WAEC Mathematics Past Questions & Answers - Page 27

131.

Simplify 2√7- 14/√7+7/√21

A.

\(\frac{√21}{21}\)

B.

7\(\frac{√21}{21}\)

C.

\(\frac{√21}{3}\)

D.

3√21

Correct answer is C

2√7-  14/√7 +7/√21

L.C.M is √21

\(\frac{√21 * 2√7  - √3 *14  + 7}{√21}\)

=\(\frac{2 * 7√3 - 14√3 + 7}{√21}\)

= \(\frac{14√3 - 14√3 + 7}{√21}\)

=\(\frac{7}{√21}\)

or 

\(\frac{7 \times √21}{√21 \times √21}\) 

= \(\frac{7 \times √21}{21}\) or  \(\frac{√21}{3}\) 

132.

The circumference of a circular track is 9km. A cyclist rides round it a number of times and stops after covering a distance of 302km. How far is the cyclist from the starting point?

A.

5km

B.

6km

C.

7km

D.

3km

Correct answer is A

Circumference of the circular track = 9km

Distance covered = 302km

Number of complete circles or revolutions from the starting point = 302/9 =33 circles and additional 5km.

So, the distance of the cyclist from the starting point would be 5km

133.

If 16 * 2\(^{(x + 1)}\) = 4\(^x\) * 8\(^{(1 - x)}\), find the value of x.

A.

-4

B.

4

C.

1

D.

-1

Correct answer is D

16 * 2\(^{(x + 1)}\) = 4\(^x\) * 8\(^{(1 - x)}\) 

= 2\(^4\) * 2\(^{(x + 1)}\) = 2\(^{2x}\) * 2\(^{3(1 - x)}\)

--> 4 + x + 1 = 2x + 3 - 3x

collect like terms

--> x - 2x + 3x = 3 - 1 - 4

--> 2x = -2

--> x = -1

134.

if p = {-3<x<1} and Q = {-1<x<3}, where x is a real number, find P n Q.

A.

0

B.

-3, -2, -1, 0 and 1

C.

-2, -1 and 0

D.

-1, 0 and 1

Correct answer is A

p = {-3<x<1} = {-2,-1 and 0}

Q = {-1<x<3} = {0,1 and 2}

P n Q = {0} or  {-1<x<1}

135.

Find the least value of x which satisfies the equation 4x = 7(mod 9)

A.

7

B.

6

C.

5

D.

4

Correct answer is D

4x = 7 (mod 9)

4x = 7 + 9 (mod 9)

\(\frac{4x}{4} = \frac{16}{4}\) (mod 9)

x = 4