POST UTME FUTO 2019 Mathematics | Objective

Practice these randomly selected questions to test your readiness.

Question 1
Solve the quadratic equation: \( x^2 + 4x + 4 = 0 \).
A. \( x = - 2 \)
B. \( x = 2 \)
C. \( x = - 1 \)
D. \( x = 1 \)
Question 2
A sequence is defined by $a_n = 2n + 1$. Find the sum of the first 5 terms of the sequence.
A. 30
B. 35
C. 40
D. 45
Question 3
A bag contains 5 red marbles, 4 blue marbles, and 3 green marbles. If a marble is drawn at random, what is the probability that it is blue?
A. \frac{1}{3}
B. \frac{1}{4}
C. \frac{1}{5}
D. \frac{1}{6}
Question 4
Solve the quadratic equation [ x^2 + 4x + 4 = 0 ].
A. x = -2
B. x = 2
C. x = -1
D. x = 1
Question 5
Solve the equation \( x^2 - 6x + 8 = 0 \) u\sing the quadratic formula.
A. \( x = 2 \) or \( x = 4 \)
B. \( x = 1 \) or \( x = 7 \)
C. \( x = 3 \) or \( x = 5 \)
D. \( x = -2 \) or \( x = -4 \)
Question 6
Find the area under the curve y = \( \frac{1}{x} \) from x = 1 to x = 2.
A. 0.5
B. 1
C. 1.5
D. 2
Question 7
A random sample of 25 students from a university had a mean height of 175.6 cm with a s\tandard deviation of 5.8 cm. If the population s\tandard deviation is unknown, calculate the 95% confidence interval for the mean height of all students in the university.
A. 173.4 cm, 177.8 cm
B. 174.2 cm, 176.9 cm
C. 175.2 cm, 175.9 cm
D. 173.9 cm, 177.3 cm
Question 8
A right-angled triangle has a hypotenuse of 10 cm and one leg of 6 cm. Find the length of the other leg.
A. 8
B. 6
C. 4
D. 2
Question 9
A die is rolled. Find the probability that the number obtained is a multiple of 3 or 5.
A. \( \frac{1}{3} \)
B. \( \frac{1}{6} \)
C. \( \frac{1}{2} \)
D. \( \frac{2}{3} \)
Question 10
A set of 5 numbers has a mean of 10 and a s\tandard deviation of 2. If the numbers are 8, 12, 15, 18, and x, find the value of x.
A. 22
B. 24
C. 26
D. 28
Question 11
Find the vector ( mathbf{a} ) such that \( mathbf{a} cdot mathbf{i} = 3 \), \( mathbf{a} cdot mathbf{j} = -2 \), and \( mathbf{a} cdot mathbf{k} = 1 \).
A. \( mathbf{a} = 3mathbf{i} - 2mathbf{j} + mathbf{k} \)
B. \( mathbf{a} = 3mathbf{i} + 2mathbf{j} - mathbf{k} \)
C. \( mathbf{a} = -3mathbf{i} + 2mathbf{j} - mathbf{k} \)
D. \( mathbf{a} = 3mathbf{i} - 2mathbf{j} - mathbf{k} \)
Question 12
Find the equation of the circle with center \( C\( -2, 3 \ \) ) and radius \( r = \sqrt{10} \).
A. \( x+2 \ \)^2 + \( y-3 \)^2 = 10 )
B. \( x-2 \ \)^2 + \( y+3 \)^2 = 10 )
C. \( x+2 \ \)^2 + \( y+3 \)^2 = 10 )
D. \( x-2 \ \)^2 + \( y-3 \)^2 = 10 )
Question 13
A line passes through the points (2, 3) and (4, 5). Find the equation of the line in slope-intercept form.
A. y = 1x + 1
B. y = 2x - 1
C. y = 3x + 2
D. y = 4x - 3
Question 14
Find the determinant of the matrix [ egin{pmatrix} 2 & 3 & 1 \ 4 & 2 & 3 \ 1 & 2 & 4 \end{pmatrix} ].
A. 0
B. 10
C. 15
D. 20
Question 15
Find the equation of the circle with centre \( -2, 3 \) 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 )

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