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.
The sum of two numbers is 5; their product is -14. Find the numbers.
x = 5 or 1
x = 7 or 1
x = 7 or 0
x = 7 or − 2
Correct answer is D
Let x represent the first number;
Then, the other is (5 − x) , since their sum is 5 and their product is 14
x(5 − x) = 14
5x − x2 = 14
x2 − 5x − 14 = 0
(x2 − 7x) + (2x − 14) = 0
x(x − 7) + 2(x − 7) = 0
(x − 7)(x + 2) = 0
Either (x − 7) = 0 or (x + 2) = 0
x = 7 or x = − 2
The two numbers are 7 and − 2
If √ (2x + 2) − √x =1 ,find x.
x = 1 twice
x = 0 or 1
x = 3 or 1
x = 2 twice
Correct answer is A
√(2x + 2 ) − √x = 1
√(2x + 2) = 1 + √x
Square both sides
√(2x + 2)2 = (1 + √x)2
((2x + 2)2)½ = 1 + √x + √x+ x
2x + 2 = 1 + 2√x +x
Collect the like term together
2x − x + 2 − 1 = 2 √x
x + 1 = 2√x
Square both sides
(x + 1)2 = (2√x)2
x2 + 2x + 1 = 4x
x2 + 2x − 4x + 1 = 0
(x2− x)(x + 1)= 0
x(x − 1) −1(x − 1)
(x − 1)(x −1)
Either (x − 1) = 0 or (x − 1) = 0
x = 1 or 1
x = 1 twice
10 √3
5 √3
20 √3
15 √3
Correct answer is C
√30 × √40
√(30 × 40)
√(3 × 10 × 4 × 10)
√(400 × 3)
√400 × √3
20 × √3
20√3
Calculate the value of x and y if (27x ÷ 81x+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
Given that Z = {1,2,4,5} what is the power of set Z?
16
8
10
12
Correct answer is A
Z has 4 elements, power = number of subset = 2p
Z = 2n = 24
= 16