# Sulvme!

### Senior School Certificate Exams Waec Mathematics 2015 (May/June) Objectives View Theory

1:

if   $\left \{ x:2\leq x\leq 18; ; x\epsilon integer \right \}$ and 7 + x = 4 (mod9), find the highest value of x

A:

2

B:

5

C:

15

D:

18

E:

No option

2:

The sum of 110112, 111112, and 10000 is 10m10n0. Find the values of m and n.

A:

m = 0, n = 0

B:

m = 1, n = 0

C:

m = 0, n = 1

D:

m = 1, n = 1

E:

No option

3:

A trader bought an engine for \$15,000.00 outside Nigeria. If the exchange rate is \$0.075 to #1.00, how much did the engine cost in naira?

A:

#250,000.00

B:

#200,000.00

C:

#150,000.00

D:

#100,000.00

E:

No option

4:

If   $\frac{27^{x} \times 3^{1 - x}}{9^{2x}} = 1$ , find the value of x

A:

1

B:

1/2

C:

-1/2

D:

-1

E:

No option

5:

Find the 7th term of the sequence: 2, 5, 10, 17, 26, .........

A:

37

B:

48

C:

50

D:

63

E:

No option

6:

Given that log64 = 3, evaluate x log8

A:

6

B:

9

C:

12

D:

24

E:

No option

7:

If 2n = y, find 2(2 + n/3)

A:

4y1/3

B:

4y-3

C:

2y1/3

D:

2y-3

E:

No option

8:

Factorize completely: 6ax - 12by - 9ay + 8bx.

A:

(2a - 3b)(4x + 3y)

B:

(3a + 4b)(2x - 3y)

C:

(3a - 4b)(2x + 3y)

D:

(2a + 3b)(4x - 3y)

E:

No option

9:

Find the equation whose roots are 3/4 and -4

A:

4x2 - 13x + 12 = 0

B:

4x2 - 13x - 12 = 0

C:

4x2 + 13x - 12 = 0

D:

4x2 + 13x + 12 = 0

E:

No option

10:

If m=4, n=9 and r=16, evaluate  $\frac{m}{n} - 1\frac{7}{9} + \frac{n}{r}$

A:

$1\frac{5}{16}$

B:

$1\frac{1}{16}$

C:

$\frac{5}{16}$

D:

$-\frac{37}{48}$

E:

No option

12:

Ada draws the graphs of y = x2 - x - 2 and y = 2x - 1 on the same axes. Which of these equations is she solving?

A:

x2 - x - 30 = 0

B:

x2 - 3x - 1 = 0

C:

x2 - 3x - 3 = 0

D:

x2 + 3x - 1 = 0

E:

No option

13:

The volume of a cone of height 3cm is 381/2 cm3. Find the radius of its base. (Take $\pi$ = 22/7)

A:

3.0cm

B:

3.5cm

C:

4.0cm

D:

4.5cm

E:

No option

14:

A sector of a circle with radius 6cm subtends an angle of 60o at the center. Calculate its perimeter in terms of $\pi$

A:

2($\pi$+6)cm

B:

2($\pi$+3)cm

C:

2($\pi$+2)cm

D:

($\pi$+12)cm

E:

No option

15:

The dimensions of a rectangular tank are 2m by 7m by 11m. If its volume is equal to that of a cylindrical tank of height 4cm, calculate the base radius of the cylindrical tank [Take $\pi$ = 22/7]

A:

14m

B:

7m

C:

$3\frac{1}{2}$ m

D:

$1\frac{3}{4}m$

E:

No option

16:

In the diagram, O is the center of the circle. If PQ//RS and <ONS = 140o, find the size of <POM.

A:

40o

B:

50o

C:

60o

D:

80o

E:

No option

17:

In the diagram, PTR is a tangent to the circle center O. If angle TON= 108o, calculate the size of angle PTN.

A:

132o

B:

126o

C:

108o

D:

102o

E:

No option

18:

In the diagram, PQ//RT, QR//SU, <PQR 48o and <RTS = x. Find the value of x.

