2015 BECE Mathematics (Maths) Past

Questions Paper One

1. List the members of the set Q = {prime factors of 30}

A. {2, 3, 5}
B. {2, 6, 10}
C. {3, 5, 15}
D. {3, 6, 15}

2. Given that set P = {m, n, o, p}, find the number of subsets of P.

A. 4
B. 8
C. 10
D. 16

between 11 and 23}, find M ∪ N

3. If M = {multiples of 4 between 10 and 25} and N = {even numbers

A. {12, 16, 20}

B. {14, 18, 22}
C. {12, 14, 16, 18, 22}
D. {12, 14, 16, 18, 20, 22, 24}

4. What is the place value of 7 in 24.376 ?

A. Unit
B. Ten
C. Tenth
D. Hundredth

5. Find the Highest Common Factor of 24, 42 and 72

A. 4
B. 6
C. 7
 D. 12

6. Express 1205 as a number in base 10

A. 25
B. 27
C. 32
D. 35

7. If p × q × r = 1197, and p = 19, q = 3, find r

A. 21
B. 49
C. 57
D. 61

8. How many integers are within the interval –5< x<7?

A. 10
B. 11
C. 12
D. 13

9. Divide 1.612 by 0.4

A. 4.3
B. 4.03
C. 0.403
D. 0.43

5 11 7
10. Arrange the following fractions in ascending order: , ,
8 20 10
5 11 7
A. , ,
8 20 10
7 5 11
B. , ,
10 8 20
11 5 7
C. , ,
20 8 10
 5 7 11
D. , ,
8 10 20

1 4
11. Abena spent 5 of her money on sweets, 7 on provisions and the rest on
gari. What fraction of her money did she spend on gari?
27
A. 35
13
B. 35
8
C. 35
5
D. 35

12. If 5 boys took 14 days to cultivate a piece of land, how long will it take
7 boys working at the same rate to cultivate the land ?
A. 14 days
B. 12 days
C. 10 days
D. 8 days

13. A man invested GHC 800.00 in a bank at a simple interest rate of 5%

per annum. Find his total amount in the bank at the end of one year.
A. GHC 840.00
B. GHC 860.00
C. GHC 900.00
D. GHC 960.00

14. John sold a car for GHC 60,000.00 and made a profit of 20%. What is
the cost price of the car?
A. GHC 48,000.00
B. GHC 50,000.00
C. GHC 72,000.00
 D. GHC132,000.00

15. What is the value of x if 10x = 1000?

A. 1
B. 2
C. 3
D. 4

16. Express 625.13 in standard form

A. 6.2513 × 10-2
B. 6.2513 × 10-4
C. 6.2513 × 102
D. 6.2513 × 104

17. Find the median of the numbers 17, 12, 15, 16, 8, 18, 13 and 14
A. 8
B. 12
C. 14.5
D. 15.5

18. The ages in years of 10 children at a party are 2, 3, 3, 3, 4, 4, 5, 5, 5 and

6. If a child is chosen at random, what is the probability that he / she is
not less than 5 years old ?
2
A. 3
2
B. 5
3
C. 10
1
D. 2

19. Expand (2x + y) (2x - y)

A. 2x2 – y2
 B. 4x2 – y2
C. 2x2 + 4xy – y2
D. 4x2 + 4xy – y2

20. Find the value of n, if 25.003 = (2 × 10) + (5 × 1) + (3 × n)

A. 0.001
B. 0.011
C. 0.01
D. 0.1

21. Evaluate (3m)2 – 3m2, when m = 2.

A. 12
B. 18
C. 20
D. 24

22. A wrist watch is priced GHC 2,000.00. A shopkeeper allows a discount

of 2% on the cost price. Find the discount on 20 of such wrist watches.
A. GHC 500.00
B. GHC 600.00
C. GHC 800.00
D. GHC 1,000.00

23. Find the value of m, if 4(m + 4) = – 8.

A. – 6
B. – 2
C. 2
D. 6

24. Find the rule for the following mapping

 A. y→x+2
B. y→2x
C. y→x2
D. y→2x+2

25. How many vertices has a cuboid?

A. 6
B. 7
C. 8
D. 14

26. The circumference of a circle is 440 m. Find the area of the circle. [Take
π=
22
7]
A. 14,400 m2
B. 15,400 m2
C. 16,400 m2
D. 18,000 m2

