POST UTME LAUTECH 2019 Mathematics | Objective

Practice these randomly selected questions to test your readiness.

Question 1
Solve the system of equations: \begin{align*} x + y + z &= 3 \ x + 2y + 3z &= 6 \ x + 3y + 5z &= 10 \end{align*}
A. \begin{pmatrix} 1 \ 2 \ 3 \end{pmatrix}
B. \begin{pmatrix} 2 \ 3 \ 4 \end{pmatrix}
C. \begin{pmatrix} 3 \ 4 \ 5 \end{pmatrix}
D. \begin{pmatrix} 4 \ 5 \ 6 \end{pmatrix}
Question 2
A random experiment consists of rolling a fair six-sided die and then tos\sing a fair coin. If the number on the die is even, the coin is tossed twice. Otherwise, the coin is tossed only once. What is the probability that the number of heads obtained is odd?
A. \frac{1}{4}
B. \frac{1}{2}
C. \frac{3}{4}
D. \frac{5}{8}
Question 3
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 - 16}}{2}
D. \\frac{-4 \\pm \\sqrt{16 + 16}}{2}
Question 4
Find the derivative of the function ( f(x) = x^3 - 2x^2 + x - 1 ) u\sing the power rule.
A. 3x^2 - 4x + 1
B. 3x^2 - 4x - 1
C. 3x^2 + 4x + 1
D. 3x^2 + 4x - 1
Question 5
Solve the inequality \( x^2 + 4x - 5 > 0 \).
A. \( -∞, -5 \) ∪ (1, ∞)
B. \( -∞, -1 \) ∪ (5, ∞)
C. \( -∞, 1 \) ∪ (5, ∞)
D. \( -∞, 5 \) ∪ (1, ∞)
Question 6
A right triangle has a base of 5 cm and a height of 12 cm. Find the length of the hypotenuse.
A. \sqrt{5^2 + 12^2}
B. \sqrt{5^2 - 12^2}
C. \sqrt{5^2 + 12^2}
D. \sqrt{5^2 - 12^2}
Question 7
Find the derivative of the function f(x) = \sin(x) + 2x.
A. \cos(x) + 2
B. \sin(x) + 2
C. 2x + 1
D. x^2 + 2
Question 8
Find the determinant of the matrix \( egin{bmatrix} 2 & 3 \ 4 & 5 \end{bmatrix} \).
A. 1
B. -1
C. 2
D. 5
Question 9
A set of 5 numbers has an average of 12. If the largest number is 25, find the sum of the remaining 4 numbers.
A. 40
B. 45
C. 50
D. 55
Question 10
Find the value of x in the equation \( x^2 + 2x - 3 = 0 \).
A. 1
B. -1
C. 3
D. -3
Question 11
A water \tank has a height of 10 m and a base radius of 4 m. Find the volume of water in the \tank.
A. \frac{1}{3} \pi (4)^2 (10)
B. \frac{1}{3} \pi (4)^3 (10)
C. \frac{1}{3} \pi (4)^2 (5)
D. \frac{1}{3} \pi (4)^3 (5)
Question 12
If \sin(x) = 3/5 and \cos(x) = 4/5, find the value of \tan(x).
A. 3/4
B. 4/3
C. 12/5
D. 5/12
Question 13
Find the area under the curve \( y = \frac{1}{2}x^2 + 2x - 3 \) from \( x = 0 \) to \( x = 2 \).
A. 4
B. 6
C. 8
D. 10
Question 14
Solve the inequality \( x^2 - 6x + 8 < 0 \).
A. (2, 4)
B. (2, 6)
C. (4, 6)
D. (6, 8)
Question 15
Solve for x in the equation \( \log_{10} \( x^2 \ \) = 4 ).
A. 2
B. 4
C. 16
D. 64

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