POST UTME CHRISTOPHER UNIVERSITY 2024 Mathematics | Objective

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Question 1 View Details
Determine the value of x in the matrix equation \(egin{bmatrix} 2 & 3 \ 4 & 5 \end{bmatrix} egin{bmatrix} x \ 2 \end{bmatrix} = egin{bmatrix} 14 \ 26 \end{bmatrix}\)
A. 3
B. 4
Correct C. 5
D. 6

Correct Answer: C

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Question 2 View Details
A binary operation ( oplus ) is defined as \(a oplus b = a + b - ab\). Find the value of ( 2 oplus 3 )
Correct A. 1
B. 2
C. 3
D. 4

Correct Answer: A

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Question 3 View Details
A random experiment consists of rolling a fair six-sided die. If the outcome is an even number, the experimenter wins a prize. Find the probability that the experimenter wins the prize
A. \(1/2\)
B. \(1/3\)
Correct C. \(2/3\)
D. \(3/4\)

Correct Answer: C

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Question 4 View Details
A histogram of exam scores is shown below. What is the mean score?
A. 40
Correct B. 50
C. 60
D. 70

Correct Answer: B

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Question 5 View Details
Find the determinant of the matrix \(egin{bmatrix} 1 & 2 \ 3 & 4 \end{bmatrix}\)
A. 0
Correct B. 1
C. 2
D. 3

Correct Answer: B

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Question 6 View Details
Find the area under the curve \(y = \frac{1}{2}x^2 + 3x - 2\) from \(x = 0\) to \(x = 4\).
A. 64
B. 80
Correct C. 96
D. 128

Correct Answer: C

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Question 7 View Details
Solve for ( x ) in the equation \(2^x + 5^x = 7^x\).
A. 1
Correct B. 2
C. 3
D. 4

Correct Answer: B

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Question 8 View Details
Find the value of (\(12\theta\) given that \\((\)12theta\(\(1\theta = \frac{3}{5}\) and 1\\(theta =\)\(\frac{4}{5}\)\).
Correct A. 0.8
B. 0.9
C. 1.2
D. 1.5

Correct Answer: A

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Question 9 View Details
A vector ( mathbf{a} ) has components \(a_x = 3\) and \(a_y = 4\). Find the magnitude of the vector.
A. 5
Correct B. 6
C. 7
D. 8

Correct Answer: B

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Question 10 View Details
Two events ( A ) and ( B ) are independent. If ( P(A) = 0.3 ) and ( P(B) = 0.4 ), find the probability that both events occur.
A. 0.12
Correct B. 0.24
C. 0.36
D. 0.48

Correct Answer: B

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Question 11 View Details
Solve for x in the equation \(\tan^2 x + $1x - 6 = 0\) using the quadratic formula.
Correct A. \(x = 0.5\),\(x = -2\)
B. \(x = 1\),\(x = -6\)
C. \(x = 2\),\(x = -3\)
D. \(x = 3\),\(x = -2\)

Correct Answer: A

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Question 12 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 13 View Details
Solve the inequality \(\frac{x - 2}{x + 1} > 0\) using a sign table.
Correct A. \(x < -1\), \(x > 2\)
B. \(x < -1\), \(x < 2\)
C. \(x > -1\), \(x > 2\)
D. \(x > -1\), \(x < 2\)

Correct Answer: A

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Question 14 View Details
Find the derivative of the function ( f(x) = \(\frac{1}{x^2 + 1}\)\)\) ) using the quotient rule.
Correct A. f'\((x) =\)\(\frac{-2x}{x^2 + 1\) ^2}\)\)
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: A

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Question 15 View Details
Solve the system of equations \(egin{cases} x + y = 4 \ x - y = 2 \end{cases}\) using substitution.
Correct A. \(x = 3\), \(y = 1\)
B. \(x = 1\), \(y = 3\)
C. \(x = 2\), \(y = 2\)
D. \(x = 4\), \(y = 0\)

Correct Answer: A

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Question 16 View Details
Find the area of the triangle with vertices (0, 0), (3, 0), and (0, 4).
Correct A. 6
B. 8
C. 10
D. 12

Correct Answer: A

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Question 17 View Details
Solve the inequality \(x^2 - 4x - 5 > 0\) using factoring.
Correct A. \(x < -1\), \(x > 5\)
B. \(x < -5\), \(x > 1\)
C. \(x < 1\), \(x > 5\)
D. \(x < 5\), \(x > 1\)

Correct Answer: A

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