JAMB Mathematics Past Questions & Answers - Page 234

1,166.

If the sum of the 8th and 9th terms of an arithmetic progression is 72 and the 4th term is -6, find the common difference

A.

4

B.

8

C.

6\(\frac{2}{3}\)

D.

9\(\frac{1}{3}\)

Correct answer is D

Let the first term and common difference = a & d respectively.

\(T_{n} = \text{nth term} = a + (n - 1) d\) (A.P)

Given: \(T_{4} = -6 \implies a + 3d = -6 ... (i)\)

\(T_{8} + T_{9} = 72\)

\(\implies a + 7d + a + 8d = 72 \implies 2a + 15d = 72 ... (ii)\)

From (i), \(a = -6 - 3d\)

\(\therefore\) (ii) becomes \(2(-6 - 3d) + 15d = 72\)

\(-12 - 6d + 15d = 72 \implies 9d = 72 + 12 = 84\)

\(d = \frac{84}{9} = 9\frac{1}{3}\)

1,167.

The solutions of x2 - 2x - 1 = 0 are the points of intersection of two graphs. if one of the graphs is y = 2 + x - x2, find the second graph

A.

y = 1 - x

B.

y = 1 + x

C.

y = x - 1

D.

y = 3x + 3

Correct answer is A

The second graph is 

\((x^{2} - 2x - 1) + (2 + x - x^{2})\)

= \(1 - x\)

1,168.

For what values of x is the curve y = \(\frac{x^2 + 3}{x + 4}\) decreasing?

A.

-3 < x \(\leq\) 0

B.

-3 \(\geq\) x < 0

C.

0 < x < 3

D.

0 \(\leq\) x \(\leq\) 3

Correct answer is D

No explanation has been provided for this answer.

1,169.

What is the solution of the equation x2 - x - 1 + 0?

A.

x = 1.6 and x = -0.6

B.

x = -1.6 and x = 0.6

C.

x = 1.6 and x = 0.6

D.

x = -1.6 and x = -0.6

Correct answer is A

\(x^{2} - x - 1 = 0\)

Using the quadratic formula, 

\(x = \frac{-b \pm \sqrt{b^{2} - 4ac}}{2a}\)

a = 1, b = -1, c = -1.

\(x = \frac{-(-1) \pm \sqrt{(-1)^{2} - 4(1)(-1)}}{2(1)}\)

\(x = \frac{1 \pm \sqrt{1 + 4}}{2} = \frac{1 \pm \sqrt{5}}{2}\)

\(x = \frac{1 + 2.24}{2} ; x = \frac{1 - 2.24}{2}\)

\(x = \frac{3.24}{2}; x = \frac{-1.24}{2}\)

\(x = 1.62 ; x = -0.61 \)

\(x \approxeq 1.6; -0.6\)

1,170.

Simplify \(\frac{x - y}{x^{\frac{1}{3}} - x^{\frac{1}{3}}}\)

A.

x2 + xy + y2

B.

x\(\frac{2}{3}\) + x \(\frac{1}{3}\) + y\(\frac{2}{3}\)

C.

x\(\frac{2}{3}\) - x\(\frac{1}{3}\)y\(\frac{2}{3}\)

D.

y\(\frac{2}{3}\)

Correct answer is B

No explanation has been provided for this answer.