ECZ 2017 GCE Paper 1 — Mathematics

On the Venn diagram in the answer space below, shade the region defined by A'∩(B∪C).

Given that E={1,2,3,4,5,6,7,8},A={1,8} and B={2,3,4,5,6,7}, list (A∪B)'.

Simplify 2a − 7b − 2(a − 3b).

Factorise completely x²4y² − 19.

Given that 2x-51 43 = 14-17, find the value of x.

Two tins are geometrically similar. If the ratio of their volumes is 27 : 64, find the ratio of their curved surface areas.

Given that a = 3-4, find |a|.

For the sequence 11, 13, 15, 17, …, find the 13th term.

If the arithmetic mean of 5 and c is 11, what is the value of c?

If A^T = (1 −2 3 −4 5), write the matrix A.

Find the derivative of y = 2x³ − 2x² − 3x + 1, with respect to x.

Solve the equation 25ˣ = 5.

A soccer match kicked off at 14 00 hours at A(20°N, 30°E). What would be the kick off time of the soccer match at B(20°N, 15°W)?

Two towns P and Q are on the same longitude. Given that P is (40°N, 15°W) and PQ is 7 200 nm, find the position of Q.

A die and a coin are rolled and tossed, respectively. What is the probability of getting a five and a tail?

Given that x = 3.2 × 3⁴ and y = 4 × 3², evaluate xy.

In the diagram below, points A, B, C and D are on a circle. BD is the diameter of the circle. AĈB = 42°, CÂD = 33° and the lines AC and BD intersect at X. Find CB̂D.

In the same diagram (BD a diameter, AĈB = 42°, CÂD = 33°), find AĈD.

In the same diagram (BD a diameter, AĈB = 42°, CÂD = 33°, AC and BD intersecting at X), find AX̂B.

The functions g and f are defined as g : x → x − 12 and f : x → 3x − 5. Find g^-1(x).

With g : x → x − 12 and f : x → 3x − 5, find x if f(x) = g(x).

With g : x → x − 12 and f : x → 3x − 5, find g^-1f(x).

y varies inversely as the square root of x, where x is positive. Write an expression for y in terms of x and the constant of variation k.

y varies inversely as the square root of x (y = k/√x). Given that y = 2 when x = 16, find the value of k.

y varies inversely as the square root of x, with y = 8/√x. Find the value of a for which y = 89 when x = a.

Maphone Manufacturing Company paid a total dividend of K12 600.00 at the end of 2015 on 6 000 shares. If Magula owned 200 shares in the company, how much was paid out in dividends to her?

The diagram shows triangle ABC in which AC = 18 cm, CÂB = 30° and AB̂C = 90°. Calculate the length of BC.

The curved surface area of a cone is 88 cm². Given that the base radius is 4 cm, calculate the slant height of the cone. [π = 227, A = πrl]

A flow chart computes tax on an income: Enter Income → Is Income < 3 000? If Yes, Tax = 0; if No, Tax = 0.3 × (Income − 3 000) → Output Tax. What tax does the program output for incomes of K2 900.00 and K5 000.00 respectively?

A bag of potatoes has mass (15.4 ± 0.05) kg. Find the tolerance of this mass.

A bag of potatoes has mass (15.4 ± 0.05) kg. Write down the relative error of the mass, as a fraction, in its simplest form.

A, B and C are three points on level ground. B is on a bearing of 070° from A and C is on a bearing of 130° from B. Calculate the bearing of A from B.

A, B and C are three points on level ground. B is on a bearing of 070° from A and C is on a bearing of 130° from B. Calculate the bearing of B from C.

The diagram shows a regular hexagonal prism with an axis drawn through the centres of its two hexagonal faces. What is the order of rotational symmetry about the indicated axis?

The diagram shows two triangles ABC and A′B′C′ on the XOY plane: A(−4½, 1½), B(−2, 3), C(−½, 1½) and A′(6½, 1½), B′(4, 3), C′(2½, 1½). Describe fully the single transformation that maps triangle ABC onto triangle A′B′C′.

The diagram shows a Cartesian plane with points A(6, 6), B(0, −2), C(0, 6) and D(6, 0). Find the equation of the line CD.

The diagram shows a Cartesian plane with points A(6, 6), B(0, −2), C(0, 6) and D(6, 0). Find the distance AB.

Write the four inequalities that define the unshaded region R on the XOY plane: R is bounded by the solid horizontal lines y = 3 (above it, shading) and y = −1 (below it, shading), the dashed vertical line x = 2 (shading to its right), and the solid line through (−2, 0) and (0, 2) (shading to its upper left).

The diagram shows a sketch of the graph of y = x² − 6x + 8, cutting the x-axis at B and C. Find the coordinates of B and C.

The diagram shows a sketch of the graph of y = x² − 6x + 8, cutting the x-axis at B(2, 0) and C(4, 0). Find the coordinates of the turning point of the graph.

The diagram below shows the speed-time graph of a 100 m sprinter who accelerates uniformly for 3 seconds until he reaches a speed of 12 m/s. He maintains the speed for 7 seconds and then uniformly retards for a further 4 seconds and comes to a stop. Calculate the acceleration during the first 3 seconds.

In the same race (12 m/s maintained until the 10th second, then uniform retardation to rest over the last 4 seconds), calculate the retardation at the end of his race.

In the same race (0 to 12 m/s over 3 s, constant 12 m/s from the 3rd to the 10th second, rest at 14 s), calculate the distance he covered in the first 10 seconds.