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BECE MATHEMATICS 1992

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OBJECTIVE TEST

1.

Find the set of prime factors of 12.

A.

{3}

B.

{2, 3}

C.

{3, 4}

D.

{2, 6}

E.

{2,3,4,6,12}

2.

If P = {7, 11, 13} and Q = {9, 11, 13}. Find P U Q.

A.

{7}

B.

{9}

C.

{7, 9}

D.

{7, 9, 11}

E.

{7, 9, 11, 13}

3.

In the diagram, set Q has 30 members and set T has 25 members. QT has 10 members.

Find the number of members of Q U T

A.

35

B.

45

C.

55

D.

65

E.

75

4.

Find the value of 6 1 4

A.

5.0

B.

4.9

C.

2.5

D.

2.4

E.

1.2

5.

Convert 39ten to a base five numeral.

A.

100111

B.

1110

C.

234

D.

124

E.

103

6.

Find the least whole number which must be added to 207 to make it divisible by 17

A.

0

B.

3

C.

13

D.

14

E.

15

7.

Simplify 2 x (3 1 3 + 1 1 6 )

A.

2 1 3

B.

4 1 4

C.

6 2 3

D.

8

E.

9

8.

If 8.51 ÷ 2.3 = 3.7, find the value of 85.1 ÷ 2.3

A.

0.037

B.

0.37

C.

3.7

D.

37

E.

370

9.

Express 0.625 as a fraction in its lowest term.

A.

7 8

B.

3 4

C.

5 8

D.

1 2

E.

1 3

10.

An amount of money is shared between Kofi and Ama in the ratio 3 : 5. If Ama received ₵4,650.00, what is Kofi's share?

A.

₵930.00

B.

₵1,550.00

C.

₵1,743.75

D.

₵2,790.00

E.

₵2,906.25

11.

If $1.00 = ₵340.00, what was the cedi value of an article which cost $6.50?

A.

₵6,630.00

B.

₵2,380.00

C.

₵2,210.00

D.

₵346.50

E.

₵333.50

12.

Find the simple interest on ₵28,000.00 at 3 1 2 % per annum for 6 months.

A.

₵490.00

B.

₵560.00

C.

₵980.00

D.

₵4,000.00

E.

₵5,880.00

13.

The bar chart shows the distances of 5 villages, P, Q, R, S and T from a market town.

Use it to answer the question below.

Which village is farthest from the market town?

A.

P

B.

Q

C.

R

D.

S

E.

T

14.

The bar chart shows the distances of 5 villages, P, Q, R, S and T from a market town.

Use it to answer the question below.

How much farther is village Q than village R from the market town?

A.

2 km

B.

3 km

C.

4 km

D.

5 km

E.

6 km

15.

There are 20 beads in a box. Some are red and some green. The chance that one bead taken at random from the box is red is 1 4 . Find the number of red beads in the box.

A.

16

B.

15

C.

10

D.

5

E.

4

16.

A bag contains 12 mangoes of which 4 are not ripe. What is the chance of picking at random a ripe mango from the bag?

A.

1 8

B.

1 4

C.

1 3

D.

1 2

E.

2 3

17.

Find the value of p2 – 6p + 9 when p = -2

A.

–7

B.

1

C.

12

D.

13

E.

25

18.

If x = 2, find the value of q in the equation 3x – 4 = x + q.

A.

8

B.

1

C.

0

D.

–1

E.

–8

19.

Which of the following inequalities is shown on the number line above, where p is a real number?

A.

p ≥ 2

B.

p > 2

C.

p = 2

D.

p ≤ 2

E.

p < 2

20.

Use the mapping below to answer the question below

-2 -1 0 2 3 4 ...... x
y -1 1 5 7 9 ...... 21

Find the value of x

A.

–7

B.

5

C.

6

D.

7

E.

10

21.

Use the mapping below to answer the question below

-2 -1 0 2 3 4 ...... x
y -1 1 5 7 9 ...... 21

Find the value of y

A.

3

B.

1

C.

–1

D.

–3

E.

-5

22.

In the diagram below, find the bearing of P from Q

A.

045°

B.

090°

C.

135°

D.

180°

E.

270°

23.

A polygon has 10 sides. Which of the following gives the sum of its interior angles?

A.

2 x 180°

B.

4 x 180°

C.

6 x 180°

D.

8 x 180°

E.

10 x 180°

24.

The diagram shows the conversion graph for miles and kilometres.

Use it to answer the question below

Find in kilometres, the equivalent of 4 miles.

A.

2.5

B.

3

C.

3.5

D.

6

E.

6.4

25.

The diagram shows the conversion graph for miles and kilometres.

Use it to answer the question below

Express 4 kilometres in miles.

A.

6.4

B.

6

C.

3.5

D.

3

E.

2.5

26.

The diagram below is a right-angled triangle.

Use it to answer the question below

Find |XZ|

A.

