# Sulvme!

### Senior School Certificate Exams Waec Mathematics 2016 (May/June) Objectives View Theory

1:

If 23x + 101x = 130x Find the value of x

A:

7

B:

6

C:

5

D:

4

E:

No option

2:

Simplify: $\left ( \frac{3}{4} - \frac{2}{3} \right ) \times 1\frac{1}{5}$

A:

$\frac{1}{60}$

B:

$\frac{5}{72}$

C:

$\frac{1}{10}$

D:

$1\frac{7}{10}$

E:

No option

3:

Simplify $\left ( \frac{10\sqrt{3}}{\sqrt{5}} - \sqrt{15} \right )^{2}$

A:

75.00

B:

15.00

C:

8.66

D:

3.87

E:

No option

4:

The distance d, through which a stone falls from rest varies directly as the square of the time t, taken. If the stone falls 45cm in 3 seconds, how far will it fall in 6 seconds?

A:

90cm

B:

135cm

C:

180cm

D:

225cm

E:

No option

5:

Which of the following is not a valid conclusion from the premise: 'Nigerian footballers are good footballers'?

A:

Joseph plays football in Nigeria therefore he is a good footballer

B:

Joseph is a good footballer therefore he is a Nigerian footballer

C:

Joseph is a Nigerian footballer therefore he is a good footballer

D:

Joseph plays good football therefore he is a Nigerian footballer

E:

No option

6:

On a map, 1cm represents 5km. Find the area on the map that is represents 100km2

A:

2cm2

B:

4cm2

C:

8cm2

D:

16cm2

E:

No option

7:

Simplify $\frac{3^{n-1} \times 27^{n+1}}{81^{n}}$

A:

$3^{2n}$

B:

$9$

C:

$3^{n}$

D:

$3^{n+1}$

E:

No option

8:

What sum of money will amount to D10,400.00 in 5 years at 6% simple interest?

A:

D8,000.00

B:

D10,000.00

C:

D12,000.00

D:

D16,000.00

E:

No option

9:

Which of the following number lines illustrates the solution of the inequality $4 \leq \frac{1}{3}(2x - 1) < 5$ ?

A:

dsdss

B:

sdcs

C:

sdsacc

D:

sdacd

E:

No option

10:

The roots of a quadratic equation are $\frac{4}{3}$ and $\frac{-3}{7}$ Find the equation

A:

21x2 - 19x - 12 = 0

B:

21x2 + 37x - 12 = 0

C:

21x2 - x + 12 = 0

D:

21x2 +7x - 4 = 0

E:

No option

11:

Find the values of y for which the expression $\frac{y^{2} - 9y + 18}{y^{2} + 4y - 21}$ is undefined

A:

6, -7

B:

3, -6

C:

3, -7

D:

-3, -7

E:

No option

12:

Given that 2x + y = 7 and 3x - 2y = 3, by how much is 7x greater than 10?

A:

1

B:

3

C:

7

D:

17

E:

No option

13:

Simplify $\frac{2}{1-x} - \frac{1}{x}$

A:

$\frac{x+1}{x(1 - x)}$

B:

$\frac{3x - 1}{x(1 - x)}$

C:

$\frac{3x + 1}{x(1 - x)}$

D:

$\frac{x - 1}{x(1 - x)}$

E:

No option

14:

Make x the subject of the relation: $p = s + \frac{sm^{2}}{nr}$

A:

$s = \frac{mrp}{nr+m^{2}}$

B:

$s = \frac{nr + m^{2}}{nrp}$

C:

$s = \frac{nrp}{mr + m^{2}}$

D:

$s = \frac{nrp}{nr + m^{2}}$

E:

No option

15:

Factorize (2x+3y)2 - (x - 4y)2

A:

(3x - y)(x + 7y)

B:

(3x + y)(2x - 7y)

C:

(3x + y)(x - 7y)

D:

(3x - y)(2x + 7y)

E:

No option

16:

The curved surface area of a cylinder 5cm high, is 110cm2, Find the radius of the base

(Take $\pi$ = 22/7)

A:

2.6cm

B:

3.5cm

C:

3.6cm

D:

7.0cm

E:

No option

17:

The volume of a pyramid with height 15cm is 90cm3, If its base is a rectangle with dimensions xcm by 6cm, Find the value of x

A:

3

B:

5

C:

6

D:

8

E:

No option

18:

In the diagram, line YW is a tangent to the circle at X, |UV| = |VX| and <VXW = 500 . Find the value of <UXW

A:

700

B:

800

C:

1050

D:

1100

E:

No option

19:

In the diagram, line PF, QT, RG intersect at S and PQ // RG. If <SPQ = 1130 and <RST = 220, find <PSQ

A:

220

B:

450

C:

670

D:

890

E:

No option

20:

In the diagram, O is the centre of the circle, <XOZ = (10m)0 and <XWZ = m0, calculate the value of m

A:

30

B:

36

C:

40

D:

72

E:

No option

21:

Kweku walked 8m up a slope and was 3m above the ground. If he walks 12m further up the slope, how far above the ground will he be?

A:

4.5m

B:

6.0m

C:

7.5m

D:

9.0m

E:

No option

22:

In the diagram, TS is a tangent to the circle at S, |PR| = |RS| and <PQR = 1170, Calculate <PST

A:

540

B:

440

C:

340

D:

270

E:

No option

23:

In the diagram, PR // SV // WY, TX // QY, <PQT = 480 and <TXW = 600. Find <TQU

A:

1200

B:

1080

C:

720

D:

600

E:

No option

24:

A straight line passes through the points P(1,2) and Q(5,8).

Use this information to answer questions 24 and 25.

