WAEC Past Questions and Answers - Page 1036

5,176.

If α and β are the roots of 3x\(^2\) - 7x + 6 = 0, find \(\frac{1}{α}\) + \(\frac{1}{β}\)

A.

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

B.

\(\frac{7}{3}\)

C.

\(\frac{14}{5}\)

D.

\(\frac{14}{3}\)

Correct answer is A

3x\(^2\) - 7x + 6 = 0

α + β = \(\frac{7}{3}\);

αβ = 2;

\(\frac{1}{α}\) + \(\frac{1}{β}\) = \(\frac{α +β}{αβ}\) 

\(\frac{7}{3}\) ÷ 2 

= \(\frac{7}{6}\)

5,177.

In how many ways can 8 persons be seated on a bench if only three seats are available?

A.

100

B.

125

C.

336

D.

427

Correct answer is C

\(^3{P}_3\) = \(\frac{8!}{8-3}!\)

= \(\frac{(8 * 7 * 6 * 5)!}{5!}\) 

= 336

5,178.

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

5,179.

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

5,180.

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 =  \(\frac{6}{7}\)