POST UTME JOSEPH AYO BABALOLA UNIVERSITY 2018 Mathematics | Objective

Practice these randomly selected questions to test your readiness.

Question 1
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 2
Solve the equation \( x^2 + 4x + 4 = 0 \) u\sing the quadratic formula.
A. \frac{-4 \pm \sqrt{16 - 16}}{2}
B. \frac{-4 \pm \sqrt{16 + 16}}{2}
C. \frac{-4 \pm \sqrt{16 - 4}}{2}
D. \frac{-4 \pm \sqrt{16 + 4}}{2}
Question 3
A histogram is constructed from the following data: 2, 4, 6, 8, 10, 12, 14, 16. What is the class width?
A. 2
B. 4
C. 6
D. 8
Question 4
A random sample of 25 students from a university had a mean height of 175.5 cm with a s\tandard deviation of 5.2 cm. If the population s\tandard deviation is unknown, calculate the 95% confidence interval for the mean height of the university students.
A. 173.5 cm to 177.5 cm
B. 171.5 cm to 179.5 cm
C. 174.5 cm to 176.5 cm
D. 172.5 cm to 178.5 cm
Question 5
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 6
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 7
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 8
Find the area under the curve of \( y = \frac{1}{2}x^2 + 3x - 2 \) from \( x = 0 \) to \( x = 4 \).
A. 40
B. 42
C. 44
D. 46
Question 9
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 10
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 11
Solve the quadratic equation: \[x^2 + 5x + 6 = 0\]
A. \[x = -2, x = -3\]
B. \[x = -1, x = -6\]
C. \[x = 2, x = 3\]
D. \[x = 1, x = 6\]
Question 12
Solve the system of equations u\sing matrices: \[\begin{align*} x + y + z &= 6 \ 2x + 3y - z &= 2 \ -x + 2y + 3z &= -1 \end{align*}\]
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. \[\begin{bmatrix} x \ y \ z \end{bmatrix} = \begin{bmatrix} 3 \ 2 \ 1 \end{bmatrix}\]
D. \[\begin{bmatrix} x \ y \ z \end{bmatrix} = \begin{bmatrix} 1 \ 3 \ 2 \end{bmatrix}\]
Question 13
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 14
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 15
A random sample of 25 students from a university had a mean height of 175.5 cm with a s\tandard deviation of 5.2 cm. If the population s\tandard deviation is unknown, calculate the 95% confidence interval for the population mean.
A. 170.1 cm, 180.9 cm
B. 168.5 cm, 182.5 cm
C. 169.5 cm, 181.5 cm
D. 171.5 cm, 179.5 cm

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