POST UTME KSU 2020 Mathematics | Objective

Practice these randomly selected questions to test your readiness.

Question 1
A vector \overrightarrow{a} has a magnitude of 5 units and makes an angle of 60\circ with the positive x-axis. Find the x and y components of the vector.
A. \begin{pmatrix} 2.5 \\ 4.33 \end{pmatrix}
B. \begin{pmatrix} 4.33 \\ 2.5 \end{pmatrix}
C. \begin{pmatrix} 5 \\ 0 \end{pmatrix}
D. \begin{pmatrix} 0 \\ 5 \end{pmatrix}
Question 2
A rec\tangular box has a length of 5 cm, a width of 3 cm, and a height of 2 cm. Find the volume of the box.
A. 30
B. 31
C. 32
D. 33
Question 3
Find the area of the triangle with vertices (0, 0), (3, 0), and (0, 4).
Question 4
Solve the quadratic equation \( x^2 + 5x + 6 = 0 \)
A. -2
B. -3
C. 2
D. 3
Question 5
Find the area under the curve y = x^2 + 2x - 3 from x = 0 to x = 4.
A. 56
B. 57
C. 58
D. 59
Question 6
A fair six-sided die is rolled. What is the probability that the number obtained is a multiple of 3 or 5?
A. 1/3
B. 1/2
C. 2/3
D. 1/6
Question 7
A line passes through the points (2, 3) and (4, 5). Find the equation of the line in slope-intercept form.
A. y = x + 1
B. y = x - 1
C. y = -x + 1
D. y = x + 2
Question 8
A sequence is defined as \( a_n = 2n + 1 \). Find the sum of the first 5 terms of the sequence.
A. 15
B. 20
C. 25
D. 30
Question 9
Find the area under the curve \( y = \frac{1}{2}x^2 + 3x - 2 \) from \( x = 0 \) to \( x = 4 \).
A. 40
B. 50
C. 60
D. 70
Question 10
Solve for x in the equation \[ \begin{array}{c} 2x + 5y = 11 \ 3x - 2y = -7 \end{array} \] u\sing the method of substitution.
A. x = 1, y = 2
B. x = 2, y = 1
C. x = 3, y = 4
D. x = 4, y = 3
Question 11
A histogram has a mean of 25 and a s\tandard deviation of 5. If the histogram has 10 bars, what is the total area of the histogram?
A. 100
B. 200
C. 300
D. 400
Question 12
Solve the system of equations $\begin{cases} x+y=4 \ x-y=2 \end{cases}$.
A. x=3, y=1
B. x=1, y=3
C. x=2, y=2
D. x=4, y=0
Question 13
Find the value of $x$ in the equation $\frac{1}{x} + \frac{1}{x+1} = \frac{1}{2}$.
A. 1
B. 2
C. 3
D. 4
Question 14
In the circuit below, find the equivalent resis\tance between points A and B.
A. 2Ω
B. 4Ω
C. 6Ω
D. 8Ω
Question 15
Find the sum of the first 10 terms of the geometric series with first term 2 and common ratio 3.
A. 11,946
B. 12,000
C. 12,054
D. 12,100

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