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UTME 2020 Mathematics | Objective

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Question 1 View Details

Find T in terms of K, Q and S if S=\(2r\sqrt{\pi(QT+K)}\)

A. \( \frac{S^2}{2\pi r^2 Q} - \frac{K}{Q} \)

B. \( \frac{S^2}{2\pi r^2 Q} - K \)

Correct C. \( \frac{S^2}{4\pi r^2 Q} - \frac{K}{Q} \)

D. \( \frac{S^2}{2\pi r^2 Q} \)

Correct Answer: C

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Question 2 View Details

The graph of f(x) = \( x^2 \) - 5x + 6 crosses the x-axis at the points:

A. (-6,0), (-1,0)

B. (-3,0), (-2,0)

C. (-6,0), (1,0)

Correct D. (2,0), (3,0)

Correct Answer: D

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Question 3 View Details

Factorize completely the expression \( abx^2 \) + 6y - 3ax - 2byx.

Correct A. (ax - 2y)(bx - 3)

B. (bx + 3)(2y - ax)

C. (bx + 3)(ax - 2y)

D. (ax - 2y)(ax - b)

Correct Answer: A

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Question 4 View Details

Solve the following inequality (x-3)(x-4) ≤ 0

Correct A. 3 ≤ x ≤ 4

B. 3

C. 3 ≤ x<4

D. 3

Correct Answer: A

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Question 5 View Details

The 4th term of an A.P. is 13 while the 10th term is 31. Find the 21st term.

A. 175

B. 85

Correct C. 64

D. 45

Correct Answer: C

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Question 6 View Details

Simplify \( \frac{x^2 -1}{ x^2 + 2x^2 - x - 2} \)

A. \( \frac{1}{x-1} \)

Correct B. \( \frac{x-1}{x+1} \)

C. \( \frac{x-1}{x+2} \)

D. \( \frac{1}{x-2} \)

Correct Answer: B

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Question 7 View Details

Express \( \frac{5x-12}{(x-2)(x-3)} \) in partial fractions

A. \( \frac{2}{x+2} \) + \( \frac{3}{x-3} \)

Correct B. \( \frac{2}{x-2} \) + \( \frac{3}{x-3} \)

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

D. \( \frac{5}{x-3} \)-\( \frac{4}{x-2} \)

Correct Answer: B

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Question 8 View Details

If \( (1P03)_4 = 115_{10} \) find P.

A. 2

Correct B. 3

C. 4

D. 5

Correct Answer: B

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Question 9 View Details

Evaluate \( 64.764^{2} -35. 236^{2} \) correct to 3 significant figures.

A. 2960

Correct B. 2950

C. 2860

D. 2850

Correct Answer: B

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Question 10 View Details

Find the value of \( (0.006)^{3} + (0.0004)^{3} \) in standard form

Correct A. \( 2.8 \times 10^{-9} \)

B. \( 2.8 \times 10^{-7} \)

C. \( 2.8 \times 10^{-5} \)

D. \( 2.8 \times 10^{-6} \)

Correct Answer: A

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Question 11 View Details

Given that \( \log_a 2 \) = 0.693 and \( \log_a 3 \) = 1.097, find \( \log_a 13.5 \).

A. 1.404

Correct B. 1.790

C. 2.598

D. 2.790

Correct Answer: B

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Question 12 View Details

Simplify \( \log_2 96 - 2\log_2 6 \)

A. \( 2 - \log_2 3 \)

Correct B. \( 3 - \log_2 3 \)

C. \( \log_2 3 - 3 \)

D. \( \log_2 3 - 2 \)

Correct Answer: B

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Question 13 View Details

If 8=(\( 2^{2x} \))(\( 4^{x} \)), find x.

A. \( \frac{3}{8} \)

Correct B. \( \frac{3}{4} \)

C. \( \frac{4}{5} \)

D. \( \frac{5}{4} \)

Correct Answer: B

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Question 14 View Details

TQ is tangent to circle XYTR, DYXT=\( 32^\circ \), RTQ= \( 40^\circ \). Find DYTR.

