl.TZ0.15c: Find the value of \(n\).
• 17M.1.sl.TZ1.14a: Calculate the value of Arthur’s initial investment, \(x\). Give your answer to two decimal places.
• 17M.1.sl.TZ1.14b: Find the value of \(n\).
• 17M.2.sl.TZ2.5a: Show that the width of the plot, in metres, is given by \(100 - x\).
• 17M.2.sl.TZ2.5b: Write down the area of the plot in terms of \(x\).
• 17M.2.sl.TZ2.5c: Find the value of \(x\) that maximizes the area of the plot.
• 17M.2.sl.TZ2.5d: Show that Violeta earns 5000 BGN from selling the flowers grown on the plot.
• 17M.2.sl.TZ2.5e.i: Find the amount of money that Violeta would have after 6 years. Give your answer correct to two...
• 17M.2.sl.TZ2.5f: Find the lowest possible value for \(r\).
• 17M.2.sl.TZ2.5e.ii: Find how long it would take for the interest earned to be 2000 BGN.
• 17N.1.sl.TZ0.9a: Calculate the original price of the bicycle.
• 17N.1.sl.TZ0.9b: Calculate the difference between the original price of the bicycle and the total amount Juan will...
• 18M.2.sl.TZ1.3a: Calculate the value of r.
• 18M.2.sl.TZ1.3b: Calculate 14 000 USD in INR.
• 18M.2.sl.TZ1.3c: Calculate the amount of this investment, in INR, in this account after five years.
• 18M.2.sl.TZ1.3d: Harinder chose option B. At the end of five years, Harinder converted this investment back to...
• 18M.1.sl.TZ2.4a: Complete the second column of the table by giving one example of a number from each set.
• 18M.1.sl.TZ2.4b: Josh states: “Every integer is a natural number”. Write down whether Josh’s statement is...