# Sulvme!

### Unified Tertiary Matriculation Examination Mathematics 2008

1:

A:

1110112

B:

1101102

C:

1010112

D:

1010102

E:

No option

2:

If 125x = 2010, find x

A:

2

B:

3

C:

4

D:

5

E:

No option

3:

Evaluate  $\frac{\frac{3}{8}\div\frac{1}{2} - \frac{1}{3}}{\frac{1}{8} \times \frac{2}{3} + \frac{1}{3}}$

A:

$\frac{1}{4}$

B:

$\frac{1}{3}$

C:

$\frac{1}{2}$

D:

$1$

E:

No option

4:

Express 123456 to 3 significant figures

A:

123 000

B:

124 000

C:

125 000

D:

126 000

E:

No option

5:

Calculate the simple interest on #7500 for 8 years at 5% per annum

A:

#3000

B:

#600

C:

#300

D:

#150

E:

No option

6:

The cost of kerosene per liter increases from #60 to #85. What is the percentage rate of increase?

A:

42%

B:

41%

C:

40%

D:

25%

E:

No option

7:

Simplify $16^{-\frac{1}{2}} \times 4^{-\frac{1}{2}} \times 27^{\frac{1}{3}}$

A:

$\frac{3}{8}$

B:

$\frac{2}{3}$

C:

$\frac{3}{4}$

D:

$\frac{3}{2}$

E:

No option

8:

If  $log_{x^{1/2}}64 = 3$ , find the value of x

A:

4

B:

16

C:

32

D:

64

E:

No option

9:

If  $\frac{1 + \sqrt{2}}{1 - \sqrt{2}}$ is expressed in the form $x + y\sqrt{2}$, find the values of x and y

A:

(-3, -2)

B:

(-2, 3)

C:

(3,2)

D:

(2,-3)

E:

No option

10:

If X = {n2 + 1: n = 0,2,3} and

Y = {n+1: n = 2,3,5}, find X $\cap$ Y

A:

{1, 3}

B:

{5, 10}

C:

null

D:

{4, 6}

E:

No option

11:

A bookseller sells mathematics and English books. If 30 customers buy mathematics books, 20 customers buy English books and 10 customers buy the two books, how many customers has he altogether?

A:

30

B:

40

C:

50

D:

60

E:

No option

12:

Make Q the subject of the formula when  $L = \frac{4}{3}M \sqrt{PQ}$

A:

$\frac{9L^{2}}{16M^{2}P}$

B:

$\frac{3L}{4M \sqrt{P}}$

C:

$\frac{\sqrt{3L}}{4MP}$

D:

$\frac{3L^{2}}{16M^{2}P}$

E:

No option

13:

If 2x2 - kx - 12 is divisible by x - 4, find the value of k.

A:

4

B:

5

C:

6

D:

7

E:

No option

14:

Factorize completely (4x + 3y)2 - (3x - 2y)2

A:

(x + 5y)(7x + y)

B:

(x + 5y)(7x - y)

C:

(x - 5y)(7x + y)

D:

(x - 5y)(7x - y)

E:

No option

15:

If x - 3 is directly proportional to the square of y and x = 5 when y = 2, find x when y = 6

A:

30

B:

21

C:

16

D:

12

E:

No option

16:

If p varies inversely as the square of q and p = 8 when q = 4, find q when p = 32

A:

$\pm16$

B:

$\pm8$

C:

$\pm4$

D:

$\pm2$

E:

No option

17:

Find the range of values of x which satisfy the inequalities $4x - 7 \leq 3x$ and $3x - 4 \leq 4x$

A:

$-4\leq x\leq 7$

B:

$-7\leq x\leq 4$

C:

$x\geq -7$

D:

$-7\leq x\leq 6$

E:

No option

18:

Solve the quadratic inequality  $x^{2} - 5x + 6\geq 0$

A:

$x\leq 2, x\geq 3$

B:

$x\leq 3,x\geq 2$

C:

$x\leq -2, x\geq -3$

D:

$x\leq -3, x\geq 2$

E:

No option

19:

The shaded area that gives the solution set for the inequalities  $x + y \leq 3, x - y\leq 3$, is

A:

A

B:

B

C:

C

D:

D

E:

No option

20:

The fifth term of an A.P is 24 and the eleventh term is 96. Find the first term

A:

12

B:

4

C:

-12

D:

-24

E:

No option

21:

A binary operation * is defined on the set of positive integers is such that x*y = 2x - 3y + 2 for all positive integers x and y. The binary operation is

A:

commutative and closed on the set of positive integers

B:

neither commutative nor closed on the set of positive integers

C:

commutative but not closed on the set of positive integers

D:

not commutative but closed on the set of positive integers

E:

No option

22:

A binary operation on the set of real numbers excluding -1 is such that for all m, n $\euro$ R, m $\Delta$ n = m + n + mn. Find the identity element of the operation

A:

1

B:

0

C:

$-\frac{1}{2}$

D:

$-1$

E:

No option

23:

Find the values of x and y respectively if

$\begin{pmatrix} 1 & 0\\ -1 & -1\\ 2 & 2 \end{pmatrix} + \begin{pmatrix} x & 1\\ -1 &0 \\ y & -2 \end{pmatrix} = \begin{pmatrix} -2 & 1\\ -2 & -1\\ -3 & 0 \end{pmatrix}$

A:

-3, -2

B:

-5, -3

C:

-2, -5

D:

-3, -5

E:

No option

24:

If  $\begin{pmatrix} -2 & 1\\ 2 & 3 \end{pmatrix}\begin{pmatrix} p & q\\ r & s \end{pmatrix} = \begin{pmatrix} 1 & 0\\ 0 & 1 \end{pmatrix}$ , what is the value of r?

