POST UTME LEAD CITY UNIVERSITY 2019 Mathematics | Objective

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Question 1 View Details
Find the equation of the circle with centre at ((2,3)) and radius (5).
Correct A. \(x-2 \\)^2 + \(y-3\)^\(2 = 25\) )
B. \(x+2 \\)^2 + \(y-3\)^\(2 = 25\) )
C. \(x-2 \\)^2 + \(y+3\)^\(2 = 25\) )
D. \(x+2 \\)^2 + \(y+3\)^\(2 = 25\) )

Correct Answer: A

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Question 2 View Details
If (y = \(\frac{1}{x}\)\), find \\((y = frac{1}{x}\(\frac{dy}{dx}\) at \(x = 2\).
A. \(-\frac{1}{4}\)
Correct B. \(\frac{1}{4}\)
C. \(-\frac{1}{2}\)
D. \(\frac{1}{2}\)

Correct Answer: B

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Question 3 View Details
Solve the system of equations using matrices: [ egin{cases} \(2x + 3y = 7\) \\(x - 2y = -3\)\end{cases} ]
Correct A. \(x = 1, y = 2\)
B. \(x = 2, y = 1\)
C. \(x = 3, y = 4\)
D. \(x = 4, y = 3\)

Correct Answer: A

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Question 4 View Details
Find the area of the triangle with vertices ( A(1,2) ), ( B(3,4) ), and ( C(2,1) ).
A. ( 5 )
B. ( 10 )
Correct C. ( 15 )
D. ( 20 )

Correct Answer: C

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Question 5 View Details
A fair six-sided die is rolled. What is the probability that the number rolled is greater than 4?
A. \(\frac{1}{6}\)
B. \(\frac{1}{3}\)
C. \(\frac{2}{3}\)
Correct D. \(\frac{5}{6}\)

Correct Answer: D

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Question 6 View Details
Find the area under the curve \(y = \frac{1}{2}x^2 + 3x - 4\) from \(x = 0\) to \(x = 2\).
A. 10
B. 12
Correct C. 14
D. 16

Correct Answer: C

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Question 7 View Details
Solve for ( x ) in the equation \(2^x + 5^x = 7^x\).
A. 1
B. 2
Correct C. 3
D. 4

Correct Answer: C

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Question 8 View Details
A cylindrical \tank with a radius of 4m and a height of 10m is filled with water. Find the volume of water in the \tank.
A. 800\pi
Correct B. 1000\pi
C. 1200\pi
D. 1500\pi

Correct Answer: B

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Question 9 View Details
Find the derivative of the function ( f(x) = \(3x^2 + 2x - 5\) ).
Correct A. 6x + 2
B. \(3x^2 + 2\)
C. 6x - 2
D. \(3x^2 - 2\)

Correct Answer: A

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Question 10 View Details
A rectangular prism with a length of 5m, a width of 3m, and a height of 2m is placed on a table. Find the surface area of the prism.
A. 62
Correct B. 64
C. 66
D. 68

Correct Answer: B

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Question 11 View Details
In a circle of radius 8 cm, a chord of length 12 cm subtends an angle of 60° at the centre. Find the area of the sector.
A. 48π cm²
Correct B. 64π cm²
C. 72π cm²
D. 80π cm²

Correct Answer: B

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Question 12 View Details
A matrix A has the following form: [\(A =\)egin{bmatrix} 2 & 1 & 3 \ 4 & 3 & 5 \ 6 & 2 & 1 \end{bmatrix} ]. Find the determinant of A.
Correct A. 0
B. 1
C. 2
D. 3

Correct Answer: A

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Question 13 View Details
A histogram represents the distribution of exam scores of 20 students. The scores are: 40, 50, 60, 70, 80, 90, 100, 110, 120, 130, 140, 150, 160, 170, 180, 190, 200, 210, 220, 230. Find the mean of the scores.
A. 100
B. 110
Correct C. 120
D. 130

