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POST UTME UNIPORT 2018 Mathematics | Objective

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Question 1 View Details

Find the determinant of the matrix [ egin{array}{ccc} 1 & 2 & 3 \ 4 & 5 & 6 \ 7 & 8 & 9 \end{array} ].

A. -120

B. 120

Correct C. 0

D. -60

Correct Answer: C

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Question 2 View Details

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

Correct A. \(x \leq -3\) or \(x \geq \frac{3}{2}\)

B. \(x \leq -3\) or \(x \geq 1\)

C. \(x \leq 1\) or \(x \geq -3\)

D. \(x \leq -1\) or \(x \geq 3\)

Correct Answer: A

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Question 3 View Details

Find the volume of the frustum of a cone with height 10 cm, lower base radius 4 cm, and upper base radius 2 cm.

A. 40\pi \(cm^3\)

Correct B. 50\pi \(cm^3\)

C. 60\pi \(cm^3\)

D. 70\pi \(cm^3\)

Correct Answer: B

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Question 4 View Details

Solve the equation \(x^2 - 4x + 4 = 0\).

A. \(x = 0\)

Correct B. \(x = 2\)

C. \(x = 4\)

D. \(x = -2\)

Correct Answer: B

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Question 5 View Details

Find the surface area of the sphere with radius 6 cm.

Correct A. 288\pi \(cm^2\)

B. 288\pi \(cm^2\)

C. 288\pi \(cm^2\)

D. 288\pi \(cm^2\)

Correct Answer: A

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Question 6 View Details

Let \(S = {1, 2, 3, 4, 5}\) be a finite set. Find the number of elements in the power set of ( S ), denoted as ( P(S) ).

Correct A. 32

B. 31

C. 30

D. 29

Correct Answer: A

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Question 7 View Details

A sequence is defined as (a_\(n = 2n + 1\)\) for \(n = 1, 2, 3, ldots\\((a_n = 2n + 1) for\). Find the sum of the first five terms of this sequence.

A. 30

B. 31

Correct C. 32

D. 33

Correct Answer: C

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Question 8 View Details

A geometric progression is defined as (a_\(n = 2a\)_{n-1} + 1\) for \(n = 2, 3, 4, ldots\\((a_n = 2a_{n-1} + 1) for\) with \(a_1 = 2\). Find the sum of the first five terms of this progression.

Correct A. 63

B. 62

C. 61

D. 60

Correct Answer: A

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Question 9 View Details

A circle has a radius of 5 cm. Find the area of the circle.

A. 50\pi

Correct B. 25\pi

C. 75\pi

D. 100\pi

Correct Answer: B

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Question 10 View Details

A rectangular prism has a length of 10 cm, a width of 5 cm, and a height of 3 cm. Find the volume of the prism.

Correct A. 150

B. 160

C. 170

D. 180

Correct Answer: A

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Question 11 View Details

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

Correct A. 16

B. 32

C. 64

D. 128

Correct Answer: A

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Question 12 View Details

A set of 10 numbers has a mean of 20 and a standard deviation of 5. Find the probability that a randomly selected number from the set is greater than 25.

Correct A. 0.1587

B. 0.3413

C. 0.5

D. 0.8413

Correct Answer: A

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Question 13 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 - 3 \\)^2 + \(y - 2\)^\(2 = 16\) )

C. \(x - 4 \\)^2 + \(y - 3\)^\(2 = 16\) )

D. \(x - 2 \\)^2 + \(y - 4\)^\(2 = 16\) )

Correct Answer: A

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Question 14 View Details

A sequence is defined by the recurrence relation \(a_n = 2a_{n-1} + 1\) with initial term \(a_1 = 3\). Find the 5th term of the sequence.

A. 31

B. 33

Correct C. 35

D. 37

Correct Answer: C

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Question 15 View Details

Find the area of the triangle with vertices ( (0, 0) ), ( (3, 0) ), and ( (0, 4) ).

A. 12

B. 16

Correct C. 20

D. 24

Correct Answer: C

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Question 16 View Details

Find the value of (x\) in the equation \(2^x + 2^{x+1} = 3 \\((x) in the equation \cdot 2^{x+1}\).

A. 1

B. 2

Correct C. 3

D. 4

Correct Answer: C

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Question 17 View Details

In the diagram below, the line (AB\) has a slope of \(2\\((AB) has a slope of\) and passes through the point ((1,3)\). Find the equation of the line in the form \(y = mx + c\\(((1,3)). Find the equation of the line in the form\).

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

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

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

D. \(y = 2x - 2\)

Correct Answer: A

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Question 18 View Details

Find the sum of the first (10\) terms of the geometric series \(1 + 2 + 4 + 8 + \\((10) terms of the geometric series \dotsb\).

A. 1023

Correct B. 1024

C. 1025

D. 1026

Correct Answer: B

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Question 19 View Details

Solve the system of equations \(x + y = 2\) and \(xy = 1\).

Correct A. (1,1)

B. \(1,-1\)

C. \(-1,1\)

D. \(-1,-1\)

Correct Answer: A

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Question 20 View Details

Find the area of the triangle with vertices \((0,0)\), \((3,0)\), and \((0,2)\).

Correct A. 6

B. 12

C. 18

D. 24

Correct Answer: A

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Question 21 View Details

Solve for x in the equation \(2^x + 2^{x+2} = 3 \cdot 2^{x+1}\).

A. \(x = -1\)

B. \(x = 0\)

Correct C. \(x = 1\)

D. \(x = 2\)

Correct Answer: C

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Question 22 View Details

A random variable X has a probability distribution given by ( P(X) = egin{cases} 0.2 & text{if } \(X = 1\) \\(text{if} (X = 1\ 0.3 & text{if} \(X = 2\) \\(text{if} (X = 2\ 0.5 & text{if} \(X = 3\) \\(text{if}\((X = 3\)\end{cases} ). Find the expected value of X.

A. 1.5

Correct B. 2

C. 2.5

D. 3

Correct Answer: B

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Question 23 View Details

Find the determinant of the matrix \(egin{bmatrix} 2 & 1 & 3 \ 4 & 2 & 5 \ 6 & 3 & 7 \end{bmatrix}\).

Correct A. -1

B. 0

C. 1

D. 2

Correct Answer: A

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Question 24 View Details

Solve the system of equations \(egin{cases} x + y = 4 \ 2x - 3y = -2 \end{cases}\).

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

Correct B. \(x = 3, y = 1\)

C. \(x = 4, y = 0\)

D. \(x = 5, y = -1\)

Correct Answer: B

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Question 25 View Details

A binary number is represented as \(1011_2\). Convert it to decimal.

A. 3

Correct B. 5

C. 7

D. 9

Correct Answer: B

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