A:

$-\frac{3}{8}$

B:

$\frac{3}{8}$

C:

$\frac{5}{8}$

D:

$\frac{1}{4}$

E:

No option

25:

In the diagram below, PQ//RS. The size of the angle marked x is

A:

100o

B:

80o

C:

50o

D:

30o

E:

No option

26:

Find the exterior angle of a 12 sided regular polygon.

A:

12o

B:

24o

C:

25o

D:

30o

E:

No option

27:

In the diagram below, <OPQ is

A:

90o

B:

53o

C:

36o

D:

26o

E:

No option

28:

Find the area of the figure below

$(\pi = \frac{22}{7})$

A:

12.5cm2

B:

75.0cm2

C:

78.5cm2

D:

84.8cm2

E:

No option

29:

Find the angle subtended at the centre of a circle by a chord which is equal in length to the radius of the circle.

A:

30o

B:

45o

C:

60o

D:

90o

E:

No option

30:

Find the capacity in liters of a cylindrical well of radius 1 metre and depth 14 metres $( \pi = \frac{22}{7})$

A:

44 000 liters

B:

4 400 liters

C:

440 liters

D:

44 liters

E:

No option

31:

The locus of a point equidistant from two points P(6,2) and R(4,2) is a perpendicular bisector of PR passing through

A:

(2,5)

B:

(5,2)

C:

(1,0)

D:

(0,1)

E:

No option

32:

Find the gradient of a line which is perpendicular to the line with the equation 3x + 2y + 1 = 0

A:

$\frac{3}{2}$

B:

$\frac{2}{3}$

C:

$-\frac{2}{3}$

D:

$-\frac{3}{2}$

E:

No option

33:

Calculate the distance between points L (-1, -6) and M (-3, -5)

A:

$\sqrt{5}$

B:

$2 \sqrt{3}$

C:

$\sqrt{20}$

D:

$\sqrt{53}$

E:

No option

34:

If  $sin \Theta = \frac{3}{5}$, find $tan \Theta$

A:

$\frac{3}{4}$

B:

$\frac{3}{5}$

C:

$\frac{2}{5}$

D:

$\frac{1}{4}$

E:

No option

35:

A student sitting on a tower 68 meters high observes his principal's car at an angle of depression of 20o. How far is the car from the bottom of the tower to the nearest metre?

A:

184m

B:

185m

C:

186m

D:

187m

E:

No option

36:

Find the derivative of  $y = \frac{x^{7} - x^{5}}{x^{4}}$

A:

x(x2 - 1)

B:

3x(x2 - 1)

C:

3x2 - 1

D:

7x6 - 5x4

E:

No option

37:

Differentiate sin x - xcos x

A:

x cosx

B:

x sinx

C:

-x cosx

D:

-x sinx

E:

No option

38:

Find the minimum value of the function y = x (1+x)

A:

$-\frac{1}{4}$

B:

$-\frac{1}{2}$

C:

$\frac{1}{4}$

D:

$\frac{1}{2}$

E:

No option

39:

Evaluate  $\int_{1}^{2}(6x^{2} - 2x)dx$

A:

16

B:

13

C:

12

D:

11

E:

No option

40:

Evaluate  $\int_{-\frac{\pi}{2}}^{\frac{\pi}{2}} cos x dx$

A:

0

B:

1

C:

2

D:

3

E:

No option

41:

On a pie chart, there are six sectors of which four angles are 30o, 45o, 60o, 90o and the remaining two angles are in the ratio 2:1. Find the smaller angles of the remaining two angles

A:

15o

B:

30o

C:

45o

D:

60o

E:

No option

42:

The bar chart above shows the number of times the words a, and , in, it, the, to appear in a paragraph in a book. What is the ratio of the least frequent word to that of the most frequent word?

Diagram coming soon

A:

$\frac{1}{4}$

B:

$\frac{1}{3}$

C:

$\frac{2}{3}$

D:

$\frac{3}{4}$

E:

No option

43:

What is the mean of the data t, 2t-1, t-2, 2t-1, 4t and 2t+2?

A:

2t

B:

2t-1

C:

2/3t+1

D:

2t - 1/3

E:

No option

44:

Find the median of 4, 1, 4, 1, 0, 4, 4, 2 and 0

A:

0

B:

1

C:

2

D:

4

E:

No option

45:

If x > 0, find the range of the numbers x-3, 3x+2, x-1, 4x, 2x-1, x-2, 2x-2, 3x and 3x+1

A:

3x+3

B:

3x+1

C:

2x+5

D:

2x+1

E:

No option

46:

Find the mean deviation of 2, 4, 5, and 9

A:

1

B:

2

C:

5

D:

7

E:

No option

47:

In how many ways can the letters of the word ACCEPTANCE be arranged?

A:

$\frac{10!}{2!2!3!}$

B:

$\frac{10!}{2!3!}$

C:

$\frac{10!}{2! 2!}$

D:

$10!$

E:

No option

48:

Find the number of ways of selecting 6 out of 10 subjects for an examination.

A:

218

B:

216

C:

215

D:

210

E:

No option

49:

The probability of picking a letter T from the word OBSTRUCTION is

A:

$\frac{1}{11}$

B:

$\frac{2}{11}$

C:

$\frac{3}{11}$

D:

$\frac{4}{11}$

E:

No option

50:

The result of rolling a fair die 150 times is as summarized in the table below

What is the probability of obtaining a 5?

Diagram coming soon

A:

$\frac{3}{10}$

B:

$\frac{1}{5}$

C:

$\frac{1}{6}$

D:

$\frac{1}{10}$

E:

No option