BECE 2014 Mathematics Past Questions Paper 2 (Essay) – Answers

JUNE 2014
MATHEMATICS 2

Paper 2 – Essay

SOLUTIONS

1. (a)

P = {1, 2, 3, 5, 6, 10, 15, 30}
Q = {5, 10, 15, 20, 25, 30, 35}
P∩Q = {5, 10, 15, 30}

1. (b)

Total amount = Simple Interest + Principal

                         = 2 × 12 × 3
Simple interest  = GHC 72.00

Total amount = Interest + Principal
= GHC 72.00 + GHC 200.00
= GHC 272.00

1. (c)

1. (c)

1. (c)

 

2.(a)(i)

Let x = Ama’s score in the fourth test

 

2.(a)(i)

Method 2
Total marks = No. of marks × mean mark
= 4 × 85
= 340
Sum of first 3 marks = 82 + 74 + 90
= 246
Ama’s fourth mark = Total mark – sum of first three
= 340 – 246
= 94

(a)(ii)

Median score
Scores arranged in order gives 74, 82, 90, 94

= 86

(b)(i)

Since angles BCF and CFG are alternate angles,
⇒ Angle BCF = 40°
Now, since base angles of isosceles triangle BFC are equal,
⇒ Angle CBF = 40°

(b)(ii) 

(angles at a point on a straight line = 180°)

⇒ angle DCF + angle BCF = 180°
⇒ angle DCF + 40° = 180°
⇒ angle DCF = 180° – 40°
= 140°

(b)(iii) 

(Sum of interior angles of a triangle = 180°)

              2x + 40° + 40° = 180°
2x + 80° = 180°
2x = 180° – 80°
2x = 100°

  x = 50°

 

3. (a)

Solving for x,

 

3. (a) 

Method 2

 

3.(b) (i)

Stem-and-leaf plot

(b) (ii)

Probability of selecting a student who scored between 40 and 50

(b) (iii)

Number of students who passed, if the pass mark was 30
= n (31, 36, 37, 39, 42, 43, 44, 47, 48, 53, 55, 59)
= 12 students

 

4.(a)(i)

Let length = l, width = w, height = h

Total surface area = 2lw + 2lh + 2wh,
= (2×8×5) + (2×8×10) + (2×5×10)
=    80 + 160 + 100
=   340 cm2

(a)(ii)

Volume   =     l × w × h
=      8cm × 5cm × 10cm
=      400 cm3

4 (b)

 

5. (a)

 

(b) (i)

 Radius   =   4.0cm (or 4.1cm)

(b)(ii)

 If    r = 4.0 cm
C = 2 π r
= 2 × 3.14 × 4 cm
= 25.12 cm

Or if r = 4.1cm
C = 2 × 3.14 × 4.1 cm
= 25.748 cm

6.(a)

6xy – 3y + 4x – 2
3y(2x – 1) + 2(2x – 1)
(2x – 1) (3y + 2)

(b)

The length of the ladder AB forms the hypotenuse of the right-angled triangle ABP
From the Pythagorean theorem,

The length of the ladder AB is 10 m

 

6. (c)

Method 1

(i)(α)

(i)(β)

(ii)

No. of bags left unsold by the end of February = 1800 – 1650
= 150

6. (c)   

6 (c) (i) (α)

(i)(β)

(ii)