POST UTME LEAD CITY UNIVERSITY 2021 Mathematics | Objective

Practice these randomly selected questions to test your readiness.

Question 1
A bakery sells 250 loaves of bread per day. If they make a profit of ₦5 per loaf, how much profit do they make in a day?
A. ₦1250
B. ₦12500
C. ₦125000
D. ₦1250000
Question 2
In a triangle $ABC$, if $\tan A = \frac{1}{3}$ and $\tan B = \frac{1}{2}$, find $\tan C$.
A. 1
B. 2
C. 3
D. 4
Question 3
In a set of numbers, the mean is 15 and the median is 10. If the mode is 12, what is the sum of the numbers in the set?
A. 60
B. 80
C. 100
D. 120
Question 4
A binary operation ( ast ) is defined on the set of integers by \( a ast b = a^2 + b^2 \) for all integers ( a ) and ( b ). Find the value of ( 2 ast 3 ).
A. 13
B. 14
C. 15
D. 16
Question 5
Solve the equation \frac{x}{2} + 3 = 7.
A. 4
B. 6
C. 8
D. 10
Question 6
A quadratic equation \( ax^2 + bx + c = 0 \) has roots \( x = 1 \) and \( x = 2 \). Find the value of ( a ).
A. 1
B. 2
C. 3
D. 4
Question 7
Solve the matrix equation \( egin{bmatrix} 1 & 2 \ 3 & 4 \end{bmatrix} egin{bmatrix} x \ y \end{bmatrix} = egin{bmatrix} 5 \ 6 \end{bmatrix} \) for x and y.
A. \( x = 1, y = 2 \)
B. \( x = 2, y = 1 \)
C. \( x = 3, y = 4 \)
D. \( x = 4, y = 3 \)
Question 8
Solve the inequality $|x^2 - 4| geq 3$.
A. x leq -1 \text{ or } x geq 2
B. x leq -2 \text{ or } x geq 1
C. x leq -3 \text{ or } x geq 2
D. x leq -1 \text{ or } x geq 3
Question 9
Solve for x in the equation \( \log_{10} \( x^2 \ \) = 4 ).
A. 10
B. 100
C. 1000
D. 10000
Question 10
A line passes through the points $(1, 2)$ and $(3, 4)$. Find the equation of the line in slope-intercept form.
A. y = x + 1
B. y = x - 1
C. y = -x + 3
D. y = x - 2
Question 11
A sequence is defined by the formula \( a_n = 2n + 1 \). Find the sum of the first 5 terms.
A. 30
B. 31
C. 32
D. 33
Question 12
A set of 5 cards is drawn from a deck of 52 cards. Find the probability that the set contains at least one ace.
A. 1/52
B. 1/26
C. 1/13
D. 1/4
Question 13
In a right-angled triangle, the length of the hypotenuse is 10 cm and one of the acute angles is 30°. Find the length of the side opposite the 30° angle.
A. 5 cm
B. 7.07 cm
C. 10 cm
D. 15 cm
Question 14
Find the area under the curve \( y = \frac{1}{x} \) from \( x = 1 \) to \( x = 2 \) u\sing integration.
A. \( \log 2 - \log 1 \)
B. \( \frac{1}{2} \log 2 \)
C. \( \frac{1}{2} \log 1 \)
D. \( \log 1 - \log 2 \)
Question 15
In a right-angled triangle, the length of the hypotenuse is 10cm and one of the acute angles is 30°. Find the length of the side opposite the 30° angle.
A. 5cm
B. 10cm
C. 15cm
D. 20cm

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