POST UTME FUTO 2018 Mathematics | Objective

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Question 1
A histogram with class boundaries ( 0, 2, 4, 6, 8 ) and corresponding frequencies ( 3, 5, 7, 2, 1 ) has a mean of ( 4 ). Find the median of the data.
A. ( 4 )
B. ( 5 )
C. ( 6 )
D. ( 7 )
Question 2
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 3
Solve for x in the equation \( 2^x = 3x + 5 \).
A. x = 2
B. x = 3
C. x = 4
D. x = 5
Question 4
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 5
Find the determinant of the matrix [ egin{pmatrix} 2 & 3 \ 4 & 5 \end{pmatrix} ].
A. 1
B. 2
C. 3
D. 4
Question 6
Determine the value of x in the equation \( \sin^2 x + \cos^2 x = 1 \) if \( \sin x = \frac{3}{5} \).
A. \( \frac{pi}{4} \)
B. \( \frac{3pi}{4} \)
C. \( \frac{5pi}{4} \)
D. \( \frac{7pi}{4} \)
Question 7
Find the area under the curve \( y = \frac{1}{2}x^2 + 3x - 2 \) from \( x = 0 \) to \( x = 4 \).
A. \( \frac{1}{2} \times 4^3 + 3 \times 4^2 - 2 \times 4 \)
B. \( \frac{1}{2} \times 4^2 + 3 \times 4 - 2 \)
C. \( \frac{1}{2} \times 4^3 + 3 \times 4^2 - 2 \times 4^2 \)
D. \( \frac{1}{2} \times 4^2 + 3 \times 4 - 2 \times 4 \)
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
Find the derivative of ( f(x) = \frac{x^2}{x^2 + 1} ) u\sing the quotient rule.
A. 2x\( x^2 + 1 \) - 2x^2
B. \( x^2 + 1 \)^2 - x^2
C. x\( x^2 + 1 \)^2
D. \( x^2 + 1 \)^2 - 2x^2
Question 10
Solve the inequality \( x^2 - 4x - 5 > 0 \).
A. \( x < -1 \) or \( x > 5 \)
B. \( x < 1 \) or \( x > 5 \)
C. \( x < -1 \) or \( x < 5 \)
D. \( x > 1 \) or \( x > 5 \)
Question 11
Solve for x in the equation \( 2x^2 + 5x - 3 = 0 \).
A. -1
B. 1
C. 2
D. 3
Question 12
Solve the equation \( \frac{d}{dx} \( x^2 \sin x \ \) = 2x \sin x + x^2 \cos x ).
A. \( x \sin x = c \)
B. \( x^2 \sin x = c \)
C. \( x \cos x = c \)
D. \( x^2 \cos x = c \)
Question 13
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 14
Solve the equation [ x^2 + 2x + 1 = 0 \] u\sing the quadratic formula.
A. x = -1
B. x = 1
C. x = -2
D. x = 2
Question 15
A polynomial function has the equation ( f(x) = x^3 - 6x^2 + 11x - 6 ). Find the value of \( f\( -1 \ \) ).
A. ( 4 )
B. ( 5 )
C. ( 6 )
D. ( 7 )

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