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POST UTME DELSU 2024 Mathematics | Objective

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Question 1 View Details

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

Correct A. \(\frac{1}{2} \left \frac{4^3}{3} + 3 \cdot 4^2 - 2 \cdot 4 \right \\) )

B. \(\frac{1}{2} \left \frac{0^3}{3} + 3 \cdot 0^2 - 2 \cdot 0 \right \\) )

C. \(\frac{1}{2} \left \frac{4^3}{3} + 3 \cdot 4^2 - 2 \cdot 4 \right \\) + \(\frac{1}{2}\)\) left\(\frac{0^3}{3} + 3 \cdot 0^2 - 2 \cdot 0 \right\) )

D. \(\frac{1}{2} \left \frac{4^3}{3} + 3 \cdot 4^2 - 2 \cdot 4 \right \\) - \(\frac{1}{2}\)\) left\(\frac{0^3}{3} + 3 \cdot 0^2 - 2 \cdot 0 \right\) )

Correct Answer: A

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Question 2 View Details

Solve for ( x ) in the equation \(2^x = 8\).

A. \(x = 2\)

Correct B. \(x = 3\)

C. \(x = 4\)

D. \(x = 5\)

Correct Answer: B

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Question 3 View Details

Find the volume of the solid formed by revolving the region bounded by the curve (y = \(x^2\)\), the ( x )-axis, and the line \(x = 2\\((y = x^2), the ( x )-axis, and the line\) about the ( x )-axis.

A. \(\frac{16}{3} \pi\)

B. \(\frac{32}{3} \pi\)

Correct C. \(\frac{64}{3} \pi\)

D. \(\frac{128}{3} \pi\)

Correct Answer: C

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Question 4 View Details

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

Correct A. ( 25 pi )

B. ( 50 pi )

C. ( 75 pi )

D. ( 100 pi )

Correct Answer: A

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Question 5 View Details

Find the equation of the line passing through the points ( (2, 3) ) and ( (4, 5) ).

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

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

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

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

Correct Answer: A

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Question 6 View Details

In a geometric sequence with first term 2 and common ratio 3, find the sum of the first five terms.

Correct A. 2 + 6 + 18 + 54 + 162

B. 2 + 6 + 18 + 54 + 162 + 486

C. 2 + 6 + 18 + 54 + 162 + 486 + 1458

D. 2 + 6 + 18 + 54 + 162 + 486 + 1458 + 4374

Correct Answer: A

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Question 7 View Details

Solve for x in the equation \(\frac{1}{2}\)\)\\((x^2 + 5x - 3\)\(= 0.\)\)

A. \(x = -10\)

Correct B. \(x = -6\)

C. \(x = 1\)

D. \(x = 2\)

Correct Answer: B

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Question 8 View Details

A circle with center (0, 0) and radius 4 passes through the point (3, 4). Find the equation of the circle.

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

B. \(x^2\) + \\((y^2\)\(= 25\)\)

C. \(x^2\) + \\((y^2\)\(= 36\)\)

D. \(x^2\) + \\((y^2\)\(= 49\)\)

Correct Answer: A

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Question 9 View Details

A polynomial f(x) has degree 3 and zeros at x = -2, \(x = 1\), and \(x = 3\). Find the polynomial.

Correct A. \(f(x) =\)\(x + 2\), x - 1\)\(x - 3\)

B. \(f(x) =\)\(x + 2\), x - 1\)\(x + 3\)

C. \(f(x) =\)\(x + 2\), x - 1\)\(x - 3\)

D. \(f(x) =\)\(x + 2\), x - 1\)\(x + 1\)

Correct Answer: A

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Question 10 View Details

A set A has 5 elements, and a set B has 3 elements. Find the number of elements in the union of sets A and B.

A. 8

Correct B. 10

C. 12

D. 15

Correct Answer: B

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Question 11 View Details

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

Correct A. \(x^2\) + \\((y^2 - 6x + 4y + 5\)\(= 0\)\)

B. \(x^2\) + \\((y^2 - 4x - 2y + 3\)\(= 0\)\)

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

D. \(x^2\) + \\((y^2 - 2x + 6y - 1\)\(= 0\)\)

Correct Answer: A

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Question 12 View Details

A right circular cone has a height of 10 cm and a base radius of 4 cm. Find the volume of the cone.

