POST UTME FUTO 2019 Mathematics | Objective

Practice these randomly selected questions to test your readiness.

Question 1
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 2
A circle has an equation of the form x^2 + y^2 + Dx + Ey + F = 0. If the circle passes through the points (1, 2) and (2, 1), find the equation of the circle.
A. x^2 + y^2 - 2x - 2y + 1 = 0
B. x^2 + y^2 - 2x + 2y + 1 = 0
C. x^2 + y^2 + 2x - 2y + 1 = 0
D. x^2 + y^2 + 2x + 2y + 1 = 0
Question 3
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 = 4 )
C. \( x - 2 \ \)^2 + \( y - 3 \)^2 = 9 )
D. \( x - 2 \ \)^2 + \( y - 3 \)^2 = 25 )
Question 4
Solve the system of equations: \( egin{cases} x + y = 2 \ 2x - 3y = - 1 \end{cases} \).
A. \( x = \frac{5}{7}, y = \frac{16}{7} \)
B. \( x = \frac{3}{7}, y = \frac{13}{7} \)
C. \( x = \frac{5}{7}, y = \frac{13}{7} \)
D. \( x = \frac{3}{7}, y = \frac{16}{7} \)
Question 5
Solve the inequality \( \frac{x}{x+1} > \frac{2x}{x-1} \) for ( x in mathbb{R} setminus {1} ).
A. \( x < -1 \)
B. \( x > 1 \)
C. \( x in \( -1, 1 \ \) cup (1, infty) )
D. \( x in \( -infty, -1 \ \) cup (1, infty) )
Question 6
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 7
Solve the equation \( 2^x + 2^{x+1} = 2^{x+2} \) for x.
A. 0
B. -1
C. 1
D. 2
Question 8
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 9
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 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 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 = 4 )
C. \( x - 2 \ \)^2 + \( y - 3 \)^2 = 9 )
D. \( x - 2 \ \)^2 + \( y - 3 \)^2 = 25 )
Question 12
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 13
A circle has a radius of 4 cm. Find the area of the circle.
A. 50.24 cm^2
B. 50.27 cm^2
C. 50.00 cm^2
D. 50.32 cm^2
Question 14
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 )
Question 15
In a triangle $ABC$, if $\tan A = \frac{1}{3}$ and $\tan B = \frac{1}{2}$, find $\tan C$.
A. \frac{11}{13}
B. \frac{13}{11}
C. \frac{13}{11}
D. \frac{11}{13}

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