# Sulvme!

### Senior School Certificate Exams Waec Mathematics 2014 (May/June) Objectives View Theory

1:

Simplify: $10\frac{2}{5} - 6\frac{2}{3} + 3$

A:

$6\frac{4}{15}$

B:

$6\frac{11}{15}$

C:

$7\frac{4}{15}$

D:

$7\frac{11}{15}$

E:

No option

2:

If 23x = 325, find the value of x.

A:

7

B:

6

C:

5

D:

4

E:

No option

3:

The volume of a cube is 512cm3. Find the length of its side.

A:

6cm

B:

7cm

C:

8cm

D:

9cm

E:

No option

4:

The bar chart below shows the scores of some students in a test.

Use it to answer question 4 and 5

How many students took the test?

A:

18

B:

19

C:

20

D:

22

E:

No option

5:

If one student is selected at random, find the probability that he/she scored at most 2 marks

A:

$\frac{11}{18}$

B:

$\frac{11}{20}$

C:

$\frac{7}{22}$

D:

$\frac{5}{19}$

E:

No option

6:

Simplify $\sqrt{12}(\sqrt{48} - \sqrt{3})$

A:

18

B:

16

C:

14

D:

12

E:

No option

7:

Which of the following number lines represents the solution to the inequality $-9 \leq \frac{2}{3}x - 7 < 5$

A:

coming

B:

sdf

C:

dsf

D:

dsf

E:

No option

8:

In the diagram, the value of x + y = 2200. Find the value of n.

A:

200

B:

400

C:

600

D:

800

E:

No option

9:

Given that x > y and 3 < y, which of the following is/are true?  i. y>3 ii. x<3  iii. x>y>3

A:

i only

B:

i and ii only

C:

i and iii only

D:

i, ii and iii

E:

No option

10:

Three quarters of a number added to two and a half of that number gives 13. Find the missing number.

A:

4

B:

5

C:

6

D:

7

E:

No option

11:

If X = {0, 2, 4, 6}, Y = {1, 2, 3, 4} and Z = {1, 3} are subsets of $U = \left \{ x: 0 \leq x \leq 6 \right \}$, find $x \cap (Y \cup Z)$

A:

{0, 2, 6}

B:

{1, 3}

C:

{0, 6}

D:

{  }

E:

No option

12:

Find the truth set of the equation x2 = 3(2x + 9)

A:

{x: x = 3, x = 9}

B:

{x: x = -3, x= -9}

C:

{x: x = 3, x = -9}

D:

{x: x = -3, x = 9}

E:

No option

13:

The coordinates of points P and Q are (4,3) and (2, -1) respectively. Find the shortest distance between P and Q

A:

$10 \sqrt{2}$

B:

$4 \sqrt{5}$

C:

$5 \sqrt{2}$

D:

$2 \sqrt{5}$

E:

No option

14:

Make u the subject of the formula, $E = \frac{m}{2g}(v^{2} - u^{2})$

A:

$u = \sqrt{v^{2} - \frac{2Eg}{m}}$

B:

$u = \sqrt{\frac{v^{2}}{m} - \frac{2Eg}{4}}$

C:

$u = \sqrt{v - \frac{2Eg}{m}}$

D:

$u = \frac{\sqrt{2v^{2}Eg}}{m}$

E:

No option

15:

In the diagram, <QPT = <PTS = 900, <PQR = 1100 and <TSR = 200. Find the size of the obtuse angle QRS

A:

1400

B:

1300

C:

1200

D:

1100

E:

No option

16:

If x varies inversely as y and y varies directly as z, what is the relationship between x and z?

A:

$x \propto z$

B:

$x \propto \frac{1}{z}$

C:

$x \propto z^{2}$

D:

$x \propto z^{\frac{1}{2}}$

E:

No option

17:

Find the gradient of the line joining the points (2, -3) and (2, 5)

A:

0

B:

1

C:

2

D:

undefined

E:

No option

18:

If (x - a) is a factor of bx - ax + x2 - ab, find the other factor

A:

(x + b)

B:

(x - b)

C:

(a + b)

D:

(a - b)

E:

No option

19:

The table shows the distribution of the heights of plants in a nursery. Calculate the mean height of the plants.

A:

3.8

B:

3.0

C:

2.8

D:

2.3

E:

No option

20:

In the diagram, PQR is a straight line, (m + n) = 1200 and (n + r) = 1000. Find (m + r)

A:

1100

B:

1200

C:

1400

D:

1600

E:

No option

21:

In the diagram, line SR is parallel to line UW, <WVT = x0, <VUT = y0, <RSV = 450 and <VTU = 200

Use this diagram to answer question 21 and 22

Find the value of x

A:

20

B:

45

C:

65

D:

135

E:

No option

22:

Calculate the value of y

A:

20

B:

25

C:

45

D:

65

E:

No option

23:

The area of a sector of a circle with diameter 12cm is 66cm2. If the sector is folded to form a cone, calculate the radius of the base of the cone. (Take pi = 22/7)

A:

3.0cm

B:

3.5cm

C:

7.0cm

D:

7.5cm

E:

No option

24:

A chord, 7cm long, is drawn in a circle with radius 3.7cm. Calculate the distance of the chord from the centre of the circle.

A:

0.7cm

B:

1.2cm

C:

2.0cm

D:

2.5cm

E:

No option

25:

Which of the following is a measure of dispersion?

A:

Range

B:

Percentile

C:

Median

D:

Quartile

E:

No option

26:

A box contains 13 currency notes, all of which are either #50 or #20 notes. The total value of the currency notes is #530. How many #50 notes are in the box?

