JAMB Mathematics Past Questions & Answers - Page 309

1,541.

The 3rd term of an arithmetic progression is -9 and the 7th term is -29. Find the 10th term of the progression

A.

-44

B.

-165

C.

165

D.

44

Correct answer is A

3rd term : a + 2d = -9 .......(1)
7th term : a + 6d = -29 ......(2)
(2) - (1): 4d = -20
:. d = -20/4 = -5
From (1) : a + 2(-5) = -9
a - 10 = -9
:. a = -9 + 10 = 1
:. 10th term of A.P is a + 9d = 1 + 9 (-5)
= 1 - 45 = -44

1,542.

If p : q = \(\frac{2}{3}\) : \(\frac{5}{6}\) and q : r = \(\frac{3}{4}\) : \(\frac{1}{2}\), find p : q : r

A.

12 : 15 : 10

B.

12 : 15 : 16

C.

10 : 15 : 24

D.

9 : 10 : 15

Correct answer is A

If p : q = \(\frac{2}{3}\) : \(\frac{5}{6}\), then the sum S1 of ratio = \(\frac{2}{3}\) + \(\frac{5}{6}\) = \(\frac{9}{6}\)

If q : r = \(\frac{3}{4}\) : \(\frac{1}{2}\), then the sum S2 of ratio = \(\frac{3}{4}\) + \(\frac{1}{2}\) = \(\frac{5}{4}\)

Let p + q = T1, then

q = (\(\frac{5}{6} \div \frac{9}{6}\))T1 = (\(\frac{5}{6} \times \frac{6}{9}\))T1 = \(\frac{5}{9}\)T1

Again, let q + r = T2, then

q = (\(\frac{3}{4} \div \frac{5}{4}\))T2 = (\(\frac{3}{4} \times \frac{4}{5}\))T2 = \(\frac{3}{5}\)T2

Using q = q

\(\frac{5}{9}\)T1 = \(\frac{3}{5}\)T2

5 x 5T1 = 9 x 3T2

\(\frac{T_1}{T_2}\) = \(\frac{9 \times 3}{5 x 5}\) = \(\frac{27}{25}\)

Giving that, T1 = 27 and T2 = 25

P = (\(\frac{2}{3} \div S_1\))T1 = (\(\frac{2}{3} \div \frac{9}{6}\))T1

= (\(\frac{2}{3} \times \frac{6}{9}\))27 = 12

q = (\(\frac{5}{6} \div S_1\))T1 = (\(\frac{5}{6} \div \frac{9}{6}\))T1

= (\(\frac{5}{6} \times \frac{6}{9}\))27 = 15

and r = (\(\frac{1}{2} \div S_2\))T2 = (\(\frac{1}{2} \div \frac{5}{4}\))T2

= (\(\frac{1}{2} \times \frac{4}{5}\))25 = 10

Hence p : q : r = 12: 15 : 10

1,543.

At what rate will the interest on N400 increases to N24 in 3 years reckoning in simple interest?

A.

3%

B.

2%

C.

5%

D.

4%

Correct answer is B

Using simple interest = \(\frac{P \times T \times R}{100}\),

where: P denoted principal = N400
T denotes time = 3 years
R denotes interest rate = ?

24 = \(\frac{400 \times 3 \times R}{100}\)

24 x 100 = 400 x 3 x R

R = \(\frac{24 \times 100}{400 \times3}\)

= 2%

1,544.

A student measures a piece of rope and found that it was 1.26m long. If the actual length of the rope was 1.25m, what was the percentage error in the measurement?

A.

0.25%

B.

0.01%

C.

0.80%

D.

0.40%

Correct answer is C

Actual length of rope = 1.25m

Measured length of rope = 1.26m

error = (1.26 - 1.25)m - 0.01m

Percentage error = \(\frac{error}{\text{actual length}}\) x 100%

= \(\frac{0.01}{1.25}\) x 100%

= 0.8%

1,545.

Simplify (\(\frac{3}{4}\) of \(\frac{4}{9}\) \(\div\) 9\(\frac{1}{2}\)) \(\div\) 1\(\frac{5}{19}\)

A.

\(\frac{1}{5}\)

B.

\(\frac{1}{4}\)

C.

\(\frac{1}{36}\)

D.

\(\frac{1}{25}\)

Correct answer is C

(\(\frac{3}{4}\) of \(\frac{4}{9}\) \(\div\) 9\(\frac{1}{2}\)) \(\div\) 1\(\frac{5}{19}\)

Applying the rule of BODMAS, we have:

(\(\frac{3}{4}\) x \(\frac{4}{9}\) \(\div\)\(\frac{19}{2}\)) \(\div\)\(\frac{24}{19}\)


(\(\frac{1}{3}\) x \(\frac{2}{19}\)) \(\div\)\(\frac{24}{19}\)

\(\frac{1}{3}\) x \(\frac{2}{19}\) x \(\frac{19}{24}\)

= \(\frac{1}{36}\)