• Syllabus

1.0

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Sub sections and their related questions

Basic use of the four operations of arithmetic, using integers, decimals and fractions, including order of operations

• 10M.2.sl.TZ1.5A.b: Determine Daniel’s best investment option.
• 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.2.sl.TZ0.3c: Village D is halfway between A and B. A new road perpendicular to AB and passing through D is...
• 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.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.2.sl.TZ2.1a: Write down the total number of fish in the pond.
• 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.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...
• 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...
• 13M.1.sl.TZ2.9c: The areas of regions A, B, and C are equal. Write down the area of region A.
• 07N.1.sl.TZ0.1a: Calculate \(\frac{{77.2 \times {3^3}}}{{3.60 \times {2^2}}}\).
• 08N.1.sl.TZ0.1a: Calculate the exact value of \(h\) when \(\ell  = 0.03625\) and \(d = 0.05\) .
• 08M.1.sl.TZ1.1a: Calculate exactly \(\frac{{{{(3 \times 2.1)}^3}}}{{7 \times 1.2}}\).
• 10M.2.sl.TZ2.4a.iii: Find how many bricks are required to pave the total area.
• 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.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...
• 13N.2.sl.TZ0.5b: Write down, in \({\text{GBP}}\), the amount of money Arthur saved by buying the car in Germany.
• 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.2.sl.TZ1.4b: It is estimated that the fastest boat in the race can travel at an average speed of...

Prime numbers, factors and multiples.

• 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.TZ0.9a.ii: List the elements of the following set. \(A \cap B'\)
• 13N.1.sl.TZ0.2a: List the elements of \(A\).
• 13N.1.sl.TZ0.2b: List the elements of \(B\).

Simple applications of ratio, percentage and proportion.

• 10M.2.sl.TZ1.4f: To calculate the cost of air conditioning, engineers must estimate the weight of air in the...
• 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.TZ0.5b: Estimate the number of students who achieved a mark greater than 32.
• 10N.2.sl.TZ0.1A.c: Write down the percentage of students who had fruit for breakfast.
• 12M.2.sl.TZ2.2a: Write down the amount of the deposit.
• 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.
• 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.TZ2.12a: Find the number of statues that are non-defective.
• 10M.2.sl.TZ2.4b.iv: Find the percentage of the rectangular area which is to be lawn.
• 14M.2.sl.TZ2.6g: The water tank is shown below. It is partially filled with water.   The water tank has a...
• 14M.1.sl.TZ1.5b: On arrival in Singapore, Dumisani changes 3000 USD to Singapore dollars (SGD) to pay for his...
• 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...
• 15M.2.sl.TZ1.3i: It is proposed that the speed limit past the hospital gate is reduced to...
• 15M.2.sl.TZ2.4d: Daniel assumes that the diameters of all of the apples from his harvest are normally distributed...

Basic manipulation of simple algebraic expressions, including factorization and expansion

• 10N.1.sl.TZ0.14a: Write down an expression for A in terms of x.
• 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.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.TZ2.15a: Write down and simplify a quadratic equation in \(x\) which links the three sides of the triangle.
• 13M.1.sl.TZ1.9d: Write down \(f (x)\) in the form \(f (x) = −(x − p) (x + q)\).
• 07N.1.sl.TZ0.10b: Factorize the expression \(x^2 + 2x − 3\).
• 08N.1.sl.TZ0.13a: Factorise the expression \({x^2} - kx\) .
• 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 \({x^2} - 3x - 10\).
• 13N.1.sl.TZ0.9a: Expand the expression \(x(2{x^3} - 1)\).

Rearranging formulae

• 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...
• SPM.2.sl.TZ0.6d: Show that the total external surface area, \(A\) , of the bin is...
• 08M.2.sl.TZ1.5ii.b: Find an expression for \(y\) in terms of \(x\).
• 14M.2.sl.TZ2.5b: Show that \(l = \frac{{150}}{w}\).
• 14M.2.sl.TZ1.6c: The volume of the lobster trap is \(0.75{\text{ }}{{\text{m}}^{\text{3}}}\). Show that...
• 14N.2.sl.TZ0.3c: A company designs cone-shaped tents to resemble the traditional tepees. These cone-shaped tents...
• 15M.1.sl.TZ1.15a: Find the value of \(a\).

Evaluating expressions by substitution.

• 10M.1.sl.TZ1.14b.i: Find the value of a.
• 11N.1.sl.TZ0.1a: Find the exact value of \(z\).
• 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.TZ0.5d: (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 \(c\) .
• 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.TZ2.6a: Write down the boiling point of water at sea level.
• 11M.1.sl.TZ1.15b: The point \((2{\text{, }}1)\) lies on the graph of \(y = f(x)\) . Calculate the value of \(a\) .
• 11M.2.sl.TZ1.3d: Find \(f'(2)\) .
• 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.TZ1.15b: Write down the value of \(f ′(0)\).
• SPM.2.sl.TZ0.6f: (i)     Find the value of \(r\) that minimizes the total external surface area of the wastepaper...
• 10M.1.sl.TZ1.14b.ii: Find the value of b.
• 14M.1.sl.TZ2.6c: The area of the carpet is \({\text{10 }}{{\text{m}}^2}\). Hence, write down the value of the...
• 15M.1.sl.TZ1.1a: Calculate the exact value of \(T\).
• 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.TZ1.5d: The graph of \(y = f(x)\) has a local minimum point at \(x = 4\). Find \(f'(2)\)
• 15M.2.sl.TZ2.2d: Temi covers the perfume bottles with a paint that costs 3 South African rand (ZAR) per...

Solving linear equations in one variable.

• 12N.2.sl.TZ0.2g: The students are asked to collect money for charity. In the first month, the students collect x...
• 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.TZ2.2b: 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....
• 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.TZ1.15c: The function has a local maximum at x = −2. Calculate the value of a.
• 13M.1.sl.TZ2.9b: Write down the value of y.
• 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...
• 07N.1.sl.TZ0.10a: Solve the following equation for x \(3(2x +1) − 2(3 − x)=13\).
• 14N.2.sl.TZ0.4b: The surveyor measures the size of angle \({\text{CDE}}\) to be twice that of angle...
• 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.TZ2.6e: All the bicycles that are produced are sold. The bicycles are sold for 304 USD each. (i)    ...

Solving systems of linear equations in two variables.

• 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.

Evaluating exponential expressions with integer values

None

Use of inequalities \( < \), \( \leqslant \), \( > \), \( \geqslant \). Intervals on the real number line

• 13M.1.sl.TZ1.6d: Write down a value of \(x\) for which \(\neg p \vee q\) is false.

Intervals on the real number line

None

Solving linear inequalities.

• 15M.2.sl.TZ2.3e: The \({n^{{\text{th}}}}\) term of the arithmetic sequence is given by \({u_n}\). Find the lowest...

Familiarity with commonly accepted world currencies

None