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.

2,341.

p = \(\begin{vmatrix} x & 3 & 0 \\ 2 & y & 3\\ 4 & 2 & 4 \end{vmatrix}\)

Q = \(\begin{vmatrix} x & 2 & z \\ 3 & y & 2\\ 0 & 3 & z \end{vmatrix}\) Where pT is the transpose P calculate /pT/ when x = 0, y = 1 and z = 2

A.

48

B.

24

C.

-24

D.

-48

Correct answer is B

p = \(\begin{vmatrix} 0 & 3 & 0 \\ 2 & 1 & 3\\ 4 & 2 & 2 \end{vmatrix}\)

PT = \(\begin{vmatrix}0 & 2 & 4 \\ 2 & 1 & 3\\ 0 & 3 & 2 \end{vmatrix}\)

/pT/ = \(\begin{vmatrix}0 & 2 & 4 \\ 3 & 1 & 3\\ 0 & 3 & 2 \end{vmatrix}\)

= 0[2 - 6] - 2[6 - 0] + 4[9 - 0]

= 0 - 12 + 36 = 24

2,342.

If the binary operation \(\ast\) is defined by m \(\ast\) n = mn + m + n for any real number m and n, find the identity of the elements under this operation

A.

e = 1

B.

e = -1

C.

e = -2

D.

e = 0

Correct answer is D

Identity(e) : a \(\ast\) e = a

m \(\ast\) e = m...(i)

m \(\ast\) e = me + m + e

Because m \(\ast\) e = m 

: m = me + m + e

m - m = e(m + 1)

e = \(\frac{0}{m + 1}\)

e = 0

2,343.

If the binary operation \(\ast\) is defined by m \(\ast\) n = mn + m + n for any real number m and n, find the identity of the elements under this operation

A.

e = 1

B.

e = -1

C.

e = -2

D.

e = 0

Correct answer is B

Identity(e) : a \(\ast\) e = a

m \(\ast\) e = m...(i)

m \(\ast\) e = me + m + e

Because m \(\ast\) e = m 

: m = me + m + e

m - m = e(m + 1)

e = \(\frac{0}{m + 1}\)

e = 0

2,344.

For an arithmetical sequence, the first term is 2 and the common difference is 3. Find the sum of the first 11 terms

A.

157

B.

187

C.

197

D.

200

Correct answer is B

a = 2, d = 3 and n = 11

To find Sn/sub> = \(\frac{n}{2}\) [2a + (n - 1) \(\delta\)]

= \(\frac{11}{2}\) [2(2) + (11 - 1) 3]

= \(\frac{11}{2}\)n [4 + 10(3)]

= \(\frac{11}{2}\)(34)

= 11 x 17

= 187

2,345.

What is the n-th term of the sequence 2, 6, 12, 20...?

A.

4n - 2

B.

2(3n - 1)

C.

n2 + n

D.

n2 + 3n + 2

Correct answer is C

Given that 2, 6, 12, 20...? the nth term = n\(^2\) + n

check: n = 1, u1 = 2

n = 2, u2 = 4 + 2 = 6

n = 3, u3 = 9 + 3 = 12

∴ n = 4, u4 = 16 + 4 = 20