A:

134o

B:

132o

C:

96o

D:

48o

E:

No option

19:

In the diagram, O is the center of the circle, RT is a diameter, <PQT 33o and <TQS 76o. Use the diagram to answer questions 19 and 20

Calculate the value of angle PTR

A:

73o

B:

67o

C:

57o

D:

37o

E:

No option

20:

Find the size of angle PRS.

A:

76o

B:

71o

C:

38o

D:

33o

E:

No option

21:

The table below shows some values for a linear graph. Use it to answer questions 21 and 22

Find the gradient of the line

A:

1

B:

2

C:

3

D:

4

E:

No option

22:

What is the value of y when x = 2?

A:

5

B:

7

C:

9

D:

11

E:

No option

23:

Given that tan x = 2/3 where $0^{o}\leq x\leq 90^{o}$, find the value of 2 sin x

A:

$\frac{2\sqrt{13}}{13}$

B:

$\frac{3\sqrt{13}}{13}$

C:

$\frac{4\sqrt{13}}{13}$

D:

$\frac{6\sqrt{13}}{13}$

E:

No option

24:

PQRS is a square. If x is the midpoint of PQ, calculate, correct to the nearest degree, <ZPX

A:

53o

B:

55o

C:

63o

D:

65o

E:

No option

25:

The angle of elevation of an aircraft from a point K on the horizontal ground is 30o. If the aircraft is 800m above the ground, how far is it from K?

A:

400.00m

B:

692.82m

C:

923.76m

D:

1,600.00m

E:

No option

26:

The population of students in a school is 810. If this is represented on a pie chart, calculate the sectoral angle for a class of 72 students.

A:

32o

B:

45o

C:

60o

D:

75o

E:

No option

27:

The scores of twenty students in a test are as follows: 44,47,48,49,50,51,52,53,53,54,58,59,60,61,63,65,67,70,73,75. Find the third quartile

A:

62

B:

63

C:

64

D:

65

E:

No option

28:

The table shows the distribution of the scores of some students in a test. Calculate the mean score.

A:

5.6

B:

6.2

C:

6.6

D:

7.0

E:

No option

29:

The probabilities that Kebba, Ebou and Omar will hit a target are $\frac{2}{3}$,  $\frac{3}{4}$ and $\frac{4}{5}$ respectively. Find the probability that only Kebba will hit the target.

A:

$\frac{2}{5}$

B:

$\frac{7}{60}$

C:

$\frac{1}{30}$

D:

$\frac{1}{60}$

E:

No option

30:

In the diagram. VW//YZ, /WX/ = 6cm, /XY/ = 16cm, /YZ/ = 20cm and /ZX/ = 12cm. Calculate /VX/

Diagram coming

A:

3cm

B:

4cm

C:

6cm

D:

8cm

E:

No option

31:

Tom will be 25 years old in n years time. If he is 5 years younger than Bade, find Bade's present age.

A:

(30 - n) years

B:

(20 - n) years

C:

(25 - n) years

D:

(30 + n) years

E:

No option

32:

If   $\frac{\sqrt{2} + \sqrt{3}}{\sqrt{3}}$ is simplified as $m + n \sqrt{6}$, find the value of (m + n)

A:

$\frac{1}{3}$

B:

$\frac{2}{3}$

C:

$1\frac{1}{3}$

D:

$1\frac{2}{3}$

E:

No option

33:

In the diagram, QT and PR are straight lines, <ROS = (3n - 20o). <POT = 2m, <SOT = n, <POL = m and <QOL is a right angle. Find the value of n.

A:

35o

B:

40o

C:

55o

D:

60o

E:

No option

34:

Make k the subject of the relation  $T = \sqrt{\frac{Tk - H}{k - H}}$

A:

$k = \frac{H(T^{2} - 1)}{T^{2} - T}$

B:

$k = \frac{HT}{(T - 1)^{2}}$

C:

$k = \frac{H(T - 1)}{T}$

D:

$k = \frac{H(T^{2} + 1)}{T}$

E:

No option

35:

Which of the following is used to determine the mode of a grouped data

A:

Bar chart

B:

Frequency polygon

C:

Ogive

D:

Histogram

E:

No option

36:

The area of a rhombus is 110cm2. If the diagonals are 20cm and (2x + 1)cm long, find the value of x.