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

B. 80\pi \(cm^3\)

Correct C. 120\pi \(cm^3\)

D. 160\pi \(cm^3\)

Correct Answer: C

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Question 13 View Details

Two events A and B are independent. If P(A) = 0.4 and P(B) = 0.6, find P(\(A \cap B\)).

Correct A. 0.2

B. 0.24

C. 0.3

D. 0.36

Correct Answer: A

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Question 14 View Details

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

Correct A. x ≤ -1 or x ≥ \(\frac{3}{2}\)\)

B. x ≤ -1 or x ≥ -\(\frac{3}{2}\)\)

C. \(x \le 1\) or x ≥ -\(\frac{3}{2}\)\)

D. x ≤ -1 or \(x \ge 1\)

Correct Answer: A

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Question 15 View Details

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

A. 20

B. 22

Correct C. 24

D. 26

Correct Answer: C

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Question 16 View Details

Solve the inequality \(x+2 \\)^2 - 4\(x-1\)^\(2 > 0)\).

Correct A. \(x < -3\) or \(x > 2\)

B. \(x > -3\) or \(x < 2\)

C. \(x < -3\) and \(x > 2\)

D. \(x > -3\) and \(x < 2\)

Correct Answer: A

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Question 17 View Details

Find the area under the curve [\(y =\)\(\frac{1}{x^2 + 1}\)\)\), \quad x \in [0, 1]\].

Correct A. \pi - 1

B. \(\frac{\pi}{2}\)\)

C. \(\frac{\pi}{4}\)\)

D. \(\frac{\pi}{8}\)\)

Correct Answer: A

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Question 18 View Details

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

Correct A. 1, 2, 3

B. 1, 2, -3

C. 2, 3, -1

D. -1, 2, 3

Correct Answer: A

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Question 19 View Details

Find the value of [\log_{10} \(x^2 + 1\)\(= 4\)].

Correct A. \(\frac{1}{10}\)\)

B. \(\frac{1}{100}\)\)

C. \(\frac{1}{1000}\)\)

D. \(\frac{1}{10000}\)\)

Correct Answer: A

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Question 20 View Details

Solve the equation [\\(\sin^2\) x + \\(\cos^2\) \(x = 1\)\].

A. \(x =\)\(\frac{\pi}{2}\)\)

Correct B. \(x =\)\(\frac{\pi}{4}\)\)

C. \(x =\)\(\frac{3\pi}{4}\)\)

D. \(x =\)\(\frac{5\pi}{4}\)\)

Correct Answer: B

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Question 21 View Details

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

Correct A. \(\frac{1}{2} \times 4^3 + 3 \times 4^2 - 2 \times 4\)

B. \(\frac{1}{2} \times 4^2 + 3 \times 4 - 2\)

C. \(\frac{1}{2} \times 4^3 - 3 \times 4^2 - 2 \times 4\)

D. \(\frac{1}{2} \times 4^2 - 3 \times 4 - 2\)

Correct Answer: A

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Question 22 View Details

Solve the vector equation \(overrightarrow{a} = egin{pmatrix} 2 \ 3 \end{pmatrix}\) and \(overrightarrow{b} = egin{pmatrix} 4 \ 5 \end{pmatrix}\). Find the magnitude of \(overrightarrow{a} + overrightarrow{b}\).

Correct A. \(\sqrt{2^2 + 3^2 + 4^2 + 5^2}\)

B. \(\sqrt{2^2 + 3^2 - 4^2 - 5^2}\)

C. \(\sqrt{2^2 + 3^2 + 4^2 - 5^2}\)

D. \(\sqrt{2^2 + 3^2 - 4^2 + 5^2}\)

Correct Answer: A

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Question 23 View Details

Solve the trigonometric equation \(\sin^2 x + \cos^2 x = 1\) for ( x ) in the interval ( [0, 2pi] ).

Correct A. \(x = \frac{\pi}{4}\)

B. \(x = \frac{\pi}{2}\)

C. \(x = \frac{3\pi}{4}\)

D. \(x = \frac{5\pi}{4}\)

Correct Answer: A

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Question 24 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 + \(y - 3\)^\(2 = 4\) )

C. \(x - 2 \\)^2 + \(y - 3\)^\(2 = 9\) )

D. \(x - 2 \\)^2 + \(y - 3\)^\(2 = 25\) )

Correct Answer: A

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Question 25 View Details

Convert the decimal number ( 123.45 ) to binary.

Correct A. ( 1111011.011 )

B. ( 1111011.110 )

C. ( 1111011.101 )

D. ( 1111011.0111 )

Correct Answer: A

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