Practice Post UTME ACHIEVERS UNIVERSITY mathematics 2023 Past Questions

Question 1 View Details

In the coordinate plane, the equation of a circle is given by \(x - h \\)^2 + \(y - k\)^\(2 = r\^2\) ). If the center of the circle is at ( (h,\(k) = (3\), 4) ) and the radius is 5 units, what is the equation of the circle?

Correct A. \(x - 3 \\)^2 + \(y - 4\)^\(2 = 25\) )

B. \(x - 4 \\)^2 + \(y - 3\)^\(2 = 25\) )

C. \(x - 3 \\)^2 + \(y - 3\)^\(2 = 25\) )

D. \(x - 4 \\)^2 + \(y - 4\)^\(2 = 25\) )

Correct Answer: A

Want to see the full step-by-step solution? Unlock AI Explanation & Analytics

Question 2 View Details

Solve for ( x ) in the equation \(\frac{1}{2}x + 3 = \frac{3}{4}x - 2\).

Correct A. \(x = -\frac{14}{5}\)

B. \(x = \frac{14}{5}\)

C. \(x = -\frac{7}{5}\)

D. \(x = \frac{7}{5}\)

Correct Answer: A

Want to see the full step-by-step solution? Unlock AI Explanation & Analytics

Question 3 View Details

Find the determinant of the matrix \(egin{bmatrix} 2 & 3 & 4 \ 5 & 6 & 7 \ 8 & 9 & 10 \end{bmatrix}\).

Correct A. ( 0 )

B. ( 1 )

C. \(-1\)

D. ( 2 )

Correct Answer: A

Want to see the full step-by-step solution? Unlock AI Explanation & Analytics

Question 4 View Details

A bakery sells a total of 250 loaves of bread per day. They sell a combination of whole wheat and white bread. If the ratio of whole wheat to white bread is 5:3, how many loaves of white bread are sold per day?

A. ( 90 )

Correct B. ( 100 )

C. ( 110 )

D. ( 120 )

Correct Answer: B

Want to see the full step-by-step solution? Unlock AI Explanation & Analytics

Question 5 View Details

In a right-angled triangle, the length of the hypotenuse is 10 cm and one of the other sides is 6 cm. What is the length of the third side?

A. ( 8 ) cm

Correct B. \(6 \sqrt{5}\) cm

C. \(8 \sqrt{5}\) cm

D. ( 10 ) cm

Correct Answer: B

Want to see the full step-by-step solution? Unlock AI Explanation & Analytics

Question 6 View Details

Let \(\mathbf{a} = egin{pmatrix} 2 \ 3 \end{pmatrix}\) and \(\mathbf{b} = egin{pmatrix} -1 \ 4 \end{pmatrix}\). Find the projection of ( mathbf{b} ) onto ( mathbf{a} ).

Correct A. 0.8

B. -0.6

C. 0.6

D. 1.2

Correct Answer: A

Want to see the full step-by-step solution? Unlock AI Explanation & Analytics

Question 7 View Details

Find the derivative of ( f(x) = \(\frac{1}{x^2 + 1}\)\)\) ) using the chain rule.

Correct A. -2x/\(x^2 + 1\)^2

B. 2x/\(x^2 + 1\)^2

C. -x/\(x^2 + 1\)^2

D. x/\(x^2 + 1\)^2

Correct Answer: A

Want to see the full step-by-step solution? Unlock AI Explanation & Analytics

Question 8 View Details

Solve the inequality \(2x^2 + 5x - 3 > 0\).

Correct A. \(-∞, -1\) ∪ (3, ∞)

B. \(-∞, -3\) ∪ (1, ∞)

C. \(-∞, 1\) ∪ (3, ∞)

D. \(-∞, -3\) \cup \(-1, ∞\)\)

Correct Answer: A

Want to see the full step-by-step solution? Unlock AI Explanation & Analytics

Question 9 View Details

Find the mean of the following data set: 2, 4, 6, 8, 10.

Correct A. 6

B. 5

C. 7

D. 8

Correct Answer: A

Want to see the full step-by-step solution? Unlock AI Explanation & Analytics

Question 10 View Details

A fair six-sided die is rolled. What is the probability that the number rolled is greater than 4?

