POST UTME NILE UNIVERSITY 2024 Mathematics | Objective

Practice these randomly selected questions to test your readiness.

Question 1
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 2
A set of 5 numbers has a mean of 10 and a s\tandard deviation of 2. If the numbers are 8, 12, 15, 18, and x, find the value of x.
A. 20
B. 22
C. 24
D. 26
Question 3
A curve is defined by the equation y = 2x^2 + 3x - 1. Find the area under the curve between x = 0 and x = 2.
A. \frac{13}{3}
B. \frac{13}{2}
C. \frac{13}{4}
D. \frac{13}{5}
Question 4
Find the area under the curve y = x^2 from x = 0 to x = 4.
A. 16
B. 32
C. 64
D. 128
Question 5
Find the value of $\sum_{n=1}^5 n^2$.
A. 55
B. 65
C. 75
D. 85
Question 6
A polynomial $p(x)$ has roots $x = 1$ and $x = -2$. If $p(0) = 12$, find the value of $p(3)$.
A. -3
B. 6
C. 9
D. 12
Question 7
Find the area under the curve $y = x^2 + 2x + 1$ from $x = 0$ to $x = 2$.
A. 10
B. 12
C. 15
D. 18
Question 8
A histogram of exam scores is shown below. If the mean score is 75, what is the median score?
A. 70
B. 75
C. 80
D. 85
Question 9
Solve for ( x ) in the equation \( \log_{10} \( x^2 \ \) = 4 ).
A. \( x = 10^2 \)
B. \( x = 10^4 \)
C. \( x = 10^{-2} \)
D. \( x = 10^{-4} \)
Question 10
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 6.1 cm, calculate the 95% confidence interval for the population mean.
A. 168.1 cm, 182.9 cm
B. 170.5 cm, 180.5 cm
C. 172.1 cm, 178.9 cm
D. 174.5 cm, 176.5 cm
Question 11
A vector $\vec{a}$ has a magnitude of 5 and points in the direction of $\frac{1}{\sqrt{2}} \hat{i} + \frac{1}{\sqrt{2}} \hat{j}$. Find the magnitude of the vector $\vec{a} + \vec{b}$, where $\vec{b}$ is a vector with a magnitude of 3 and points in the opposite direction of $\vec{a}$.
A. 2
B. 4
C. 6
D. 8
Question 12
Solve the following system of linear equations u\sing matrices: \[ \begin{align*} x + y + z &= 6 \ 2x - 3y + z &= 9 \ x - 2y + 3z &= 2 \end{align*} \]
A. \[ \begin{align*} x &= 1 \ y &= 2 \ z &= 3 \end{align*} \]
B. \[ \begin{align*} x &= 2 \ y &= 1 \ z &= 3 \end{align*} \]
C. \[ \begin{align*} x &= 3 \ y &= 2 \ z &= 1 \end{align*} \]
D. \[ \begin{align*} x &= 1 \ y &= 3 \ z &= 2 \end{align*} \]
Question 13
A sequence is defined as: \[ a_n = \frac{1}{n} + \frac{1}{n+1} \] Calculate the sum of the first 10 terms of the sequence.
A. 2.928968253
B. 2.928968253
C. 2.928968253
D. 2.928968253
Question 14
A histogram represents the distribution of exam scores for a class of 50 students. If the mean score is 60 and the s\tandard deviation is 10, what is the probability that a randomly selected student scored above 70?
A. 0.25
B. 0.5
C. 0.75
D. 0.9
Question 15
A right-angled triangle has a hypotenuse of length 10cm and one leg of length 6cm. Find the length of the other leg.
A. 8\sqrt{3}
B. 8\sqrt{2}
C. 8\sqrt{5}
D. 8\sqrt{6}

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