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POST UTME ABU 2021 Mathematics | Objective

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Question 1 View Details

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

Correct A. ( 16 )

B. ( 20 )

C. ( 22 )

D. ( 24 )

Correct Answer: A

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Question 2 View Details

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

Correct A. \(x < -1\) or \(x > \frac{3}{2}\)

B. \(x < -1\) or \(x < \frac{3}{2}\)

C. \(x > -1\) or \(x < \frac{3}{2}\)

D. \(x > -1\) or \(x > \frac{3}{2}\)

Correct Answer: A

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Question 3 View Details

Find the volume of the frustum of a cone with radii 6 cm and 4 cm and height 10 cm.

A. ( 100pi ) cm³

Correct B. ( 120pi ) cm³

C. ( 140pi ) cm³

D. ( 160pi ) cm³

Correct Answer: B

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Question 4 View Details

Solve the system of equations \(x + y = 3\) and \(xy = 2\).

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

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

C. \(x = 2, y = -1\)

D. \(x = -1, y = 2\)

Correct Answer: A

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Question 5 View Details

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

Correct A. ( 0 )

B. ( 1 )

C. ( 2 )

D. ( 3 )

Correct Answer: A

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Question 6 View Details

Let \(\mathbf{a} = egin{pmatrix} 2 \ 3 \end{pmatrix}\) and \(\mathbf{b} = egin{pmatrix} 4 \ 5 end{pmatrix}\). Find the unit vector in the direction of \(\\(end{pmatrix}). Find the unit vector in the direction of \mathbf{a} + \mathbf{b}\).

Correct A. \begin{pmatrix} \(\frac{6}\){\(\sqrt{221}\)}\) \\ \(\frac{9}\){\(\sqrt{221}\)}\) \end{pmatrix}

B. \begin{pmatrix} \(\frac{12}\){\(\sqrt{221}\)}\) \\ \(\frac{15}\){\(\sqrt{221}\)}\) \end{pmatrix}

C. \begin{pmatrix} \(\frac{6}\){\(\sqrt{221}\)}\) \\ \(\frac{15}\){\(\sqrt{221}\)}\) \end{pmatrix}

D. \begin{pmatrix} \(\frac{12}\){\(\sqrt{221}\)}\) \\ \(\frac{9}\){\(\sqrt{221}\)}\) \end{pmatrix}

Correct Answer: A

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Question 7 View Details

A rectangular box has dimensions 3 cm, 4 cm, and 5 cm. Find the volume of the box.

A. 60 \(cm^3\)

B. 80 \(cm^3\)

Correct C. 120 \(cm^3\)

D. 150 \(cm^3\)

Correct Answer: C

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Question 8 View Details

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

A. 32

B. 64

Correct C. 128

D. 256

Correct Answer: C

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Question 9 View Details

Solve the equation \(x^3 - 6x^2 + 11x - 6 = 0\).

Correct A. (1, 2, 3)

B. (1, 2, 6)

C. (1, 3, 6)

D. (2, 3, 6)

Correct Answer: A

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Question 10 View Details

Find the value of ( x ) in the equation \(2^x = 32\).

A. 5

Correct B. 6

C. 7

D. 8

Correct Answer: B

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Question 11 View Details

In a survey of 100 students, the mean height was 170 cm with a standard deviation of 5 cm. If the heights of the students are normally distributed, what is the probability that a randomly selected student will be taller than 180 cm?

A. 0.1587

B. 0.5

Correct C. 0.8413

D. 0.9772

Correct Answer: C

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Question 12 View Details

Solve the inequality \(\frac{x^2-4x-3}{x\)^2-4x+3}\)\\()>0.\)

Correct A. \left\(-\infty,-1\right)\cup\left 3,\infty\right \\)

B. \left\(-\infty,1\right)\cup\left 3,\infty\right \\)

C. \left\(-\infty,-1\right)\cup\left 1,\infty\right \\)

D. \left\(-\infty,3\right)\cup\left 3,\infty\right \\)

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

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

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

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

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 sum of the first 5 terms of the sequence.

A. 63

B. 65

Correct C. 67

D. 69

Correct Answer: C

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Question 15 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. 8.6 cm

D. 9.8 cm

Correct Answer: A

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Question 16 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 17 View Details

In the diagram below, the circle passes through points ( A(2, 3) ) and ( B(4, 5) ). Find the equation of the circle.

Correct A. \(x^2 + y^2 - 4x + 2y + 4 = 0\)

B. \(x^2 + y^2 - 4x - 2y + 4 = 0\)

C. \(x^2 + y^2 + 4x - 2y + 4 = 0\)

D. \(x^2 + y^2 - 4x + 2y - 4 = 0\)

Correct Answer: A

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Question 18 View Details

Simplify the expression \(\frac{1}{2} \left \frac{1}{3} \right \\)^{-2} \left\(\frac{1}{4} \right\)^{-1} \left\(\frac{1}{5} \right\)^{-3} \).

A. 120

B. 240

Correct C. 360

D. 480

Correct Answer: C

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Question 19 View Details

Find the volume of the frustum of the cone with height (h = 6\) cm and radii of the bases \(r_1 = 4\\((h = 6) cm and radii of the bases\) cm and \(r_2 = 2\) cm.

A. 48\pi

B. 64\pi

Correct C. 80\pi

D. 96\pi

Correct Answer: C

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Question 20 View Details

In the sequence ( 1, 2, 4, 8, 16, ... ), find the 7th term.

A. 32

B. 64

Correct C. 128

D. 256

Correct Answer: C

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Question 21 View Details

Find the derivative of the function ( f(x) = \(\frac{1}\){\sqrt{\(x^2 + 1}}\)\) ) using the chain rule.

Correct A. \(\frac{-x}\){ \(x^2 + 1\) \)^{\(3/2\)}}\)

B. \(\frac{x}\){ \(x^2 + 1\) \)^{\(3/2\)}}\)

C. \(\frac{1}\){ \(x^2 + 1\) \)^{\(3/2\)}}\)

D. \(\frac{-1}\){ \(x^2 + 1\) \)^{\(3/2\)}}\)

Correct Answer: A

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Question 22 View Details

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

A. \(x = -1\)

B. \(x = 0\)

Correct C. \(x = 1\)

D. \(x = 2\)

Correct Answer: C

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Question 23 View Details

Find the area of the triangle with vertices ( A(0, 0) ), ( B(2, 0) ), and ( C(1, 3) ).

A. 3

B. 6

Correct C. 9

D. 12

Correct Answer: C

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Question 24 View Details

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

A. \(x < -1\)

Correct B. \(x > -1\)

C. \(x < 3\)

D. \(x > 3\)

Correct Answer: B

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Question 25 View Details

Find the equation of the line passing through the points ( (1, 2) ) and ( (3, 4) ).

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

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

C. \(y = 3x - 2\)

D. \(y = 3x + 2\)

Correct Answer: A

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