2.4 cm

B.

7 cm

C.

13 cm

D.

17 cm

E.

60 cm

27.

The diagram below is a right-angled triangle.

Use it to answer the question below

Find tan ∠YXZ

A.

5 13

B.

5 12

C.

12 13

D.

12 5

E.

13 5

28.

The diagram below shows two points P and Q in the number plane. Find the vector PQ.

A.

( 6 4 )

B.

( 6 -4 )

C.

( -6 4 )

D.

( 4 -6 )

E.

( -4 -6 )

29.

Find the length of the vector p = ( -5 12 )

A.

7

B.

10

C.

13

D.

17

E.

25

30.

In the diagram, square P1Q1R1S1 is an enlargement of square PQRS from centre O. The area of PQRS is 4 cm2 and the area of P1Q1R1S1 is 9 cm2.

Find the scale factor of the enlargement.

A.

2 3

B.

4 9

C.

1 1 2

D.

- 2 3

E.

2 1 4

31.

The volume of a cube is 27 cm3. Find the area of one of its faces.

A.

3 cm2

B.

6 cm2

C.

9 cm2

D.

18 cm2

E.

54 cm2

32.

A cylinder is of height 3 cm and radius 2 cm. Find its curved surface area.

[Take π = 3.142]

A.

7 cm2

B.

12 cm2

C.

18 cm2

D.

38 cm2

E.

54 cm2

33.

Find the area of the parallelogram PQRS

A.

20 cm2

B.

21 cm2

C.

48 cm2

D.

60 cm2

E.

240 cm2

34.

If one-third of a number is added to one-fifth of the same number, the result is 8. Find the number.

A.

3

B.

5

C.

15

D.

40

E.

45

35.

If 1 : x is equivalent to 6 1 4 : 25, find x.

A.

4

B.

5

C.

6.25

D.

24

E.

100

36.

Express 3 8 as a percentage.

A.

0.373%

B.

12%

C.

25%

D.

37 1 2 %

E.

40%

37.

Akosua buys 480 pineapples for ₵24,000.00. She sells all the pineapples for ₵28,000.00. Find her profit percent.

A.

13.9%

B.

16.7%

C.

20%

D.

40%

E.

83.3%

38.

How many edges has a cuboid?

A.

4

B.

6

C.

8

D.

10

E.

12

39.

The pie chart shows the distribution of crops on a farm of area 250 hectares.

Use it to answer the question below.

Find the area of the plot with corn.

A.

48.6

B.

55.3

C.

62.5 ha

D.

83.3 ha

E.

125.0 ha

40.

The pie chart shows the distribution of crops on a farm of area 250 hectares.

Use it to answer the question below.

What fraction of the farm is planted with pepper?

A.

1 3

B.

1 4

C.

1 5

D.

2 9

E.

7 32

THEORY QUESTIONS

1.

(a)

Solve 5 – 2x > x + 2, where x is a real number.

Illustrate your result on the number line.

(b)

Find the truth set of the equation: 2 3 (3y - 1) - (y + 2) = 1 3

(c)

Factorize completely: mp + npmtnt

(d)

Make t the subject of the relation v = u + at

Show Solution
2.

A landlady rented out her house for ₵240,000.00 for one year. During the year she paid 15% of the rent as income tax. She also paid 25% of the rent as property tax and spent ₵10,000.00 on repairs.

Calculate:

(a)

The landlady's total expenses.

(b)

The remainder of the rent after the landlady's expenses.

(c)

The percentage of the rent she spent on repairs.

Show Solution
3.

(a)

Using a scale of 2 cm to 1 unit on both axes, draw perpendicular lines OX and OY on a graph sheet.

(b)

On this graph sheet, mark the x-axis from –5 to 5 and the y-axis from –6 to 6

(c)

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

(d)

Using the y-axis as the mirror line, draw the image A1B1C1 of the triangleABC, such that AA1, BB1 and CC1. Write down the co-ordinates of A1, B1 and C1.

(e)

Using the x-axis as the mirror line, draw the image A2B2C2 of triangle ABC where AA2, BB2 and CC2.

Show Solution
4.

The table below gives the frequency distribution of the marks obtained in a class test by a group of 64 pupils.

Marks (Out of ten) Frequency
2 9
3 14
4 13
5 10
6 5
7 8
8 2
9 3

(a)

Draw a bar chart for the distribution.

(b)

A pupil is chosen at random from the class. What is the probability that the pupil obtained 7 marks?

Show Solution
5.

Using a ruler and a pair of compasses only,

(a)

draw |PQ| = 9 cm

(b)

construct a perpendicular to PQ at Q

(c)

construct angle QPS = 60° at the point P on PQ such that |PS| = 6.5cm

(d)

construct a line parallel to PQ through S. let the perpendicular through Q and the parallel through S, meet at R. Measure |PR|.

Show Solution

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