Calculate the gradient of the line PQ

A:

$\frac{3}{5}$

B:

$\frac{2}{3}$

C:

$\frac{3}{2}$

D:

$\frac{5}{3}$

E:

No option

25:

Calculate the length PQ

A:

$4\sqrt{11}$

B:

$4 \sqrt{10}$

C:

$2 \sqrt{17}$

D:

$2 \sqrt{13}$

E:

No option

26:

In the diagram, TX is perpendicular to UW. |UX| = 1cm and $TX = |WX| = \sqrt{3cm}$. Find the <UTW.

A:

1350

B:

1050

C:

750

D:

600

E:

No option

27:

If $cos \theta = x$ and sin 600 = x + 0.5, 00 < $\theta$ < 900,

Find correct to the nearest degree, the value of $\theta$

A:

660

B:

670

C:

680

D:

690

E:

No option

28:

The table below shows the ages of students in a club. Use it to answer questions 28 and 29.

How many students are in the club ?

A:

50

B:

55

C:

60

D:

65

E:

No option

29:

Find the median age

A:

13

B:

14

C:

15

D:

16

E:

No option

30:

The figure is a pie chart which represents the expendiure of a family in a year. If the total income of the family was Le 10,800,000.00, how much was spent on food?

A:

Le 2,250,000.00

B:

Le 2,700,000.00

C:

Le 3,600,000.00

D:

Le 4,500,000.00

E:

No option

31:

A fair die is thrown two times. What is the probabiliity that the sum of the score is at least 10?

A:

$\frac{5}{36}$

B:

$\frac{1}{6}$

C:

$\frac{5}{18}$

D:

$\frac{2}{3}$

E:

No option

32:

The marks of eight students in a test are: 10, 4, 5, 3, 14, 16 and 7. Find the range

A:

16

B:

14

C:

13

D:

11

E:

No option

33:

If log(3x - 1) = 5, find x

A:

2.00

B:

3.67

C:

8.67

D:

11.00

E:

No option

34:

A sphere of radius r cm has the same volume as a cylinder of radius 3 cm and height 4 cm. Find the value of r

A:

$\frac{2}{3}$

B:

2

C:

3

D:

6

E:

No option

35:

Express 1975 correct to 2 significant figures

A:

20

B:

1,900

C:

1,980

D:

2,000

E:

No option

36:

In the diagram, MOPO is a trapezium with QP // MO, MQ//NP, NQ//OP, |QP| = 9cm and the height of

$\Delta$QNP = 6cm, calculate the area of the trapezium.

A:

96cm2

B:

90cm2

C:

81cm2

D:

27cm2

E:

No option

37:

The perimeter of a sector of a circle of radius 21cm is 64cm. Find the angle of the sector .

(Take $\pi = \frac{22}{7}$)

A:

700

B:

600

C:

550

D:

420

E:

No option

38:

Determine $M \cap N$ from the venn diagram

A:

{f,g}

B:

{e}

C:

{c, f, g}

D:

{e, f, g}

E:

No option

39:

If 20 (mod 9) is equivalent to y (mod 6), find y

A:

1

B:

2

C:

3

D:

4

E:

No option

40:

Simplify $\frac{(p - r)^{2} - r^{2}}{2p^{2} - 4pr}$

A:

$\frac{1}{2}$

B:

$p - 2r$

C:

$\frac{1}{p - 2r}$

D:

$\frac{2p}{p - 2r}$

E:

No option

41:

In the diagram, O is the centre of the circle, <QPS = 1000, <PSQ = 600 and <QSR = 800. Calculate <SQR

A:

200

B:

400

C:

600

D:

800

E:

No option

42:

A bag contains 5 red and 4 blue identical balls. If two balls are selected at random from the bag, one after the other, with replacement, find the probability that the first is red and the second is blue

A:

$\frac{2}{9}$

B:

$\frac{5}{18}$

C:

$\frac{20}{81}$

D:

$\frac{5}{9}$

E:

No option

43:

The relation y = x2 + 2x + k passes through the point (2, 0). Find the value of k

A:

-8

B:

-4

C:

4

D:

8

E:

No option

44:

Find the next three terms of the sequence: 0, 1, 1, 1, 2, 3, 5, 8...

A:

13, 19, 23

B:

9, 11, 13

C:

11, 15, 19

D:

13, 21, 34

E:

No option

45:

Find the lower quartile of the distribution illustrated by the cummulative frequency curve

A:

17.5

B:

19.0

C:

27.5

D:

28.0

E:

No option

46:

The ratio of the exterior angle to the interior angle of a regular polygon is 1:11. How many sides has the polygon?

A:

30

B:

24

C:

18

D:

12

E:

No option

47:

Halima is n years old. Her brother's age is 5 years more than half of her age. How old is her brother?

A:

$\frac{n}{2}+\frac{5}{2}$

B:

$\frac{n}{2} - 5$

C:

$5 - \frac{n}{2}$

D:

$\frac{n}{2} + 5$

E:

No option

48:

In the diagram, line MN is a chord of a circle KMN centre O and radius 10 cm. If <MON = 1400, find correct to the nearest cm, the length of the chord MN.

A:

19cm

B:

18cm

C:

17cm

D:

12cm

E:

No option

49:

An object is 6m away from the base of a mast. If the angle of depression of the object from the top of the mast is 500, find, correct to 2 decimal places, the height of the mast.

A:

8.60m

B:

7.83m

C:

7.51m

D:

7.15m

E:

No option

50:

From the diagram, which of the following is true?

A:

m + n + p = 1800

B:

m + n = 1800

C:

m - p + n

D:

n = m + p

E:

No option