WAEC Further Mathematics Past Questions & Answers - Page 24

116.

Using binomial expansion of ( 1 + x)\(^6\) = 1 + 6x + 15x\(^2\) + 20x\(^3\) + 6x\(^5\) + x)\(^6\), find, correct to three decimal places, the value of (1.998))\(^6\)

A.

63.616

B.

63.167

C.

62.628

D.

62.629

Correct answer is B

Put 1 + (0.998) = 1 + x;

x = (0.998)

Hence; 1 + 6(0.998) + 15(0.998)(0.998)\(^2\) + 20(0.998)\(^3\) + 15(0.998)\(^4\) + 6(0.998)\(^5\) + (0.998)\(^6\)

= 1 + 5.988 + 14.790 + 19.880 + 14.880 + 5.940 + 0.990

≈ 63.167

117.

g(x) = 2x + 3 and f(x) = 3x\(^2\) - 2x + 4

find f {g (-3)}.

A.

37

B.

1

C.

-3

D.

-179

Correct answer is A

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

F(-3) = 3 (-3)\(^2\) - 2(-3) + 4

= 27 + 6 + 4 = 37

118.

Solve (\(\frac{1}{9}\))\(^{x + 2}\) = 243\(^{x - 2}\) 

A.

\(\frac{7}{5}\)

B.

\(\frac{6}{7}\)

C.

\(\frac{-7}{6}\)

D.

\(\frac{-6}{7}\)

Correct answer is A

(\(\frac{1}{9}\))\(^{x + 2}\) = 243\(^{x - 2}\)

3\(^{-2(x + 2)}\) =  3\(^{5(x - 2)}\);

-2(x+2) = 5(x - 2)

-2x -4 = 5x - 10

-7x = -6

x =  \(\frac{6}{7}\)

119.

Simplify \(\frac{1}{3}\) log8 + \(\frac{1}{3}\) log 64 - 2 log6

A.

log \(\frac{2}{7}\)

B.

log 2

C.

log \(\frac{2}{9}\)

D.

log 9

Correct answer is C

\(\frac{1}{3}\) log8 + \(\frac{1}{3}\) log 64 - 2 log6

= log 2 + log 4 - log 36

= log \(\frac{8}{36}\)

= log \(\frac{2}{9}\)

120.

Given that M = \(\begin{pmatrix} 3 & 2 \\ -1 & 4 \end{pmatrix}\) and N = \(\begin{pmatrix} 5 & 6 \\ -2 & -3 \end{pmatrix}\), calculate (3M - 2N)

A.

\(\begin{pmatrix} 1 & 6 \\ 1 & 18 \end{pmatrix}\)

B.

\(\begin{pmatrix} -1 & -6 \\ 1 & 18 \end{pmatrix}\)

C.

\(\begin{pmatrix} 1 & 6 \\ -1 & -18 \end{pmatrix}\)

D.

\(\begin{pmatrix} -1 & -6 \\ -1 & -18 \end{pmatrix}\)

Correct answer is B

3M = 3 \(\begin{pmatrix} 3 & 2 \\ -1 & 4 \end{pmatrix}\)

 = \(\begin{pmatrix} 9 & 6 \\ -3 & 12 \end{pmatrix}\)

2N = 2 \(\begin{pmatrix} 5 & 6 \\ -2 & -3 \end{pmatrix}\) 

= \(\begin{pmatrix} 10 & 12 \\ -4 & -6 \end{pmatrix}\)

(3M - 2N) = \(\begin{pmatrix} 9 & 6 \\ -3 & 12 \end{pmatrix}\) - \(\begin{pmatrix} 10 & 12 \\ -4 & -6 \end{pmatrix}\)