Correct A. \(\frac{1}{3}\)\)

B. \(\frac{1}{2}\)\)

C. \(\frac{2}{3}\)\)

D. \(\frac{1}{6}\)\)

Correct Answer: A

Want to see the full step-by-step solution? Unlock AI Explanation & Analytics

Question 11 View Details

Let \(\mathbf{a} = egin{pmatrix} 2 \ 3 \end{pmatrix}\) and \(\mathbf{b} = egin{pmatrix} 1 \ -2 end{pmatrix}\). Find the projection of ( mathbf{b} ) onto ( mathbf{a} ) using the formula \(\\(end{pmatrix}). Find the projection of ( mathbf{b} ) onto ( mathbf{a} ) using the formula \mathrm{proj}_{\mathbf{a}} \mathbf{b} \\) = \(\frac{\mathbf{a} \cdot \mathbf{b}}{|\mathbf{a}|^2}\) mathbf{a} ).

Correct A. \begin{pmatrix} \(\frac{7}{13}\)\) \\ \(\frac{12}{13}\)\) \end{pmatrix}

B. \begin{pmatrix} \(\frac{1}{13}\)\) \\ -\(\frac{2}{13}\)\) \end{pmatrix}

C. \begin{pmatrix} \(\frac{2}{13}\)\) \\ -\(\frac{3}{13}\)\) \end{pmatrix}

D. \begin{pmatrix} \(\frac{3}{13}\)\) \\ -\(\frac{4}{13}\)\) \end{pmatrix}

Correct Answer: A

Want to see the full step-by-step solution? Unlock AI Explanation & Analytics

Question 12 View Details

Find the area under the curve \(y = x^2 - 2x + 1\) from \(x = 0\) to \(x = 2\) using the definite integral.

A. \(\frac{1}{3}\)\)

B. \(\frac{2}{3}\)\)

Correct C. \(\frac{3}{2}\)\)

D. \(\frac{4}{3}\)\)

Correct Answer: C

Want to see the full step-by-step solution? Unlock AI Explanation & Analytics

Question 13 View Details

Solve the inequality \(2x^2 + 5x - 3 > 0\) using the quadratic formula.

A. \left\(-\frac{5}{4}, \frac{3}{2} \right\)

B. \left\(-\frac{3}{2}, \frac{5}{4} \right\)

Correct C. \left\(-\infty, -\frac{3}{2} \right\) \cup \left\(\frac{5}{4}, \infty \right\)

D. \left\(-\infty, \frac{5}{4} \right\) \cup \left\(-\frac{3}{2}, \infty \right\)

Correct Answer: C

Want to see the full step-by-step solution? Unlock AI Explanation & Analytics

Question 14 View Details

Find the value of ( x ) in the equation \(2^x + 3^x = 5^x\).

A. 1

Correct B. 2

C. 3

D. 4

Correct Answer: B

Want to see the full step-by-step solution? Unlock AI Explanation & Analytics

Question 15 View Details

Solve the system of linear equations \(egin{cases} 2x + 3y = 7 \ 4x - 2y = -3 \end{cases}\) using substitution or elimination.

Correct A. \left\(x, y \right\) = \left\(1, 2 \right\)

B. \left\(x, y \right\) = \left\(2, 1 \right\)

C. \left\(x, y \right\) = \left\(3, -1 \right\)

D. \left\(x, y \right\) = \left\(-1, 3 \right\)

Correct Answer: A

Want to see the full step-by-step solution? Unlock AI Explanation & Analytics

Question 16 View Details

Let X and Y be independent random variables with probability density functions f_\(X(x) = 2x\), \(0 < x\)\(< 1\), and f_\(Y(y) =\)\(3y^2\),\((0 < y\)\) < 1. Find the probability that \(X + Y < 1\\((0 < y) < 1. Find the probability that\).

A. \(1/3\)

B. \(1/4\)

Correct C. \(1/2\)

D. \(2/3\)

Correct Answer: C

Want to see the full step-by-step solution? Unlock AI Explanation & Analytics

Question 17 View Details

Find the derivative of the function f(x) = \(\frac{\sin(x)}{x^2}\)\)\) using the chain rule.

