BECE 2001 Mathematics (Maths) Paper 2 Essay

BECE 2001

MATHEMATICS (MATHS)

ESSAY (Paper 2)

Answer four questions only from this section All working must be clearly shown.

The use of calculators is not allowed

Marks will not be awarded for correct answers without corresponding working. All questions carry equal marks

1. (a) M is a set consisting of all positive integers between 1 and 10. P and Q are subsets of M such that
P = {factors of 6}, Q = {multiples of 2}
(i) List the elements of M, P and Q
(ii) Represent M, P and Q on a Venn diagram
(iii) Find P ∩ Q

(b) (i) Solve the inequality: 2x -2 - 2x -1 < 1

2 3

(ii) Illustrate your answer on the number line

2. (a) Express 131five as a binary numeral

(b) Three children, Kwabena, Esi and Yaw were given 160 oranges to share. Kwabena gets ¼ of
the oranges. Esi and Yaw share the remainder in the ratio 3:2 respectively.

(i) Find how many oranges Esi received
(ii) How many more oranges did Yaw receive than Kwabena?

3. (a) Using a ruler and a pair of compasses only, construct triangle XYZ, such that |XY| = 6cm, |XZ| = 8cm and |YZ| = 10cm.

(b) (i) Construct the mediator of line YZ
      (ii) construct the mediator of line XZ
     (iii) Locate O, the point of intersection of the mediators of lines YZ and XZ.
     (iv) With centre O and radius OY, draw a circle.

(c) Measure the radius of the circle you have drawn in (b) (iv) above and hence calculate the
circumference of the circle. [ Take π = 3.14]

4. a) (i) Using a scale of 2cm to 1 unit on both axes, draw two perpendicular axes OX and
OY on a graph sheet.

(ii) On the same graph sheet, mark the x-axes from –5 to 5 and the y-axis from –6 to 6.

b) On the same graph sheet, plot the points A (2, 5), B(4, 3) and C (1, 1). Join the points A,B
and C to form a triangle.

c) Reflect triangle ABC in the y-axis such that A→A1, B→B1 and C→C1. Label the vertices of
triangle A1B1C1

5. (a) A cylinder closed at one end has radius 7 cm and height 20 cm.

         (i) Find its total surface area.

         (ii) If the cylinder is filled with water to a depth of 5cm, calculate the volume of the water in
               it. Take π = 22/7]

(b) Evaluate 0.07 x 0.6 , leaving your answer in standard form

0.014 x 0.03