27. What name is given to a triangle which has all its sides equal?
A. Isosceles triangle
B. Scalene triangle
C. Equilateral triangle
D. Right-angle triangle

28. At eight o’clock, which of the following is the angle between the hour
and the minute hands of the clock?
A. 150°
B. 120°
C. 90°
D. 60°
29. A rectangular field 50 m wide and y m long requires 260 m of fencing.
Find y.
A. 15 m
B. 40 m
C. 80 m
D. 105 m

30. Which of the following best describes the statement: ‘The locus of a
point which moves so that its distance from two fixed points are always
equal’?
A. Bisector of an angle
B. Perpendicular bisector
C. Circle
D. Two parallel lines

31. The point K (1, 5) is rotated through 90° anti-clockwise about the
origin. Find the coordinates of the image of K.
A. (5, -1)
B. (-5, 1)
C. (-1, 5)
D. (1, -5)

32. Kwame is facing west. Through how many degrees should he turn anti-
clockwise to face north?
A. 90°
B. 180°
C. 270°
D. 360°

33. Given that vectors u = (−35) and v = (−32 ), find 2v – u

A. (−11 )
 B. (−11)
C. (−11
−7
)
D. (−11
7
)

34.

What is the name of the figure above?

A. Cuboid
B. Kite
C. Triangle
D. Pyramid

13 12 17
E F 10
11 16 G

Use the magic square above to answer questions 35 to 37

35. Find the value of F

A. 14
B. 15
C. 18
D. 23
36. Find the value of E.
A. 14
B. 15
C. 18
D. 23

37. Evaluate E + G
A. 29
B. 30
C. 33
D. 38

38. The hypotenuse and a side of a right-angled triangle are 13 cm and 5 cm

respectively. Find the length of the third side.
A. 8 cm
B. 9 cm
C. 12 cm
D. 17 cm

39. Find the missing number in the sequence below:

11, 16, 22, 29, __, 46, 56
A. 30
B. 36
C. 37
D. 39

40. A hall which is 20 m long is represented on a diagram as 10 cm long.

What is the scale of the diagram?
A. 1:200
B. 1:250
C. 1:400
D. 1:500
 Objective Test
SOLUTIONS

1. A. {2, 3, 5}
2. D. 16
3. D. {12, 14, 16, 18, 20, 22, 24}
4. D. Hundredth
5. B. 6
6. D. 35
7. A. 21
8. B. 11
9. B. 4.03
10. C. 11/20 , 5/8 , 7 /10

11. C. 8 /35

12. C. 10 days
13. A. GHC 840.00
14. B. GHC 50,000.00
15. C. 3
16. C. 6.2513 × 102
17. C. 14.5
2
18. B. 5

19. B. 4x2 – y2
20. A. 0.001
21. D. 24
22. C. GHC 800.00
23. A. – 6
24. C. y→x2
25. C. 8
26. B. 15,400 m2
27. C. Equilateral triangle
28. B. 120°
29. C. 80 m
30. B. Perpendicular bisector
31. B. (-5, 1)
32. C. 270°

33. D. (−11
7
)
34. D. Pyramid
35. A. 14
36. C. 18
37. C. 33
38. C. 12
39. C. 37
40. A. 1:200
2015 BECE Mathematics (Maths) Past
Questions Paper Two
1. (a) Find the difference between the product of 2.5 and 7.5 and the sum of
2.75 and 9.55.
3 x +2 3−x 1
(b) Solve − =
3 8 6
(c) A container is 24 m long, 9 m wide and 8 m high. How many books can
it hold if each book is 20 cm long, 16 cm wide and 6 cm thick.

2. (a) In a test consisting of 90 questions, Ama answered 75% of the first 40

questions correctly. If she had to get a score of 80% in the test,
(i) how many questions did she answer correctly out of the first 40
questions?
(ii) how many questions should she answer correctly out of the 90
questions ?
(iii) what percentage of the remaining 50 questions should she answer
correctly in order to get the 80%?

(b) Three interior angles of a pentagon are 100°, 120° and 108°. Find the
size of each of the remaining two interior angles, if one of them is three
times the other.

