POST UTME FUTO 2018 Mathematics | Objective

Practice these randomly selected questions to test your readiness.

Question 1
Solve the equation [ x^2 + 4x + 4 = 0 ].
A. x = -2
B. x = 2
C. x = -1
D. x = 1
Question 2
A fair six-sided die is rolled. What is the probability that the number obtained is greater than 4?
A. \( \frac{1}{6} \)
B. \( \frac{1}{2} \)
C. \( \frac{2}{3} \)
D. \( \frac{5}{6} \)
Question 3
Solve the inequality \( \log_{10} \( x^2 \ \) > 4 ).
A. \( x > 10 \)
B. \( x < 10 \)
C. \( x > 100 \)
D. \( x < 100 \)
Question 4
A circle with a radius of 4cm has a chord that is 6cm long. Calculate the dis\tance from the center of the circle to the midpoint of the chord.
A. 2
B. 3
C. 4
D. 5
Question 5
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 = 16 )
C. \( x + 2 \ \)^2 + \( y + 3 \)^2 = 16 )
D. \( x - 2 \ \)^2 + \( y - 3 \)^2 = 16 )
Question 6
Determine the volume of the frustum of a cone with height 6 cm, lower base radius 4 cm, and upper base radius 2 cm. The slant height of the frustum is 8 cm.
A. 48\pi
B. 64\pi
C. 80\pi
D. 96\pi
Question 7
A circle with center ( C(2, 3) ) and radius ( 4 ) has a chord ( AB ) of length ( 6 ). Find the dis\tance from the center ( C ) to the chord ( AB ).
A. \( 2 \sqrt{5} \)
B. \( \sqrt{5} \)
C. \( 2 \sqrt{3} \)
D. \( \sqrt{3} \)
Question 8
A vector (vec{a}) has magnitude 5 and direction 60°. Find the magnitude of the vector \( vec{a} + vec{b} \), where (vec{b}) is a vector with magnitude 3 and direction 120°.
A. 4
B. 5
C. 6
D. 7
Question 9
Solve for x in the equation \( 2x^2 + 5x - 3 = 0 \).
A. -1
B. 1
C. 2
D. 3
Question 10
Solve the system of equations \( egin{cases} x + y = 4 \ 2x - 3y = -1 \end{cases} \) u\sing matrices.
A. \( egin{pmatrix} 1 & 1 \ 2 & -3 \end{pmatrix} \)
B. \( egin{pmatrix} 1 & 2 \ 1 & -3 \end{pmatrix} \)
C. \( egin{pmatrix} 1 & 1 \ 2 & -1 \end{pmatrix} \)
D. \( egin{pmatrix} 1 & 1 \ 2 & 3 \end{pmatrix} \)
Question 11
If [ \overrightarrow{a} = \begin{pmatrix} 2 \ 3 \ 4 \end{pmatrix} \] and [ \overrightarrow{b} = \begin{pmatrix} 1 \ 2 \ 3 \end{pmatrix} \], find the value of [ \overrightarrow{a} \cdot \overrightarrow{b} \].
A. 25
B. 26
C. 27
D. 28
Question 12
A binary operation \(*\) on the set \{0, 1, 2\} is defined as follows: \begin{align*}\n0\*0&=0,\quad 0\*1=1,\quad 0\*2=2,\\n1\*0&=1,\quad 1\*1=0,\quad 1\*2=2,\\n2\*0&=2,\quad 2\*1=2,\quad 2\*2=0.\n\end{align*}Find the value of \(\( 1\*2)\*0\ \).
A. 0
B. 1
C. 2
D. 3
Question 13
A polynomial function f(x) = ax^3 + bx^2 + cx + d has roots at x = -2, x = 1, and x = 3. If f(0) = 10, calculate the value of a.
A. -2
B. 2
C. 4
D. 6
Question 14
Find the derivative of the function \( y = \sin^2 x \) u\sing the chain rule.
A. \( 2 \sin x \cos x \)
B. \( \cos^2 x \)
C. \( \sin x \cos x \)
D. \( \sin^2 x \)
Question 15
Find the sum of the first 5 terms of the geometric series with first term 2 and common ratio 3.
A. 242
B. 243
C. 244
D. 245

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