JAMB Mathematics Past Questions & Answers - Page 23

111.

The 10th term of an AP is 32. If the first term is 3/2, what is the 4th term?

A.

35/3

B.

64

C.

16

D.

35/2

Correct answer is A

Tn = a + (n-1)d

10th term = 32

32 = 3/2 + 9d 

9d = 32 - 3/2

9d = 61/2

d = 61/18

: T4 = 3/2 + 3(61/18)

T4 = 3/2 + 61/6 → 35/3

112.

A rectangular pyramid has an area 24cm\(^2\) and height 7.5cm. Find its volume?

A.

65.0cm\(^3\)

B.

70.5cm\(^3\)

C.

56.5cm\(^3\)

D.

60.0cm\(^3\)

Correct answer is D

Volume of a rectangular pyramid = \(\frac{length * width * height}{3}\) or \(\frac{area * height}{3}\)

= \(\frac{24 * 7.5}{3}\) → \(\frac{180}{3}\)

Volume of the rectangular pyramid = 60cm\(^3\)

114.

Find the length of a chord 3cm from the centre of a circle of radius 5cm

A.

8cm

B.

5.6cm

C.

7cm

D.

6.5cm

Correct answer is A

Using pythagoras formula:

Hyp\(^2\) = adj\(^2\) + opp\(^2\)

5\(^2\) = opp\(^2\) + 3\(^2\) 

5\(^2\) - 3\(^2\) = adj\(^2\)

4 = adj

length of the chord = 2 * 4 = 8cm

115.

Simplify \(\frac{1}{3-√2}\) in the form of p + q√2

A.

\(\frac{7}{3}\) - \(\frac{1}{7√2}\)

B.

\(\frac{7}{3}\) + \(\frac{1}{7√2}\)

C.

\(\frac{3}{7}\) - \(\frac{1}{7√2}\)

D.

\(\frac{3}{7}\) + \(\frac{√2}{7}\)

Correct answer is D

Rationalization with conjugate \({3+√2}\)

 \(\frac{1}{3-√2}\)

→ \(\frac{1 * [3+√2]}{[3-√2][3+√2]}\)

=  \(\frac{3+√2}{9 -3√2 + 3√2 + √4}\)

=  \(\frac{3+√2}{9 - 2}\) →  \(\frac{3+√2}{7}\)

= \(\frac{3}{7}\) +  \(\frac{√2}{7}\)