Correct A. \(\frac{\cos(x)}{x^2}\)\)\) - \(\frac{2\sin(x)}{x^3}\)\)\)

B. \(\frac{\cos(x)}{x^2}\)\)\) + \(\frac{2\sin(x)}{x^3}\)\)\)

C. \(\frac{\cos(x)}{x^2}\)\)\) - \(\frac{\sin(x)}{x^3}\)\)\)

D. \(\frac{\cos(x)}{x^2}\)\)\) + \(\frac{\sin(x)}{x^3}\)\)\)

Correct Answer: A

Want to see the full step-by-step solution? Unlock AI Explanation & Analytics

Question 18 View Details

Solve the system of linear equations using the method of substitution: \(x + y = 2\) and \(x - y = 1\).

Correct A. \(x = 1\), \(y = 1\)

B. \(x = 1\),\(y = -1\)

C. \(x = -1\), \(y = 1\)

D. \(x = -1\),\(y = -1\)

Correct Answer: A

Want to see the full step-by-step solution? Unlock AI Explanation & Analytics

Question 19 View Details

Find the area under the curve \(y = x\^2\) from \(x = 0\) to \(x = 1\) using integration.

A. \(1/3\)

Correct B. \(1/2\)

C. \(2/3\)

D. 1

Correct Answer: B

Want to see the full step-by-step solution? Unlock AI Explanation & Analytics

Question 20 View Details

Let A = \begin{pmatrix} 1 & 2 \ 3 & 4 \end{pmatrix} and B = \begin{pmatrix} 5 & 6 \ 7 & 8 \end{pmatrix}. Find the product AB.

Correct A. \begin{pmatrix} 19 & 22 \ 43 & 50 \end{pmatrix}

B. \begin{pmatrix} 23 & 26 \ 47 & 54 \end{pmatrix}

C. \begin{pmatrix} 17 & 20 \ 39 & 46 \end{pmatrix}

D. \begin{pmatrix} 21 & 24 \ 41 & 48 \end{pmatrix}

Correct Answer: A

Want to see the full step-by-step solution? Unlock AI Explanation & Analytics

Question 21 View Details

Solve the quadratic equation \\((x^2 + 4x + 4\)\(= 0\)\) using the quadratic formula.

Correct A. \(x = -2\)

B. \(x = -1\)

C. \(x = 1\)

D. \(x = 2\)

Correct Answer: A

Want to see the full step-by-step solution? Unlock AI Explanation & Analytics

Question 22 View Details

Find the derivative of the function f(x) = \sin\(x^2\) using the chain rule.

Correct A. 2x \cos\(x^2\)

B. \(x^2\) \cos\(x^2\)

C. x \cos\(x^2\)

D. \cos\(x^2\)

Correct Answer: A

Want to see the full step-by-step solution? Unlock AI Explanation & Analytics

Question 23 View Details

Let X and Y be independent random variables with probability density functions f_\(X(x) = 2x\), \(0 < x\)\(< 1\), and f_\(Y(y) =\)\(3y^2\),\((0 < y\)\) < 1. Find the probability that \(X + Y < 1\\((0 < y) < 1. Find the probability that\).

A. \(1/3\)

B. \(1/4\)

Correct C. \(1/2\)

D. \(2/3\)

Correct Answer: C

Want to see the full step-by-step solution? Unlock AI Explanation & Analytics

Question 24 View Details

Let ( X ) and ( Y ) be independent random variables with probability density functions \(f_X x \\) = egin{cases} 2x & 0 leq x leq 1 \ 0 & \text{otherwise} \end{cases} ) and \(f_Y y \\) = egin{cases} \(3y^2\) & 0 leq y leq 1 \ 0 & text{otherwise} \end{cases} ). Find the probability that \(X + Y \\(text{otherwise} end{cases} ). Find the probability that \leq 1\).

Correct A. \(\frac{5}{12}\)

B. \(\frac{1}{3}\)

C. \(\frac{2}{3}\)

D. \(\frac{7}{12}\)

Correct Answer: A

Want to see the full step-by-step solution? Unlock AI Explanation & Analytics

Question 25 View Details

Find the equation of the line passing through the points ( (2,3) ) and ( (4,5) ).

Correct A. \(y = \frac{1}{2}x + \frac{1}{2}\)

B. \(y = \frac{1}{2}x - \frac{1}{2}\)

C. \(y = 2x - 1\)

D. \(y = 2x + 1\)

Correct Answer: A

Want to see the full step-by-step solution? Unlock AI Explanation & Analytics

POST UTME ACHIEVERS UNIVERSITY 2023 Mathematics | Objective

Master the Exam!

Help others prepare! Share this practice hub: