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POST UTME RSU 2018 Mathematics | Objective

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Question 1 View Details

In a circle of radius 4 cm, a chord of length 6 cm subtends an angle of 60° at the centre. Find the area of the sector.

A. 12π cm²

Correct B. 16π cm²

C. 20π cm²

D. 24π cm²

Correct Answer: B

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Question 2 View Details

If \((x^2 + 2x + 1\) = 0\), find the value of \(x^3 + 2x^2 + x + 1\\((x^2 + 2x + 1 = 0), find the value of\).

Correct A. -1

B. 0

C. 1

D. 2

Correct Answer: A

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Question 3 View Details

A random variable (X\) has a probability distribution given by \(P X = x\\((X) has a probability distribution given by\)=\(\frac{1}{2}\)\)\). Find the expected value of \(X\).

A. 0

Correct B. 1

C. 2

D. 3

Correct Answer: B

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Question 4 View Details

In a triangle (ABC\), the length of side \(AB\\((ABC), the length of side\) is 5 cm, the length of side (BC\) is 6 cm, and the length of side \(AC\\((BC) is 6 cm, and the length of side\) is 7 cm. Find the area of the triangle.

A. 12 cm²

B. 15 cm²

Correct C. 18 cm²

D. 20 cm²

Correct Answer: C

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Question 5 View Details

If (f(x) = \(\frac{\(x^2-4}{x-2}\)\)\), find the value of \\((f(x) = frac{x^2-4}{x-2}\(f(4)\).

A. 0

Correct B. 2

C. 4

D. 6

Correct Answer: B

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Question 6 View Details

Find the area under the curve \(y = \frac{1}{2}x^2 + 3x - 4\) from \(x = 0\) to \(x = 2\).

A. 10

B. 12

Correct C. 14

D. 16

Correct Answer: C

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Question 7 View Details

A right circular cone has a height of 15 cm and a base radius of 8 cm. Find its volume.

A. 1000π \(cm^3\)

B. 1200π \(cm^3\)

Correct C. 1500π \(cm^3\)

D. 1800π \(cm^3\)

Correct Answer: C

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Question 8 View Details

Solve the inequality \(2x^2 + 5x - 3 > 0\).

Correct A. \(-∞, -1\) ∪ (3, ∞)

B. \(-∞, -3\) ∪ (1, ∞)

C. \(-∞, -1\) ∪ (1, ∞)

D. \(-∞, -3\) ∪ (3, ∞)

Correct Answer: A

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Question 9 View Details

Find the equation of the circle with center \(-2, 3 \\) ) and radius 4.

Correct A. \(x + 2 \\)^2 + \(y - 3\)^\(2 = 16\) )

B. \(x - 2 \\)^2 + \(y + 3\)^\(2 = 16\) )

C. \(x + 2 \\)^2 + \(y + 3\)^\(2 = 16\) )

D. \(x - 2 \\)^2 + \(y - 3\)^\(2 = 16\) )

Correct Answer: A

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Question 10 View Details

A number is 5 times the sum of its digits. If the number is divisible by 3, what is the number?

A. 135

Correct B. 315

C. 531

D. 753

Correct Answer: B

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Question 11 View Details

Find the value of x in the equation \(\log_{10} x^2 \\)\(= 4 ).\)

A. 10

B. 100

C. 1000

Correct D. 10000

Correct Answer: D

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Question 12 View Details

Solve the quadratic equation \(x^2 + 5x + 6 = 0\).

Correct A. \(x = -2\)

B. \(x = -3\)

C. \(x = 2\)

D. \(x = 3\)

Correct Answer: A

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Question 13 View Details

A right-angled triangle has a hypotenuse of length 10 cm and one leg of length 6 cm. Find the length of the other leg.

Correct A. 8 cm

B. 6 cm

C. 10 cm

D. 12 cm

Correct Answer: A

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Question 14 View Details

A car travels from city A to city B at an average speed of 60 \((km/h\)\) and returns at an average speed of 40 \(km/h\\((km/h) and returns at an average speed of 40\). What is the average speed for the round trip?

A. 48 \(km/h\)

B. 50 \(km/h\)

Correct C. 52 \(km/h\)

D. 55 \(km/h\)

Correct Answer: C

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Question 15 View Details

A solid cylinder has a height of 10 cm and a radius of 4 cm. Find the volume of the cylinder.

A. 800π \(cm^3\)

Correct B. 1000π \(cm^3\)

C. 1200π \(cm^3\)

D. 1600π \(cm^3\)

Correct Answer: B

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Question 16 View Details

In a random sample of 100 students, the mean height is 175 cm with a standard deviation of 5 cm. If the population standard deviation is 3 cm, calculate the standard error of the mean.

Correct A. 1.67 cm

B. 2.5 cm

C. 3.33 cm

D. 4.24 cm

Correct Answer: A

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Question 17 View Details

Find the equation of the circle with center \(-2, 3\) and radius 4.

Correct A. \left\(x + 2 \right\)^2 + \left\(y - 3 \right\)^\(2 = 16\)

B. \left\(x - 2 \right\)^2 + \left\(y + 3 \right\)^\(2 = 16\)

C. \left\(x + 3 \right\)^2 + \left\(y - 2 \right\)^\(2 = 16\)

D. \left\(x - 3 \right\)^2 + \left\(y + 2 \right\)^\(2 = 16\)

Correct Answer: A

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Question 18 View Details

A sequence is defined by the recurrence relation a_\(n = 2a\)_{n-1} + 1, with \(a_1 = 3\). Find the sum of the first 5 terms of the sequence.

Correct A. 3 + 7 + 15 + 31 + 63

B. 3 + 5 + 11 + 23 + 47

C. 3 + 6 + 12 + 24 + 48

D. 3 + 8 + 16 + 32 + 64

Correct Answer: A

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Question 19 View Details

Find the determinant of the matrix \begin{bmatrix} 2 & 3 & 1 \\ 4 & 5 & 2 \\ 1 & 2 & 3 \end{bmatrix}.

Correct A. 0

B. 1

C. 2

D. 3

Correct Answer: A

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Question 20 View Details

In a right-angled triangle, the length of the hypotenuse is 10 cm and one of the other sides is 6 cm. Find the length of the third side.

Correct A. 8 cm

B. 6 cm

C. 10 cm

D. 12 cm

Correct Answer: A

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Question 21 View Details

Solve the inequality (\(\frac{x-2}{x+1}\(> 0\)\) for x in \\((frac{x-2}{x+1} > 0\(-\infty, -1 \ cup -1, 2\) cup (2\), infty) ).

Correct A. \(x < -1\) or \(x > 2\)

B. \(x > -1\) and \(x < 2\)

C. \(x < -1\) or \(x = 2\)

D. \(x > -1\) or \(x = 2\)

Correct Answer: A

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Question 22 View Details

Find the equation of the circle with center \(C -2, 3 \\) ) and radius ( 4 ).

Correct A. \(x+2 \\)^2 + \(y-3\)^\(2 = 16\) )

B. \(x-2 \\)^2 + \(y+3\)^\(2 = 16\) )

C. \(x+2 \\)^2 + \(y+3\)^\(2 = 16\) )

D. \(x-2 \\)^2 + \(y-3\)^\(2 = 16\) )

Correct Answer: A

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Question 23 View Details

If ( f(x) = \(\frac{1}{x^2 + 1}\)\)\) ), find ( f'(x) ).

A. ( f'\((x) =\)\(\frac{-2x}{x^2 + 1\) ^2}\)\) )

Correct B. ( f'\((x) =\)\(\frac{2x}{x^2 + 1\) ^2}\)\) )

C. ( f'\((x) =\)\(\frac{2}{x^2 + 1\) ^2}\)\) )

D. ( f'\((x) =\)\(\frac{-2}{x^2 + 1\) ^2}\)\) )

Correct Answer: B

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Question 24 View Details

A fair six-sided die is rolled. What is the probability that the number rolled is greater than 4?

A. \(\frac{1}{6}\)

B. \(\frac{1}{3}\)

C. \(\frac{2}{3}\)

Correct D. \(\frac{5}{6}\)

Correct Answer: D

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Question 25 View Details

Solve the system of equations \(egin{cases} x + y = 3 \ 2x - 3y = - 5 \end{cases}\).

Correct A. \(x = 2, y = 1\)

B. \(x = 1, y = 2\)

C. \(x = 2, y = 2\)

D. \(x = 1, y = 1\)

Correct Answer: A

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