Mathematics questions and answers

Mathematics Questions and Answers

How good are you with figures and formulas? Find out with these Mathematics past questions and answers. This Test is useful for both job aptitude test candidates and students preparing for JAMB, WAEC, NECO or Post UTME.

2,021.

The table below is drawn for a graph y = x3 - 3x + 1
\(\begin{array}{c|c} x & -3 & -2 & -1 & 0 & 1 & 2 & 3 \\\hline y = x^3 - 3x + 1 & 1 & -1 & 3 & 1 & -1 & 3 & 1\end{array}\)
From x = -2 to x = 1, the graph crosses the x-axis in the range(s)

A.

-1 < x < 0 and 0 < x < 1

B.

-2 < x < -1 and 0 < x < 1

C.

-2 < x < -1 and -1 < x < 0

D.

0 < x < 1

Correct answer is B

If the graph of y = x3 - 3x + 1 is plotted,the graph crosses the x-axis in the ranges -2 < x < -1 and 0 < x < 1

2,022.

A straight line y = mx meets the curve y = x2 - 12x + 40 in two distinct points. If one of them is (5, 5) find the other

A.

(5, 6)

B.

(8, 8)

C.

(8, 5)

D.

(7,7)

E.

(7, 5)

Correct answer is E

When y = 5, y = x2 - 12x + 40, becomes

x2 - 12x + 40 = 5

x2 - 12x + 40 - 5 = 0

x2 + 12x + 35 = 0

x2 - 7x - 5x + 35 = 0

x(x - 7) - 5(x - 7) = 0

= (x - 5)(x - 7)

x = 5 or 7

2,023.

Factorize 6x2 - 14x - 12

A.

2(x + 3)(3x - 2)

B.

6(x - 2)(x + 1)

C.

2(x - 3)(3x + 2)

D.

6(x + 2)(x - 1)

E.

(3x - 4)(2x + 3)

Correct answer is C

6x2 - 14x - 12 = 6x2 - 18x + 4x - 12

(3x + 2)(2x - 6)

= 3x(2x - 6) + 2(2x - 6)

= (3x + 2) 2(x - 3)

2,024.

p varies directly as the square of q and inversely as r. If p = 36, when q = 36, when q = 3 and r = 4, find p when q = 5 and r = 2

A.

72

B.

100

C.

90

D.

200

E.

125

Correct answer is D

P \(\alpha\) \(\frac{q^2}{r}\)

P = \(\frac{kq^2}{r}\)

k = \(\frac{pr}{q^2}\)

= \(\frac{36 x 4}{(3)^2}\)

p = \(\frac{16q^2}{r}\)

= \(\frac{16 \times 25}{2}\)

= 200

2,025.

Simplify \(\frac{3^n - 3^{n - 1}}{3^3 \times 3^n - 27 \times 3^{n - 1}}\)

A.

1

B.

6

C.

\(\frac{1}{27}\)

D.

\(\frac{4}{3}\)

Correct answer is C

\(\frac{3^n - 3^{n - 1}}{3^3 \times 3^n - 27 \times 3^{n - 1}}\) = \(\frac{3^n - 3^{n - 1}}{3^3(3^n - 3^{n - 1})}\)

= \(\frac{3^n - 3^{n - 1}}{27(3^n - 3^{n - 1})}\)

= \(\frac{1}{27}\)