Correct Answer: C

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Question 14 View Details
A rectangular prism has a length of 10 cm, a width of 5 cm, and a height of 8 cm. Find the volume of the prism.
A. 400 cm³
B. 500 cm³
C. 600 cm³
Correct D. 800 cm³

Correct Answer: D

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Question 15 View Details
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.
Correct A. 5 cm
B. 7.5 cm
C. 10 cm
D. 12.5 cm

Correct Answer: A

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Question 16 View Details
Let \(\mathbf{a} = egin{pmatrix} 2 \ 3 \end{pmatrix}\) and \(\mathbf{b} = egin{pmatrix} 4 \ 5 \end{pmatrix}\). Find the projection of ( mathbf{b} ) onto ( mathbf{a} ).
Correct A. \(egin{pmatrix} 0.8 \ 1.2 \end{pmatrix}\)
B. \(egin{pmatrix} 1.2 \ 1.8 \end{pmatrix}\)
C. \(egin{pmatrix} 0.4 \ 0.6 \end{pmatrix}\)
D. \(egin{pmatrix} 1.6 \ 2.4 \end{pmatrix}\)

Correct Answer: A

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Question 17 View Details
Solve the trigonometric equation \(\sin^2 x + \cos^2 x = 1\) for ( x ) in the interval ( [0, 2pi] ).
Correct A. \(x = \frac{\pi}{4}\)
B. \(x = \frac{\pi}{2}\)
C. \(x = \frac{3\pi}{4}\)
D. \(x = \frac{5\pi}{4}\)

Correct Answer: A

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Question 18 View Details
Find the sum of the first 10 terms of the geometric series \(2x^2 + 4x^3 + 8x^4 + ldots\).
Correct A. \(2048x^{20}\)
B. \(1024x^{20}\)
C. \(512x^{20}\)
D. \(256x^{20}\)

Correct Answer: A

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Question 19 View Details
A fair six-sided die is rolled. What is the probability that the number rolled is greater than 4?
A. \(\frac{1}{6}\)
B. \(\frac{1}{3}\)
C. \(\frac{2}{3}\)
Correct D. \(\frac{5}{6}\)

Correct Answer: D

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Question 20 View Details
Find the derivative of the function ( f(x) = \(3x^2\) \sin x ) using the product rule.
A. \(6x \(1x + 3x^2\)1x\)
Correct B. \(3x^2 \(1x + 6x\)1x\)
C. \(6x^2 \(1x + 3x\)1x\)
D. \(3x^2 \(1x + 6x\)1x\)

Correct Answer: B

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Question 21 View Details
Find the determinant of the matrix [ egin{pmatrix} 2 & 3 & 1 \ 4 & 2 & 3 \ 1 & 2 & 4 \end{pmatrix} ].
A. 4
Correct B. -2
C. 6
D. 8

Correct Answer: B

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Question 22 View Details
A coin is tossed three times. What is the probability that at least two of the tosses result in heads?
A. \(1/4\)
B. \(1/2\)
Correct C. \(3/4\)
D. \(7/8\)

Correct Answer: C

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Question 23 View Details
The equation of a circle is given by \(x^2 + y^2 = 16\). Find the equation of the line that passes through the point ( (4, 0) ) and is perpendicular to the given circle.
Correct A. \(x + y = 4\)
B. \(x - y = 4\)
C. \(x + y = 8\)
D. \(x - y = 8\)

Correct Answer: A

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Question 24 View Details
Simplify the expression \(\frac{3x^2 + 2x - 1}{2x^2 - 5x + 1}\).
Correct A. x + 1
B. x - 1
C. 3x - 2
D. 2x + 1

Correct Answer: A

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Question 25 View Details
Find the value of ( x ) in the equation \(2^x + 5^x = 10^x\).
A. 1
Correct B. 2
C. 3
D. 4

Correct Answer: B

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