3. (2 ) ( x)
(a) Given that vectors p = 2 and q = y , find :

(i) (12)
q if q – p = 9 ;
(ii) the magnitude of the vector q - p

A
(b)
50°

7x-25° 30°
B C D
NOT DRAWN TO SCALE
 In the diagram |AB| = |AC|, angle ADC = 30° and angle ACD = 7x –
25°. Find

(i) the value of x;

(ii) angle DAC;
(iii) angle BAD.

4. (a) The Value Added Tax (VAT) paid by a man on a deep freezer was GHC
90.00. If VAT was charged at 15%,
(i) what was the price of the deep freezer?
(ii) How much did the man pay including VAT?

(b) The average of the numbers 5, 7, 2, 6, x, (x+1), 7 and 4 is 5. Find the

value of x.
mn+ mp+ nq+ pq
(c) Simplify: n+ p

5. (a) A cylinder which has a height of 90 cm and diameter 14 cm is closed at

both ends.
Find:
(i) its total surface area;

[Take π = 22/7]
(ii) the volume of the cylinder

(b) (i) Using a ruler and a pair of compasses only, construct triangle PQR
such that

|PQ| = 8cm, angle PQR = 120° and |QR| = 6 cm.

(ii) Measure:

(α) |PR|;
 (β) angle QPR

6. The table shows the distribution of grades of candidates in

an examination.

Grade 1 2 3 4 5 6

Frequency 2 3 6 5 4 10

(a) Using a graph sheet, draw a bar chart for the distribution

(b) If all candidates who obtained grades above grade 3 were awarded credit,
find the probability that a candidate selected at random obtained credit.

(c) Calculate, correct to the nearest whole number, the mean grade of the
candidates.

END OF ESSAY TEST

 MATHEMATICS 2
ESSAY
SOLUTIONS

1. (a) Product of 2.5 and 7.5

= 2.5 × 7.5
25 75
= 10 × 10
1875
= 100
= 18.75

Sum of 2.75 and 9.55

= 2.75
+ 9.55
12.30

Difference between 18.75 and 12.30

=
– 12.30
18.75

6.45

3 x +2 3−x 1
(b)Solving − =
3 8 6
⇒ ( ) ( ) ()
3 x +2 3−x 1
24 −24 =24
3 8 6

⇒ 8 ( 3 x+ 2 )−3 ( 3−x ) =4 ( 1 )

⇒ 24x + 16 – 9 + 3x = 4

⇒ 24x + 3x = 4 – 16 + 9

⇒ 27x = – 3

⇒
27 x −3
=
27 27
 ⇒ = 9
−1
x

(c) Volume of container = length × width × height

= 24m × 9m × 8m
= 2400cm × 900cm × 800cm
= 1728000000 cm3

Volume of each book = 20 cm × 16 cm × 6 cm

= 320 cm2 × 6 cm
= 1920 cm3

Volume of container
No. of books the container can hold = Volume of eac h book
3
1728000000 cm
= 3
1920 cm
= 900,000 books

2. (a) (i) No.of questions Ama answered correctly out of first 40

questions
= 75% of first 40 questions
75
= 100 × 40
75× 4
= 10
= 30 questions

(ii)To score 80% in the test, then she needs to answer

= 80% × 90 questions
80
= 100 × 90

= 8×9
= 72 questions correctly
 (iii) No. of questions she must answer correctly in the remaining 50
questions
= 72 – 30 questions
= 42 questions

Percentage of 42 out of 50 questions

42
= 50 × 100 %

= 42 × 2%
= 84%

(b)Sum of interior angles of a pentagon (5-sided polygon)

= (n – 2) × 180° , where n = no.of sides
= (5 – 2) × 180° [n = 5 sides]
= 3 × 180°
= 540°

Let size of smaller missing angle = x

then, size of bigger missing angle = 3x

⇒ 100° + 120° + 108° + x + 3x

Now, if sum of interior angles = 540°,

⇒
= 540°

⇒
328° + 4x = 540°

⇒
4x = 540° – 328°
4x = 212°
⇒
212
x =
⇒
4
x = 53°

Hence, the other missing angle = 3x

= 3 × 53°
= 159°
The sizes of the two remaining interior angles = 53° and 159°

3. (a) (i) If q–p = (129 )

x
() ()( )
2 12
Then, y − 2 = 9
 ⇒ ( xy )=(129)+(22)
⇒ ( xy )=(12+2
9+2 )

