JAMB Mathematics Past Questions & Answers

471.

Calculate the value of x and y if (27^x ÷ 81^x+2y = 9 ,x + 4y = 0

x = 1, y = 1/2

x = 2, y = – 1/2

x − 0, y = 1

x = 2, y = –1

Correct answer is B

$27^x ÷ 81^{(x + 2y)} = 9 \\ (27)x = 9 × 81^{(x+2y)} \\ (3^3 )^x =32 \times 3^{4(x + 2y)} \\ =3^{(2 + 4x + 8y)}\\ 3^{3x} = 3^{ (2 + 4x + 8y)}\\ 3x = 2 + 4x + 8y\\ 3x − 4x − 8y = 2 … … … (1)\\ x + 4y = 0 … … … (2)\\ − 4y = 2\\ y = (− 2) ÷ 4 = − ½\\ y = − ½\\$

Substitute the value of y into equation (2)

i.e x + 4y = 0

x + 4( − 1/2) = 0

x − 2 = 0

x = 2

∴ x = 2,y = − ½)

Method II

$27^x ÷ 31^{(x + 2y) }= 9\\ 3^{3x} × 3^{( − 4x − 8y)} = 32\\ 3^{(3x − 8y)} = 32\\ − x − 8y=2 ……… (1)\\ x + 4y = 0 ……… (2)\\ − 4 = 2\\ y= 2/4 = ½\\ y = ½$

Substitute the value of y into equation 2

x + 4y=0

x + 4 (− 1) ÷ 2) = 0

x − 2 = 0

x = 2

x = 2, y = ½

472.

Given that Z = {1,2,4,5} what is the power of set Z?

View answer & explanation

Correct answer is A

Z has 4 elements, power = number of subset = 2p

Z = 2_n = 2₄

= 16

473.

The probability of an outcome A is 1/6 . The probability of the B outcome is 1/4 . If the probability of A or B or both is 1/12 . What is the probability of both outcomes A and B?

1/2

1/3

2/5

3/4

View answer & explanation

Correct answer is B

Prob.(A outcome) = $\frac{1}{6}$ , Prob.(B outcome) = ¼

P(A ∪ B) = 1/12, Prob.(A ∩ B)

Prob.(A ∩ B) = Prob.(A) + Prob.(B) − Prob.(A ∪ B)

1/6 + 1/4 − 1/12

= (2 + 3 − 1) ÷ 12

= 4/12

= 1/3

Prob.(A ∩ B) = 1/3