Hello and Welcome to UTME CBT Practice Test - Mathematics (Diagnostic Test) - Set 8

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Geometry/Trigonometry

If cot θ = \frac{8}{15}, where θ is acute, find sin θ.

A. \frac{13}{15}    B. \frac{15}{17}    C. \frac{8}{17}    D. \frac{16}{17}


If the mean of five consecutive integers is 30, find the largest of the numbers

A. 28     B. 30     C. 32     D. 34


Calculus

At what value of x does the function y = -3 – 2x + x2 attain minimum value?

A. -1    B. -4    C. 4    D. 1


Geometry/Trigonometry

Find the equation of a line parallel to y = -4x + 2 passing through (2, 3).

A. y + 4x + 11 = 0   
B. y – 4x – 11 = 0   
C. y + 4x – 11 = 0   
D. y – 4x + 11 = 0


Statistics

In how many ways can a committee of 2 women and 3 men be chosen from 6 men and 5 women?

A. 100    B. 200    C. 30    D. 50


Number and Numeration

Find r, if 6r78 = 5119.

A. 5    B. 2    C. 3    D. 6


Algebra

If  , find the value of x.

A. 4    B. 5    C. 2    D. 3


Statistics

If three unbiased coins are tossed, find the probability that they are all heads.

A. \frac{1}{8}    B. \frac{1}{3}    C. \frac{1}{6}    D. \frac{1}{9}


Algebra

Make Q the subject of the formula if

A.     B.     C.     D.


Geometry/Trigonometry

Find the distance between the points and

A.    B. 0    C. 1    D.


Number and Numeration

Which of the Venn diagrams below represents P' ∩ Q ∩ R'?

Number and Numeration

Simplify

A. \frac{1}{25}     B. \frac{1}{4}     C. \frac{1}{5}     D. \frac{1}{36}


Calculus

If y = x cos x, find  \frac{dy}{dx} 

A. sin x - x cos x     B. sin x + x cos x     C. cos x + x sin x     D. cos x - x sin x


Geometry/Trigonometry

An arc subtends an angle 50° at the centre of circle of radius 6 cm. Calculate the area of the sector formed. [π = \frac{22}{7}]

A. \frac{90}{7} cm2    B. \frac{110}{7} cm2    C. \frac{100}{7} cm2    D. \frac{80}{7} cm2


Rationalize

A.     B.     C.     D.


Geometry/Trigonometry

From the cyclic quadrilateral TUVW above, find the value of x.

A. 24°    B. 26°    C. 20°    D. 23°


Algebra

If x is inversely proportional to y and x = 2½ when y =2, find x if y = 4.

A. 2\frac{1}{4}     B. 5     C. 4     D. 1\frac{1}{4}


Number and Numeration

If p : q = \frac{2}{3} : \frac{5}{6} and q : r = \frac{3}{4} : \frac{1}{2} , find p : q : r.

A. 12 : 15 : 10     B. 12 : 15 : 16     C. 10 : 15 : 24     D. 9 : 10 : 15


Geometry/Trigonometry

What is the locus of points equidistant from points P(1, 3) and Q(3, 5)?

A. y = -x – 6    B. y = x + 6     C. y = x – 6     D. y = -x + 6


Calculus

Find the value of x for which the function f(x) = 2x3 - x2 - 4x + 4 has a minimum value.

A. \frac{2}{3}     B. 1     C. -\frac{2}{3}     D. -1


Geometry/Trigonometry

From the diagram above, find x.

A. 65°    B. 50°    C. 55°    D. 75°


Algebra

If 9x2 + 6xy + 4y2 is a factor of 27x3 – 8y3, find the other factor.

A. 2y + 3x     B. 2y – 3x     C. 3x + 2y     D. 3x – 2y



From the table above, if the pass mark is 5, how many students failed the test?

A. 6    B. 2    C. 9    D. 7


Number and Numeration

Express the product of 0.21 and 0.34 in standard form

A. 7.14 x 10-2    B. 7.14 x 10-1    C. 7.14 x 10-4    D. 7.14 x 10-3

Calculus

If y = (2x + 1)3,  find  \frac{dy}{dx} .

A. 6(2x + 1)     B. 3(2x + 1)    C. 6(2x + 1)2    D. 3(2x + 1)2


Statistics

A bag contains 5 black, 4 white and x red marbles. If the probability of picking a red marble is \frac{2}{5} find the value of x.

A. \frac{2}{3}     B. 2     C.     D. 6


Find the standard deviation of 2, 3, 5 and 6.

A.     B.     C.     D.


Algebra

For what range of values of x is  \frac{1}{2} x + \frac{1}{4}  >  \frac{1}{3} x + \frac{1}{2}

A. x > -\frac{3}{2}    B. x > \frac{3}{2}    C. x < \frac{3}{2}    D. x < -\frac{3}{2}


Algebra

If x * y = x + y2, find the value of (2 * 3) * 5

A. 25    B. 11    C. 55    D. 36


Calculus If y = x sinx, find \frac{dy}{dx}.

A. sinx - xcosx     B. sinx + xcosx    C. sinx – cosx    D. sinx + cosx




The table above shows the marks obtained in a given test. How many students took the test?

A. 16    B. 20    C. 13    D. 15


Algebra

Find the sum of infinity of the following series 0.5 + 0.05 + 0.005 + 0.0005 + …

A. \frac{5}{9}    B. \frac{5}{7}    C. \frac{5}{8}    D. \frac{5}{11}


Calculus

Find (sin x + 2) dx.

A. -cosx + 2x + k   
B. cosx + 2x + k
C. -cosx + x2 + k
D. cosx + x2 + k




The table above shows the marks obtained in a given test. Find the mean mark.

A. 3.1    B. 3.0    C. 3.3    D. 3.2


Geometry/Trigonometry

The interior angles of a quadrilateral are (x + 15)°, (2x – 45)°, (x – 30)° and (x + 10)°. Find the value of the least interior angle.

A. 82°    B. 52°    C. 112°    D. 102°


Algebra

Factorize completely  

A.      B.      C.      D.


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