Year : 
2008
Title : 
Mathematics (Core)
Exam : 
WASSCE/WAEC MAY/JUNE

Paper 1 | Objectives

11 - 20 of 45 Questions

# Question Ans
11.

If 4y is 9 greater than the sum of y and 3x, by how much is greater than x?

A. 3

B. 6

C. 9

D. 12

Detailed Solution

4y - 9 > y + 3x; 4y - y > 3x + 9

3y > 3(x + 3); y = > \(\frac{3(x + 3)}{3}\)

y > x + 3; y - 3 > x

y is greater than x
12.

If p = \(\frac{3}{5} \sqrt{\frac{q}{r}}\), express q in terms of p and r

A. \(\frac{9}{25} pr^2\)

B. \(\frac{9}{25} p^2r\)

C. \(\frac{25}{9} p^2r\)

D. \(\frac{25}{9} pr^2\)

Detailed Solution

p = \(\frac{3}{5} \sqrt{\frac{q}{r}}; \frac{5p}{3} = \sqrt{\frac{q}{r}}\)

= (\(\frac{5}{3}p\))2

= \(\frac{q}{r}\)

= \(\frac{25p^2}{9} = \frac{q}{r}\)

q = \(\frac{25}{9} p^2 r\)
13.

Simplify: \(\frac{2x^2 - 5x - 12}{4x^2 - 9}\)

A. \(\frac{x + 4}{2x + 3}\)

B. \(\frac{x + 4}{2x - 3}\)

C. \(\frac{x - 4}{2x + 3}\)

D. \(\frac{x - 4}{2x - 3}\)

Detailed Solution

\(\frac{2x^2 - 5x - 12}{4x^2 - 9}\) = \(\frac{3x^2 - 8x + 3x - 12}{(2x)^2 - 3^2}\)

= \(\frac{32(x - 4) + 3(x - 4)}{(2x - 3)(2x + 3)} - \frac{(x - 4) + (2x + 3)}{(2x - 3) (2x + 3)}\)

= \(\frac{x - 4}{2x - 3}\)
14.

PQR is a sector of a circle centre O, radius 4cm. If PQR = 30o, find, correct to 3 significant figures, the area of sector PQR. [Take \(\pi = \frac{22}{7}\)]

A. 4.19cm2

B. 8.38cm2

C. 10.5cm2

D. 20.9cm2

Detailed Solution

Given q2 = 25 - r2.....(1)

from pythagora's theorem

P2 = q2 + r2.......(2)

put (1) into (2)

p2 = 25 - p2 + x2

p2 = 25

p = \(\sqrt{25}\)

= 5
15.

If the volume of a cube is 343cm3, find the length of its side

A. 3cm

B. 6cm

C. 7cm

D. 96cm

Detailed Solution

Volume of a cube = (side)3

= (side)3

(side)3 = 343

side = 3\(\sqrt{343}\)

side = 7cm
16.

The angles of a quadrilateral are (x + 10)o, 2yo, 90o and (100 - y)o, Find y in terms of x

A. y = 160 + x

B. y = 100 + x

C. y = 160 - x

D. y = x - 100

Detailed Solution

Sum of the angles in a quadrilateral = 360o

(x + 10o) + 2y + 90o + 100 - y = 360o

x + y + 200 = 360o

y = 360 - 200 - x

y = 160 - x
17.

If xo is obtuse, which of the following is true?

A. 90

B. 180 < x < 270

C. x < 90

D. 90 < x < 180

Detailed Solution

obtuse angle \(\to\) 90o < x < 180o
18.

If tan x = 1, evaluate sin x + cos x, leaving your answer in the surd form

A. 2\(\sqrt{2}\)

B. \(\frac{1}{2} \sqrt{2}\)

C. \(\sqrt{2}\)

D. 2

Detailed Solution

tan x = 1; x = tan-1(10 = 45o

sin x + cos x

= sin 45o + cos 45o

= \(\frac{\sqrt{2}}{2} + \frac{\sqrt{2}}{2}\)

= \(\frac{\sqrt{2} + \sqrt{2}}{2}\)

= \(\frac{2\sqrt{2}}{2}\)

= \(\sqrt{2}\)
19.

If cos (x + 25)o = sin 45o, find the value of x

A. 20

B. 30

C. 45

D. 60

Detailed Solution

cos(x + 25o) = sin 45o

using cos \(\theta\) = sin(90 - \(\theta\))

cos(x + 25o) = cos(90 - 45)

cos(x + 25o) = cos 45

x + 25 = 45

x = 45 - 25

x = 20o
20.

If 2n = 128, find the value of (2n - 1)(5n - 1)

A. 5(106)

B. 2(106)

C. 5(105)

D. 2(105)

Detailed Solution

2n = 128

2n = 27

n = 7

(2n - 1)(5n - 2) = (2n - 2.2)(5n - 2) put n = 7

(2n - 1)(5n - 2) = 2(2n - 2 x 5n - 2)

= 2(2 x 5)n - 2

= 2(10n - 2) put n = 7

(2n-1)(5n-2) = 2(105)
11.

