POST UTME JOSEPH AYO BABALOLA UNIVERSITY 2018 Mathematics | Objective

Practice these randomly selected questions to test your readiness.

Question 1
A polynomial f(x) has roots at x = -2, x = 1, and x = 3. What is the product of the roots?
A. -6
B. -12
C. -18
D. -24
Question 2
Find the equation of the circle with center (2, 3) and radius 4.
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
Question 3
A binary operation \(*\) on the set \{1, 2, 3, 4, 5\} is defined as \[\begin{align*} *: \{1, 2, 3, 4, 5\} \times \{1, 2, 3, 4, 5\} &\to \{1, 2, 3, 4, 5\} \end{align*}\]. If \(a * b = 3\), find the value of \(a\) and \(b\).
A. \(a = 2, b = 1\)
B. \(a = 3, b = 2\)
C. \(a = 4, b = 3\)
D. \(a = 5, b = 4\)
Question 4
Find the sum of the first 10 terms of the geometric series with first term 2 and common ratio 3.
A. 1.999999999
B. 2.999999999
C. 3.999999999
D. 4.999999999
Question 5
A histogram of exam scores has a mean of 75 and a s\tandard deviation of 10. If the scores are normally distributed, what is the probability that a randomly selected student scored above 90?
A. 0.1587
B. 0.3413
C. 0.4772
D. 0.6915
Question 6
Solve the quadratic equation \( x^2 + 4x + 4 = 0 \).
A. \left\{ -2 \right\}
B. \left\{ -1, -3 \right\}
C. \left\{ -2, 2 \right\}
D. \left\{ -2, -4 \right\}
Question 7
A binary operation \(*\) is defined as: \[a * b = a^2 + b^2\]. Find the value of \(\( 2 * 3 \) * 4\)
A. 52
B. 64
C. 72
D. 80
Question 8
Find the equation of the \tangent line to the curve \( y = x^3 - 6x^2 + 9x + 2 \) at the point \( 1, -4 \ \) ).
A. y = 3x - 5
B. y = 3x - 7
C. y = 3x - 9
D. y = 3x - 11
Question 9
Solve the trigonometric equation \( \tan^2 x + 2 \tan x - 6 = 0 \) for ( x ) in the interval ( [0, 2 pi] ).
A. \frac{3 pi}{12}
B. \frac{5 pi}{12}
C. \frac{7 pi}{12}
D. \frac{11 pi}{12}
Question 10
Find the area under the curve y = x^2 from x = 0 to x = 4.
A. 16
B. 32
C. 64
D. 128
Question 11
Solve the system of linear equations u\sing matrices: \[\begin{align*} x + 2y - 3z &= 7 \ 2x - y + z &= -3 \ 3x + y + 2z &= 2 \end{align*}\]
A. \[\begin{bmatrix} x \ y \ z \end{bmatrix} = \begin{bmatrix} 1 \ 2 \ 3 \end{bmatrix}\]
B. \[\begin{bmatrix} x \ y \ z \end{bmatrix} = \begin{bmatrix} 2 \ -1 \ 3 \end{bmatrix}\]
C. \[\begin{bmatrix} x \ y \ z \end{bmatrix} = \begin{bmatrix} 3 \ 1 \ 2 \end{bmatrix}\]
D. \[\begin{bmatrix} x \ y \ z \end{bmatrix} = \begin{bmatrix} 1 \ 2 \ 3 \end{bmatrix}\]
Question 12
Find the value of \( \sqrt[3]{64} \).
A. 4
B. 8
C. 16
D. 32
Question 13
Find the equation of the circle with center (2, 3) and radius 4.
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
Question 14
Find the equation of the line pas\sing through the points (2, 3) and (4, 5) in the slope-intercept form.
A. y = 1x + 1
B. y = 2x + 2
C. y = 3x + 3
D. y = 4x + 4
Question 15
Solve the system of equations: \( x + y = 4 \) and \( x^2 + y^2 = 16 \).
A. \left\{ (2, 2) \right\}
B. \left\{ (2, 2), \( -2, -2 \) \right\}
C. \left\{ (2, 2), \( -2, 2 \) \right\}
D. \left\{ (2, 2), \( 2, -2 \) \right\}

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