JAMB Mathematics Past Questions & Answers - Page 382

1,906.

If the 7th term of an AP is twice the third term and the sum of the first four terms is 42, find the common difference.

A.

6

B.

3

C.

2

D.

1

Correct answer is B

U7 = a + (7 - 1)d
= a + 6d
U3 = a + (3 - 1)d
= a + 2d
But U7 = 2(U3)
∴a + 6d = 2(a + 2d)
a + 6d = 2a + 4d
2a - a + 4d - 6d = 0
a - 2d = 0 → eqn1
Sn = n/2 (2a + (n - 1)d)
42 = 4/2 (2a + (4 - 1)d)
42 = 2(2a + 3d)
21 = 2a + 3d → eqn2
eqn1 * eqn2 0 = 2a - 4d
21 = 7d
∴d = 21/7
d = 3

1,907.

Find the range of values of x for which 7x - 3 > 25 + 3x

A.

x >7

B.

x<7

C.

x>-7

D.

x<-7

Correct answer is A

7x - 3 > 25 + 3x
7x - 3x > 25 + 3
4x > 28
x > 28/4
x > 7

1,908.

The weight W kg of a metal bar varies jointly as its length L meters and the square of its diameter d meters. If w = 140 when d = 42/3 and L = 54, find d in terms of W and L.

A.

\(\sqrt{\frac{42W}{5L}}\)

B.

\(\sqrt{\frac{6L}{42W}}\)

C.

\(\frac{42W}{5L}\)

D.

\(\frac{5L}{42W}\)

Correct answer is A

\(W\infty LD^2\\W=KLd^2\\K=\frac{W}{Ld^2}\\=\frac{140}{54}\times\left(4\frac{2}{3}\right)^2 \\=\frac{140}{54}\times\left(\frac{14}{3}\right)^2\\=\frac{140\times 9}{54\times 14\times 14}\\=\frac{5}{42}\\∴W=\frac{5}{42Ld^2}\\42W=5Ld^2\\\frac{42W}{5L}=d^2\\d=\sqrt{\frac{42W}{5L}}\)

1,909.

The time taken to do a piece of work is inversely proportional to the number of men employed. If it takes 30 men to do a piece of work in 6 days, how many men are required to do the work in 4 days?

A.

20

B.

35

C.

45

D.

60

Correct answer is C

t = time taken and N = number of men
t ∝ 1/N
t = K/N
K = Nt
K = 30 * 6
K = 180
∴t = 180/N
4 = 180/N
4N = 180
N = 180/4
45 men

1,910.

A polynomial in x whose zeros are -2, -1 and 3 is

A.

x3 - 7x + 6

B.

x3 + 7x - 6

C.

x3 + 7x + 6

D.

x3 - 7x - 6

Correct answer is D

x = -2, x = -1 and x = 3
∴x+2 = 0, x+1 = 0 and x-3 = 0
Product of the factors
(x+2)(x+1)(x-3) = 0
(x2 + 3x + 2)(x-3)
x(x2 + 3x + 2) -3(x2 + 3x + 2) = 0
x3 + 3x2 + 2x - 3x2 - 9x - 6 = 0
x3 - 7x - 6 = 0