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POST UTME CRAWFORD UNIVERSITY 2023 Mathematics | Objective

Practice these randomly selected questions to test your readiness.

Question 1

Solve the matrix equation \begin{bmatrix} 1 & 2 \ 3 & 4 \end{bmatrix} \begin{bmatrix} x \ y \end{bmatrix} = \begin{bmatrix} 3 \ 7 \end{bmatrix}.

A. \begin{bmatrix} x \ y \end{bmatrix} = \begin{bmatrix} 1 \ 2 \end{bmatrix}

B. \begin{bmatrix} x \ y \end{bmatrix} = \begin{bmatrix} 2 \ 1 \end{bmatrix}

C. \begin{bmatrix} x \ y \end{bmatrix} = \begin{bmatrix} 1 \ 1 \end{bmatrix}

D. \begin{bmatrix} x \ y \end{bmatrix} = \begin{bmatrix} 2 \ 2 \end{bmatrix}

Question 2

A binary operation ( odot ) is defined as $ a odot b = ab^2 $. Find the value of ( 2 odot 3 ).

A. 6

B. 12

C. 18

D. 24

Question 3

Find the area of the triangle with vertices (0, 0), (3, 0), and (0, 4).

A. 6

B. 12

C. 18

D. 24

Question 4

Find the derivative of the function ( f(x) = \frac{x^2 - 4x + 3}{x^2 + 2x + 1} ) u\sing the quotient rule.

A. ( f'(x) = \frac{$ 2x - 4 $$ x^2 + 2x + 1 $ - $ x^2 - 4x + 3 $$ 2x + 2 $}{$ x^2 + 2x + 1 $^2} )

B. ( f'(x) = \frac{$ 2x - 4 $$ x^2 + 2x + 1 $ - $ x^2 - 4x + 3 $$ 2x + 2 $}{$ x^2 + 2x + 1 $^3} )

C. ( f'(x) = \frac{$ 2x - 4 $$ x^2 + 2x + 1 $ + $ x^2 - 4x + 3 $$ 2x + 2 $}{$ x^2 + 2x + 1 $^2} )

D. ( f'(x) = \frac{$ 2x - 4 $$ x^2 + 2x + 1 $ + $ x^2 - 4x + 3 $$ 2x + 2 $}{$ x^2 + 2x + 1 $^3} )

Question 5

Find the value of x in the equation $ egin{bmatrix} 1 & 2 \ 3 & 4 \end{bmatrix} egin{bmatrix} x \ 1 \end{bmatrix} = egin{bmatrix} 7 \ 11 \end{bmatrix} $.

A. 3

B. 4

C. 5

D. 6

Question 6

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 7

Solve the equation $ \sin^2 x + \cos^2 x = 1 $ for ( x ) in the interval ( [0, 2 pi] ).

A. $ x = 0, pi, 2 pi $

B. $ x = \frac{pi}{2}, \frac{3 pi}{2} $

C. $ x = \frac{pi}{4}, \frac{3 pi}{4} $

D. $ x = \frac{pi}{6}, \frac{5 pi}{6} $

Question 8

Solve the inequality $ 2x^2 + 5x - 3 > 0 $ u\sing the quadratic formula.

A. $ x < -\frac{5}{2} $ or $ x > \frac{3}{2} $

B. $ x < -\frac{3}{2} $ or $ x > \frac{5}{2} $

C. $ x < -\frac{5}{2} $ or $ x < \frac{3}{2} $

D. $ x > -\frac{5}{2} $ or $ x < \frac{3}{2} $

Question 9

Find the area under the curve $ y = \frac{1}{x^2 + 1} $ from $ x = 0 $ to $ x = 1 $ u\sing integration by substitution.

A. $ \frac{pi}{4} - 1 $

B. $ \frac{pi}{4} + 1 $

C. $ \frac{pi}{4} - \frac{1}{2} $

D. $ \frac{pi}{4} + \frac{1}{2} $

Question 10

Solve the equation \sin(x) = 0.5 for 0 ≤ x ≤ 2π.

A. π/6

B. π/2

C. 5π/6

D. 3π/2

Question 11

A function $f(x)$ is defined as $f(x) = \sin(x) + \cos(x)$. What is the value of $f$ \frac{\pi}{4} $$?

A. \frac{1}{\sqrt{2}}

B. \frac{1}{2}

C. \frac{1}{4}

D. \frac{1}{8}

Question 12

Find the volume of the solid formed by rotating the region bounded by the curves $ y = x^2 $ and $ y = 2x $ about the x-axis.

A. $ \frac{4}{3} pi $

B. $ \frac{8}{3} pi $

C. $ \frac{16}{3} pi $

D. $ \frac{32}{3} pi $

Question 13

Solve the inequality $ \frac{x}{x-2} > 0 $ for $ x in \( -infty, infty \ $ ).

A. $ -infty, 2 $ \cup (2, infty)

B. $ -infty, 0 $ \cup (2, infty)

C. $ -infty, 0 $ \cup (0, 2)

D. $ -infty, 2 $ \cup (0, infty)

Question 14

Find the sum of the first 10 terms of the geometric series with first term 2 and common ratio 3/4.

A. 2047

B. 2048

C. 2049

D. 2050

Question 15

Solve the inequality $ 2x^2 + 5x - 3 > 0 $.

A. $ -∞, -1 $ ∪ (3, ∞)

B. $ -∞, -3 $ ∪ (1, ∞)

C. $ -∞, 1 $ ∪ (3, ∞)

D. $ -∞, -3 $ ∪ (1, ∞)

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POST UTME CRAWFORD UNIVERSITY 2023 Mathematics | Objective

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