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.

2,536.

The locus of all points at a distance 8cm from a point N passes through points T and S. If S is equidistant from T and N, find the area of triangle STN.

A.

4\(\sqrt{3cm^2}\)

B.

16\(\sqrt{3cm^2}\)

C.

32cm2

D.

64cm2

Correct answer is B

No explanation has been provided for this answer.

2,537.

A cylindrical drum of diameter 56 cm contains 123.2 litres of oil when full. Find the height of the drum in centimetres

A.

12.5

B.

25.0

C.

45.0

D.

50.00

Correct answer is D

V = \(\pi r^2 h\)

= 123.2 x 1000

= \(\frac{22}{7}\) x 28 x 28 x h

= 123200 = 88 x 28h

= 2464h

∴ h = \(\frac{123200}{2464}\)

= 50cm

N.B: 1 litre = 1 dm3

= 1000cm3

2,538.

Let = \(\begin{pmatrix} 1 & 0 \\ 0 & 1 \end{pmatrix}\) p = \(\begin{pmatrix} 2 & 3 \\ 4 & 5 \end{pmatrix}\) Q = \(\begin{pmatrix} u & 4+u \\ -2v & v \end{pmatrix}\) be 2 x 2 matrices such that PQ = 1. Find (u, v)

A.

(-\(\frac{5}{2}\) - 1)

B.

(-\(\frac{5}{2}\) - \(\frac{3}{2}\))

C.

(-\(\frac{5}{6}\) - 1)

D.

(\(\frac{5}{2}\) - \(\frac{3}{2}\))

Correct answer is A

PQ = \(\begin{pmatrix} 2 & 3 \\ 4 & 5 \end{pmatrix}\)\(\begin{pmatrix} u & 4+u \\ -2v & v \end{pmatrix}\)

= \(\begin{pmatrix} (2u-6v & 2(4+u) +3v)\\ 4u-10v & 4(4+u)+5v \end{pmatrix}\)

= \(\begin{pmatrix} 1 & 0 \\ 0 & 1 \end{pmatrix}\)

2u - 6v = 1.....(i)

4u - 10v = 0.......(ii)

2(4 + u) + 3v = 0......(iii)

4(4 + u) + 5v = 1......(iv)

2u - 6v = 1 .....(i) x 2

4u - 10v = 0......(ii) x 1

\(\frac{\text{4u - 12v = 0}}{\text{-4u - 10v = 0}}\)

-2v = 2 = v = -1

2u - 6(-1) = 1 = 2u = 5

u = -\(\frac{5}{2}\)

∴ (U, V) = (-\(\frac{5}{2}\) - 1)

2,539.

The determinant of matrix \(\begin{pmatrix} x & 1 & 0 \\ 1-x & 2 & 3 \\ 1 & 1+x & 4\end{pmatrix}\) in terms of x is

A.

-3x2 - 17

B.

-3x2 + 9x - 1

C.

3x2 + 17

D.

3x2 - 9x + 5

Correct answer is B

\(\begin{vmatrix} x & 1 & 0 \\ 1-x & 2 & 3 \\ 1 & 1+x & 4\end{vmatrix}\) = x\(\begin{vmatrix}2 & 3 \\ 1+x & 4\end{vmatrix}\) - \(\begin{vmatrix}1-x & 3 \\ 1 & 4\end{vmatrix}\) = 0

= x[8 - 3(1 + x)] - [4(1 - x)-3] - 0 = x[5 - 3x] - [1 - 4x]

= 5x - 3x2 -1 + 4x

= -3x2 + 9X - 1

2,540.

The binary operation \(\oplus\) is defined by x \(\ast\) y = xy - y - x for all real values x and y. If x \(\ast\) 3 = 2\(\ast\), find x

A.

-1

B.

4

C.

1

D.

5

Correct answer is C

x \(\ast\) y = xy - y - x, x \(\ast\) 3 = 3x - 3 - x = 2x - 3

2 \(\ast\) x = 2x - x - 2 = x - 2

∴ 2x - 3 = x - 2

x = -2 + 3

= 1