A:

5.0

B:

4.0

C:

3.0

D:

2.5

E:

No option

37:

Simplify: $\frac{3x - y}{xy} - \frac{2x + 3y}{2xy} + \frac{1}{2}$

A:

$\frac{4x + 5y - xy}{2xy}$

B:

$\frac{5x - 4x + xy}{2xy}$

C:

$\frac{5x + 4x - xy}{2xy}$

D:

$\frac{4x - 5y + xy}{2xy}$

E:

No option

38:

Illustrate graphically, the solution of  $\frac{y}{2} + \frac{1}{8} > \frac{5y}{8}$

A:

coming

B:

coming

C:

coming

D:

coming

E:

No option

39:

A farmer uses $\frac{2}{5}$ of his land to grow cassava, $\frac{1}{3}$ of the remainder for yam and the rest for maize. Find the part of the land used for maize

A:

$\frac{2}{15}$

B:

$\frac{2}{5}$

C:

$\frac{2}{3}$

D:

$\frac{4}{5}$

E:

No option

40:

The rate of consumption of petrol by a vehicle varies directly as the square of the distance covered. If 4 liters of petrol is consumed on a distance of 15km, how far would the vehicle go on 9 liters of petrol?

A:

221/km

B:

30 km

C:

333/km

D:

45 km

E:

No option

41:

A trader bought 100 oranges at 5 for #40.00 and sold them at 20 for #120.00. Find the profit or loss percent

A:

20% profit

B:

20% loss

C:

25% profit

D:

25% loss

E:

No option

42:

Describe the shaded portion in the diagram.

A:

$P'\cap Q\cap R'$

B:

$(P\cap R)'\cap Q$

C:

$P'\cap Q\cap R$

D:

$\left ( P\cup Q \right )' \cap R$

E:

No option

43:

Find the value of p if 1/4p + 3q = 10 and 2p - 1/3q = 7

A:

4

B:

3

C:

-3

D:

-4

E:

No option

44:

Calculate the mean deviation of 5,3,0,7,2,1

A:

0.0

B:

2.0

C:

2.5

D:

3.0

E:

No option

45:

In the diagram, the shaded part is a carpet laid in a room with dimensions 3.5m by 2.2m leaving a margin of 0.5m round it. Find the area of the margin.

A:

4.7 m2

B:

4.9 m2

C:

5.7 m2

D:

5.9 m2

E:

No option

46:

Two angles of a pentagon are in the ratio 2:3. The others are 60o each. Calculate the smaller of the two angles.

A:

72o

B:

100o

C:

120o

D:

144o

E:

No option

47:

A letter is selected from the letters of the English alphabet. What is the probability that the letter selected is from the word MATHEMATICS?

A:

$\frac{9}{13}$

B:

$\frac{11}{26}$

C:

$\frac{4}{13}$

D:

$\frac{1}{26}$

E:

No option

48:

In a circle radius r cm, a chord $16\sqrt{3} cm$ long is 10 cm from the center of the circle. Find, correct to the nearest cm, the value of r

A:

22cm

B:

17cm

C:

16cm

D:

15cm

E:

No option

49:

Consider the following statements:

X: Locally manufactured tyres are attractive.

Y: Many locally manufactured tyres do not last long.

Denoting locally manufactured tyres by M, attractive tyres by R and long lasting tyres by L, which of these Venn diagrams illustrates the statemtent?

A:

coming

B:

coming

C:

coming

D:

coming

E:

No option

50:

In the diagram, OX bisects <YXZ and OZ bisects <YZX. If <XYZ = 68o, calculate the value of <XOZ.

A:

68o

B:

72o

C:

112o

D:

124o

E:

No option