DP Mathematical Studies Questionbank

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Directly related questions

• 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.
• 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.TZ2.5d: Show that Violeta earns 5000 BGN from selling the flowers grown on the plot.
• 17M.2.sl.TZ2.5c: Find the value of \(x\) that maximizes the area of the plot.
• 17M.2.sl.TZ2.5b: Write down the area of the plot in terms of \(x\).
• 17M.2.sl.TZ2.5a: Show that the width of the plot, in metres, is given by \(100 - x\).
• 17M.1.sl.TZ2.1c: Write your answer to part (b)(ii) in the form \(a \times {10^k}\), where...
• 17M.1.sl.TZ2.1b.ii: Write down your answer to part (a) correct to three significant figures.
• 17M.1.sl.TZ2.1b.i: Write down your answer to part (a) correct to two decimal places;
• 17M.1.sl.TZ2.1a: Calculate \(\sqrt[3]{{\frac{p}{q}}}\). Give your full calculator display.
• 16M.1.sl.TZ1.13d: Find the value of \(x\) .
• 16M.1.sl.TZ1.13c: Phidias designs the windows so that the ratio between the longer side, \(y\) , and the...
• 16M.1.sl.TZ1.13b: Phidias is designing rectangular windows with adjacent sides of length \(x\) metres...
• 16M.1.sl.TZ1.13a: The golden ratio, \(r\) , was considered by the Ancient Greeks to be the perfect ratio...
• 16N.2.sl.TZ0.6h: Find the least number of cans of water-resistant material that will coat the area in part (g).
• 16N.2.sl.TZ0.6g: Find the value of this minimum area.
• 16N.2.sl.TZ0.6f: Using your answer to part (e), find the value of \(r\) which minimizes \(A\).
• 16N.2.sl.TZ0.6e: Find \(\frac{{{\text{d}}A}}{{{\text{d}}r}}\).
• 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.TZ0.6b: Express this volume in \({\text{c}}{{\text{m}}^3}\).
• 16N.2.sl.TZ0.6a: Write down a formula for \(A\), the surface area to be coated.
• 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 ;
• 16N.2.sl.TZ0.6d: Show that \(A = \pi {r^2} + \frac{{1\,000\,000}}{r}\).
• 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.TZ0.12b: 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...
• 07M.1.sl.TZ0.12a: Using simplest terms, write an equation in b and m for Thursday’s sales.
• 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.TZ1.5i.b: Solve the equation \(3{x^2} + 13x - 10 = 0\).
• 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.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 \(b\).
• 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...
• 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 \(a\).