⇒ ( xy )=(1411)
⇒q = (1411)
(ii)Magnitude of vector q – p
= magnitude of (129)
= √ 122+ 92
= √ 144+ 81
= √ 225
= 15 units

Since |AB| = |AC|

⇒ angle ABC = angle ACB [Base angles
(b)(i)

of isosceles triangle equal]

Let angle ABC = angle ACB = y

Then, y + y + 50° = 180° [interior

angles of a triangle =180°]
⇒ 2y = 180° – 50°
⇒ 2y = 130°
⇒ y =
130

⇒ y = 65°
2

Now, 65° + (7x – 25°) = 180° [angles at

a point on a straight line=180°]
⇒ 7x + 65° – 25°
⇒ 7x + 40 = 180°
= 180°

⇒ 7x = 180° – 40°
⇒ 7x = 140°
⇒
140°
x =
⇒
7
x = 20°
 180° [interior
angles of a triangle =180°]
(ii)Angle DAC + 7x – 25° + 30° =

⇒ a + 7x – 25° + 30°
Let angle DAC = a

⇒
= 180°

⇒ a + 140° – 25° + 30°

a + 7(20°) – 25° + 30° = 180°

⇒ a + 115° + 30°
= 180°

⇒a
= 180°

⇒
+ 145° = 180°

⇒
a = 180° – 145°

⇒ angle DAC
a = 35°
= 35°

(iii) angle BAD = angle BAC + angle DAC

= 50° + 35°
= 85°

15% → GH¢ 90.00

Then (Original price) 100% → ? (more)
4. (a) (i) If (VAT)

If more, less (15%) divides, hence

=
100 %
× GHc 90
15 %

= 100 × GHc 6
= GHc 600
Original price = GHc 600.00

(ii)Total amount paid = Original price + VAT

= GHc 600.00 + GHc 90.00
= GHc 690.00

(b)If the average of 8 no.s: 5, 7, 2, 6, x, (x+1), 7 and 4 = 5, then

⇒
5+7+2+6+ x+ x +1+7+ 4
=5

⇒
8
32+ 2 x
=5
8
 ⇒ 8 ( 32+28 x )=8 (5)
⇒ 32 + 2x = 40

⇒
⇒
2x = 40 – 32

⇒
2x = 8

⇒
x = 8/2
x = 4

mn+ mp+ nq+ pq

(c) Simplification of n+ p
m(n+ p)+ q(n+ p)
=
n+ p
( n+ p ) (m+q)
=
n+ p
( n+ p ) (m+q)
=
n+ p
= m+q

⇒
5. (a) (i) h = 90cm, d = 14 cm,
r = 14cm÷2
r = 7cm

Total Surface Area of closed cylinder

= 2πr2 + 2πrh , where r = radius, h =

height

= (2 × 227 ×7 × 7)+(2 × 227 × 7 ×90)

= (2 × 22 × 7) + (2 × 22 × 90)

= 308 + 3960

= 4268 cm2
 (ii) Volume of cylinder

= π r2 h , where r = radius, h = height

22
= ×7 × 7× 90
7

= 22 × 7 × 90

= 154 × 90

= 13860 cm3

(b)(i)

(ii)Measure:
(α)|PR| = 12.1 cm (± 0.1cm)

(β) angle QPR = 25° (± 1°)

6. (a) Bar chart for the frequency distribution table below

Grade 1 2 3 4 5 6

Frequency 2 3 6 5 4 10
(b) Number of candidates who obtained credit (grades above grade 3
for the distribution)
= Frequencies of Grade 1 and Grade 2
= 2 + 3
= 5

Total number of candidates = 2 + 3 + 6 + 5 + 4 + 10

= 30

Probability of selecting a candidate who obtained credit

No . of candidates who obtained credit

= Total no . of candidates
5 1
= =
30 6
(c) Mean grade=
∑ of all grades
Total no . of candidates

( 1× 2 )+ ( 2× 3 ) + ( 3 ×6 )+ ( 4 × 5 ) + ( 5× 4 ) +(6× 10)
=
2+3+6 +5+4 +10

2+ 6+18+20+ 20+60
= 2+3+ 6+5+ 4+10

126 42 2
= = = 4
30 10 10

1
= 4 or 4.2
5

≈ 4 (to nearest whole number)