A:

4

B:

6

C:

8

D:

9

E:

No option

27:

The graph below is for the relation y = 2x2 + x - 1

Use it to answer questions 27 and 28.

What are the coordinates of the point S?

A:

(1, 0.2)

B:

(1, 0.4)

C:

(1, 2.0)

D:

(1, 4.0)

E:

No option

28:

Find the minimum value of y

A:

0.00

B:

-0.65

C:

-1.25

D:

-2.10

E:

No option

29:

A ship sails x km due east to a point E and continues x km due north to F. Find the bearing of F from the starting point.

A:

0450

B:

0900

C:

1350

D:

2250

E:

No option

30:

If x:y = 3:2 and y:z = 5:4, find the value of x in the ratio x:y:z

A:

8

B:

10

C:

15

D:

20

E:

No option

31:

A trader bought sachet water for GHc55.00 per dozen and sold them at 10 for GHc50.00. Calculate, correct to 2 decimal places, his percentage gain.

A:

8.00%

B:

8.30%

C:

9.09%

D:

10.00%

E:

No option

32:

In the figure, PQ is a tangent to the circle at R and UT is parallel to PQ. If <TRQ = x0, find <URT in terms of x.

A:

2x0

B:

(90 - x)0

C:

(90 + x)0

D:

(180 - 2x)0

E:

No option

33:

Given that $cos x = \frac{12}{13}$, evaluate $\frac{1 - tan x}{tan x}$

A:

$\frac{5}{13}$

B:

$\frac{5}{7}$

C:

$\frac{7}{5}$

D:

$\frac{13}{5}$

E:

No option

34:

Approximate 0.0033780 to 3 significant figures

A:

338

B:

0.338

C:

0.00338

D:

0.003

E:

No option

35:

Simplify $\sqrt{\frac{8^{2} \times 4^{n} + 1}{2^{2n} \times 16}}$

A:

16

B:

8

C:

4

D:

1

E:

No option

36:

If $\frac{2}{x - 3} - \frac{3}{x - 2}$ is equal to $\frac{P}{(x - 3)(x - 2)}$, find P

A:

-x - 5

B:

- (x + 3)

C:

5x - 13

D:

5 - x

E:

No option

37:

Subtract $\frac{1}{2}(a - b - c)$ from the sum of $\frac{1}{2}(a - b + c)$ and $\frac{1}{2}(a + b - c)$

A:

$\frac{1}{2}(a+b+c)$

B:

$\frac{1}{2}(a - b - c)$

C:

$\frac{1}{2}(a - b + c)$

D:

$\frac{1}{2}(a + b - c)$

E:

No option

38:

A man's eye level is 1.7m above the horizontal ground and 13m from a vertical pole. If the pole is 8.3m high, calculate, correct to the nearest degree, the angle of elevation of the top of the pole from his eyes

A:

330

B:

320

C:

270

D:

260

E:

No option

39:

A chord subtends an angle of 1200 at the centre of a circle of radius 3.5cm. Find the perimeter of the minor sector containing the chord (Take $\pi = 22/7$)

A:

$14\frac{1}{3}cm$

B:

$12\frac{5}{6}cm$

C:

$8\frac{1}{7}cm$

D:

$7\frac{1}{3}cm$

E:

No option

40:

In parallelogram, PQRS, line QR is produced to M such that |QR| = |RM|. What fraction of the area of PQMS is the area of PRMS?

A:

$\frac{1}{4}$

B:

$\frac{1}{3}$

C:

$\frac{2}{3}$

D:

$\frac{3}{4}$

E:

No option

41:

Determine the value of m in the diagram.

A:

800

B:

900

C:

1100

D:

1500

E:

No option

42:

In a cummulative frequency graph, the lower quartile is 18 years while the 60th percentile is 48 years. What percentage of the distribution is at most 18 years or greater than 48 years

A:

15%

B:

35%

C:

65%

D:

85%

E:

No option

43:

If a number is selected at random from each of the sets P = {1, 2, 3} and Q = {2, 3, 5}, find the probability that the sum of the numbers is prime

A:

$\frac{5}{9}$

B:

$\frac{4}{9}$

C:

$\frac{1}{3}$

D:

$\frac{2}{9}$

E:

No option

44:

In the diagram, O is the centre of the circle, line PR is a tangent to the circle at Q and <SOQ = 860. Calculate the value of <SQR

A:

430

B:

470

C:

540

D:

860

E:

No option

45:

If log 5.957 = 0.7750, find $log \sqrt[3]{0.0005957}$

A:

sdfdsf

B:

sdfsdf

C:

dsf

D:

sdfsdf

E:

No option

46:

The probability of an event P happening is $\frac{1}{5}$ and that of event Q is $\frac{1}{4}$. If the events are independent, what is the probability that neither of them happens

A:

$\frac{4}{5}$

B:

$\frac{3}{4}$

C:

$\frac{3}{5}$

D:

$\frac{1}{20}$

E:

No option

47:

Each exterior angle of a polygon is 300. Calculate the sum of the interior angles.

A:

5400

B:

7200

C:

10800

D:

18000

E:

No option

48:

Find the number of terms in the Arithmetic Progression (A.P) 2, -9, -20, ..., -141

A:

11

B:

12

C:

13

D:

14

E:

No option

49:

In what modulus is it true that 9 + 8 = 5?

A:

mod10

B:

mod11

C:

mod12

D:

mod13

E:

No option

50:

The radii of the base of two cylinderical tins, P and Q are r and 2r respectively. If the water level in P is 10cm high, what would be the height of the same quantity of water in Q?

A:

2.5cm

B:

5.0cm

C:

7.5cm

D:

20.0cm

E:

No option