A. \( 108^\circ \)

Correct B. \( 121^\circ \)

C. \( 140^\circ \)

D. \( 148^\circ \)

Correct Answer: B

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Question 15 View Details

A chord of a circle radius √3 cm subtends an angle of 60° on the circumference of the circle. Find the length of the chord.

A. \( \frac{ \sqrt{3} }{2} \)

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

C. 3

Correct D. √3 cm

Correct Answer: D

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Question 16 View Details

A cylindrical drum of diameter 56 cm contains 123.2 litres of oil when full. Find the height of the drum in centimetres. ( \(\pi\) = \( \frac{22}{7} \))

A. 12.5

Correct B. 25.0

C. 45.0

D. 50.00

Correct Answer: B

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Question 17 View Details

The locus of all points at a distance 8 cm from a point N passes through points T and S. If S is equidistant from T and N, find the area of triangle STN.

A. \( 4 \sqrt{3} cm^{2} \)

Correct B. \( 16 \sqrt{3} cm^{2} \)

C. \( 32 cm^{2} \)

D. \( 64 cm^{2} \)

Correct Answer: B

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Question 18 View Details

If the distance between the points (x, 3) and (-x, 2) is 5. Find x.

A. 6,0

B. 2,5

Correct C. \( \sqrt{6} \)

D. \( \sqrt{3} \)

Correct Answer: C

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Question 19 View Details

The sum of two numbers is twice their difference. If the difference of the numbers is p, find the larger of the two numbers.

A. \( \frac{P}{2} \)

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

C. \( \frac{5P}{2} \)

D. 3P

Correct Answer: B

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Question 20 View Details

The first term of a geometrical progression is twice its common ratio. Find the sum of the first two terms of the progression if its sum to infinity is 8.

A. \( \frac{8}{5} \)

B. \( \frac{8}{3} \)

C. \( \frac{72}{25} \)

Correct D. \( \frac{56}{9} \)

Correct Answer: D

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Question 21 View Details

\( \text{If m * n} = \frac{n}{m} - \frac{m}{n} \) \( \text{for m, n} \in R \), evaluate -3 * 4.

A. \( \frac{-25}{12} \)

Correct B. \( \frac{-7}{12} \)

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

D. \( \frac{25}{12} \)

Correct Answer: B

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Question 22 View Details

A binary operation * is defined by a*b=ab+a+b for any real number a and b. If the identity element is zero, find the inverse of 2 under this operation.

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

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

C. -\( \frac{1}{2} \)

Correct D. -\( \frac{2}{3} \)

Correct Answer: D

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Question 23 View Details

Find the matrix T if ST=I where S= \( \begin{pmatrix}-1 & 1 \\ 0 & 1 \end{pmatrix} \) and I is the identity matrix.

A. \( \begin{pmatrix}-2 & 1 \\ 1 & 1\end{pmatrix} \)

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

Correct C. \( \begin{pmatrix}-1 & -1 \\ 0 & -1\end{pmatrix} \)

D. \( \begin{pmatrix}-1 & 1 \\ 0 & 1\end{pmatrix} \)

Correct Answer: C

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Question 24 View Details

Given that Q= \( \begin{pmatrix}6 & 0 \\ 4 & 5\end{pmatrix} \) and Q+P= \( \begin{pmatrix}7 & -2 \\ 6 & 8\end{pmatrix} \) evaluate |Q+2P|

A. 90

B. 96

C. 102

Correct D. 120

Correct Answer: D

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Question 25 View Details

Find the locus of a particle which moves in the first quadrant so that it is equidistant from the lines x=0 and y=0 (where k is a constant).

A. x+y=0

Correct B. x-y=0

C. x+y+k=0

D. x-y-k=0

Correct Answer: B

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