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.

11.

Solve: \(log_3 x + log_3 (x - 8) = 2\)

A.

8

B.

6

C.

9

D.

7

Correct answer is C

\(log_3 x + log_3 (x - 8) = 2\)

 

\(log_3 x(x - 8) = log_39\) since 2 =   \(log_39\)


\(log_3\) cancels out


⇒ x(x - 8) = 9

⇒ \(x^2 - 8x = 9\)

⇒ \(x^2 - 8x - 9 = 0\)

⇒ \(x^2 - 9x + x - 9 = 0\)

⇒ x(x - 9) + 1(x - 9) = 0

⇒ (x - 9)(x + 1) = 0

⇒ x = 9 or x = -1

Since we can't have a log of negative numbers,

∴ x = 9.

12.

In the diagram, NR is a diameter, ∠MNR = x° and, ∠SRN = (5x + 20)°. Find the value of 2x.

A.

\(42^0\)

B.

\(35^0\)

C.

\(20^0\)

D.

\(90^0\)

Correct answer is B

∠RMN = 90° (angles in a semicircle is a right angle)
∠SRN = ∠RMN + ∠MNR (ext. angle of a ∆ is equal to the sum of two opp. int. angles)
⇒ 5x + 20 = 90 + x
⇒ 5x - x = 90 - 20
⇒ 4x = 70

x = \(\frac{70}{4}\)

 = 17.4°

therefore, 2x = 2\(\times17.5\) = 35°

13.

The price of a shoe was decreased by 22%. If the new price is $27.3. what is the original price.

A.

$62.30

B.

$42.30

C.

$72.00

D.

$35.00

Correct answer is D

Let x = original price

A decrease of 22% = (100-22)% = 78% of the original price.

78% of x = 27.30

= \(\frac{78x}{100} = 27.30\)

78x = 2730

then, x = \(\frac{2730}{78}\)

x =  35

Therefore, the original price of the shoe was  $35.00.

14.

Write the name of a triangle with the vertices (1, -3), (6, 2) and (0,4)?

A.

Scalene triangle

B.

Isosceles triangle

C.

Right -angle triangle

D.

Equilateral triangle

Correct answer is B

 Let A = (1, -3), B = (6, 2) and C = (0,4)

\(d =\sqrt{ (y_2 - y_1)^2 + (x_2 - x_1)^2}\)
|AB| = \(\sqrt{(2 - (-3))^2 + (6 - 1)^2}\) 
= \(\sqrt{(2 + 3)^2 + (6 - 1)^2}\) 
= \(\sqrt{5^2 + 5^2}\) 
= \(\sqrt{25 + 25}\)
= \(\sqrt50\)
= 5\(\sqrt2\) units

|BC| = \(\sqrt{(4 - 2)^2 + (0 - 6)^2}\)
= \(\sqrt{2^2 + (-6)^2}\)
= \(\sqrt{4 + 36}\)
= \(\sqrt40\) 
= 2\(\sqrt10\)  units

|AC| = \(\sqrt{(4 - (-3)^2 + (0 - 1)^2}\)
= \(\sqrt{(4 + 3)^2 + (0 - 1)^2}\)
= \(\sqrt{7^2 + (-1)^2}\) 
= \(\sqrt{49 + 1}\) 
= \(\sqrt50\)
= 5\(\sqrt{2}\)  units

Since two sides are equal (|AB| = |AC|), then the triangle is Isosceles.

15.

Consider the statements:
p: Siah is from Foya.
q: Foya is in Lofa.
Write in symbolic for the statement: "If Siah is from Foya, then Foya is in Lofa"

A.

~q ⇔ p

B.

q ⇒ p

C.

p ⇒ q

D.

p ⇔ q

Correct answer is C

The symbolic form for the statement "If Siah is from Foya, then Foya is in Lofa" is:

p ⇒ q

This is read as "p implies q". It means that if p is true, then q must also be true.

In other words, if Siah is from Foya, then Foya must be in Lofa.