If 4y is 9 greater than the sum of y and 3x, by how much is greater than x?

A. 3

B. 6

C. 9

D. 12

Detailed Solution

4y - 9 > y + 3x; 4y - y > 3x + 9

3y > 3(x + 3); y = > \(\frac{3(x + 3)}{3}\)

y > x + 3; y - 3 > x

y is greater than x
12.

If p = \(\frac{3}{5} \sqrt{\frac{q}{r}}\), express q in terms of p and r

A. \(\frac{9}{25} pr^2\)

B. \(\frac{9}{25} p^2r\)

C. \(\frac{25}{9} p^2r\)

D. \(\frac{25}{9} pr^2\)

Detailed Solution

p = \(\frac{3}{5} \sqrt{\frac{q}{r}}; \frac{5p}{3} = \sqrt{\frac{q}{r}}\)

= (\(\frac{5}{3}p\))2

= \(\frac{q}{r}\)

= \(\frac{25p^2}{9} = \frac{q}{r}\)

q = \(\frac{25}{9} p^2 r\)
13.

Simplify: \(\frac{2x^2 - 5x - 12}{4x^2 - 9}\)

A. \(\frac{x + 4}{2x + 3}\)

B. \(\frac{x + 4}{2x - 3}\)

C. \(\frac{x - 4}{2x + 3}\)

D. \(\frac{x - 4}{2x - 3}\)

Detailed Solution

\(\frac{2x^2 - 5x - 12}{4x^2 - 9}\) = \(\frac{3x^2 - 8x + 3x - 12}{(2x)^2 - 3^2}\)

= \(\frac{32(x - 4) + 3(x - 4)}{(2x - 3)(2x + 3)} - \frac{(x - 4) + (2x + 3)}{(2x - 3) (2x + 3)}\)

= \(\frac{x - 4}{2x - 3}\)
14.

PQR is a sector of a circle centre O, radius 4cm. If PQR = 30o, find, correct to 3 significant figures, the area of sector PQR. [Take \(\pi = \frac{22}{7}\)]

A. 4.19cm2

B. 8.38cm2

C. 10.5cm2

D. 20.9cm2

Detailed Solution

Given q2 = 25 - r2.....(1)

from pythagora's theorem

P2 = q2 + r2.......(2)

put (1) into (2)

p2 = 25 - p2 + x2

p2 = 25

p = \(\sqrt{25}\)

= 5
15.

If the volume of a cube is 343cm3, find the length of its side

A. 3cm

B. 6cm

C. 7cm

D. 96cm

Detailed Solution

Volume of a cube = (side)3

= (side)3

(side)3 = 343

side = 3\(\sqrt{343}\)

side = 7cm
16.

The angles of a quadrilateral are (x + 10)o, 2yo, 90o and (100 - y)o, Find y in terms of x

A. y = 160 + x

B. y = 100 + x

C. y = 160 - x

D. y = x - 100

Detailed Solution

Sum of the angles in a quadrilateral = 360o

(x + 10o) + 2y + 90o + 100 - y = 360o

x + y + 200 = 360o

y = 360 - 200 - x

y = 160 - x
17.

If xo is obtuse, which of the following is true?

A. 90

B. 180 < x < 270

C. x < 90

D. 90 < x < 180

Detailed Solution

obtuse angle \(\to\) 90o < x < 180o
18.

If tan x = 1, evaluate sin x + cos x, leaving your answer in the surd form

A. 2\(\sqrt{2}\)

B. \(\frac{1}{2} \sqrt{2}\)

C. \(\sqrt{2}\)

D. 2

Detailed Solution

tan x = 1; x = tan-1(10 = 45o

sin x + cos x

= sin 45o + cos 45o

= \(\frac{\sqrt{2}}{2} + \frac{\sqrt{2}}{2}\)

= \(\frac{\sqrt{2} + \sqrt{2}}{2}\)

= \(\frac{2\sqrt{2}}{2}\)

= \(\sqrt{2}\)
19.

If cos (x + 25)o = sin 45o, find the value of x

A. 20

B. 30

C. 45

D. 60

Detailed Solution

cos(x + 25o) = sin 45o

using cos \(\theta\) = sin(90 - \(\theta\))

cos(x + 25o) = cos(90 - 45)

cos(x + 25o) = cos 45

x + 25 = 45

x = 45 - 25

x = 20o
20.

If 2n = 128, find the value of (2n - 1)(5n - 1)

A. 5(106)

B. 2(106)

C. 5(105)

D. 2(105)

Detailed Solution

2n = 128

2n = 27

n = 7

(2n - 1)(5n - 2) = (2n - 2.2)(5n - 2) put n = 7

(2n - 1)(5n - 2) = 2(2n - 2 x 5n - 2)

= 2(2 x 5)n - 2

= 2(10n - 2) put n = 7

(2n-1)(5n-2) = 2(105)