ECZ 2016 GCE Paper 1 — Mathematics

A set has three elements. How many subsets does it have?

Using the Venn diagram in the answer space, shade the region represented by B'∩(A∩C).

Simplify 2m − 4n − 3(3n − m).

Evaluate 3² + 2³ × 2⁰.

It is given that 10ˣ = 3 and 10ʸ = 9. What is the value of 10^y−x?

A plane flew from town A(67°S, 40°E) to a town B(23°N, 40°E). Calculate the distance AB in kilometres. (R = 6370 km and π = 227)

Bronze is made up of zinc, tin and copper in the ratio 1 : 4 : 25 respectively. A bronze statue contains 120 g of tin. Find the required quantities of the other metals.

In the diagram below, MP = 13 km, QR = 6 km and MR = 24 km. MR is parallel and equal to TQ, PM̂R = QR̂M = 90° and TP̂Q = 75°. Find PQ̂T.

In the diagram below, MP = 13 km, QR = 6 km and MR = 24 km. MR is parallel and equal to TQ, PM̂R = QR̂M = 90° and TP̂Q = 75°. Find the length PQ.

What is the position of 999 in the sequence represented by the nth term n³ − 1?

Given that AB = -34, find |AB|.

If A = 1-2-14 and C = -13, calculate AC.

DEFG is a rectangular piece of land in which GE = 12.5 m (a diagonal) and DE = 7.5 m. Find the value of cos EĜF.

The cost of advertising in a local newspaper for one week is K15.40 per word plus a fixed charge of K41.25. What is the cost of advertising 15 words for one week?

The diagram shows an isosceles triangle ABC where AB = BC = (x − 3) cm and AB̂C = 90°. Find the value of x for which the area of triangle ABC is 18 cm².

The pie chart shows how members of a club voted for the position of chairperson: Emelia x°, Inonge 120° and Mercy 135°. What fraction of the members voted for Emelia?

In the same pie chart (Emelia 105°, Inonge 120°, Mercy 135°), 20 members voted for Inonge. How many members did NOT vote for her?

A function h is defined as h(x) = 3x + 24. Find h(−2).

A function h is defined as h(x) = 3x + 24. Find the value of x for which h(x) = 5.

A function h is defined as h(x) = 3x + 24. Find h^-1(x).

A target is a square piece of wood ABCD of side 50 cm. M and N are midpoints of AB and CD respectively, and O is the centre of the square. The diagonal from D to B is drawn, and the regions between the mid-line NM and the diagonal (triangle DNO above the centre and triangle OMB below it) are shaded. A bullet fired at the target lands at a random point. Expressing your answer in its simplest form, find the probability that it lands in the shaded region.

In the diagram below, TR is diameter of the circle with centre O, and QR and PS are parallel. Angle TÔS = 80° and angle TR̂P = 10°. Find RP̂S.

In the same diagram (TR a diameter, QR ∥ PS, TÔS = 80°, TR̂P = 10°), find PŜT.

In the same diagram (TR a diameter, QR ∥ PS, TÔS = 80°, TR̂P = 10°), find PŜO.

The diagram below shows the positions of three towns Kime (K), Teswa (T) and Luwaya (L). Angle KTL = 110° and the bearing of L from T is 123°. Find the bearing of T from L.

The diagram below shows the positions of three towns Kime (K), Teswa (T) and Luwaya (L). Angle KTL = 110° and the bearing of L from T is 123°. Find the bearing of T from K.

At 07 30 hours, an old Mini Bus starts off from Luwaya to Teswa at an average speed of 25 km/h. Given that the distance between Luwaya and Teswa is 40 km, find the time at which the bus reaches Teswa.

The boundary of the shaded region R is formed by the lines y = 2, L₁ (through (0, 6) and (2, 4)) and L₂ (through (0, 0) and (2, 4)). Write three inequalities which define the region R.

A is a point (3, −4). Find the coordinates of the image of point A under a reflection in the line y = x.

A is a point (3, −4). Find the coordinates of the image of point A under a translation with vector T = -4-2.

Solve the equation 3x² = 5x.

The diagram below is a speed-time graph of a car which starts from rest and accelerates uniformly for 20 seconds till it reaches a speed of 30 m/s. It then moves at a constant speed for some time before it starts decelerating. It comes to rest after 100 seconds. Given that the total distance travelled is 2 400 metres, calculate the value of t.

In the same journey (30 m/s constant speed until t = 80 s, rest at 100 s), calculate the retardation in the last part of the journey.

In the same journey (constant 30 m/s until 80 s, then uniform deceleration to rest at 100 s), find the speed of the car at the ninety fifth second.

Find the value of 3 − 3 × 3 + 3.

Evaluate 42 ÷ 0.07.

An ultra modern stadium has a capacity of 43 492. Express this number in standard form correct to 2 significant figures.

Solve the simultaneous equations x + 4y = 16, x + y = 1.

The median of 2x + 3, x and 2x + 12 is 9, where x is a positive integer. Find the value of x.

It is given that vt − a = d. Find the value of d when v = 10, t = −2 and a = −4.

It is given that vt − a = d. Express a in terms of v, t and d.

A map is drawn to a scale of 1 to 50 000. Calculate the length of a road, in kilometres, which is 5 cm long on the map.

A map is drawn to a scale of 1 to 50 000. Calculate the actual area of a small town, in square kilometres, represented by an area of 10 cm² on the map.

Find an integer value of q such that 2q − 7 ≤ 8 ≤ 3q − 11.

Two similar solids have surface areas in the ratio 4:25. If the volume of the bigger solid is 62.5 cm³, calculate the volume of the smaller solid.