# Sulvme!

### Unified Tertiary Matriculation Examination Mathematics 2010

1:

What mathematics Question Paper Type is given to you?

A:

Type A

B:

Type B

C:

Type C

D:

Type D

E:

No option

2:

Find r, if 6r78 = 5119

A:

5

B:

2

C:

3

D:

6

E:

No option

3:

Simplify   ${\left ( \frac{3}{4} of \frac{4}{9} \div 9\frac{1}{2} \right )} \div 1\frac{5}{19}$

A:

$\frac{1}{25}$

B:

$\frac{1}{4}$

C:

$\frac{1}{5}$

D:

$\frac{1}{36}$

E:

No option

4:

A student measures a piece of rope and found that it was 1.26m long. If the actual length of the rope was 1.25m, what was the percentage error in the measurement?

A:

0.40%

B:

0.01%

C:

0.25%

D:

0.80%

E:

No option

5:

At what rate will the interest on #400 increase to #24 in 3 years reckoning in simple interest?

A:

4%

B:

2%

C:

3%

D:

5%

E:

No option

6:

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

A:

9:10:15

B:

12:15:16

C:

12:15:10

D:

10:15:24

E:

No option

7:

Evaluate   $\left ( \frac{81}{16} \right )^{-\frac{1}{4}} \times 2^{-1}$

A:

$\frac{1}{3}$

B:

$6$

C:

$3$

D:

$\frac{1}{6}$

E:

No option

8:

Given that log 2 = 0.3010, log 7 = 0.8451. Evaluate log 112

A:

2.5441

B:

2.0491

C:

2.1461

D:

3.1461

E:

No option

9:

Rationalize   $\frac{2\sqrt{3} + \sqrt{5}}{\sqrt{5} - \sqrt{3}}$

A:

$\frac{3\sqrt{15} + 11}{2}$

B:

$\frac{3\sqrt{15} - 11}{2}$

C:

$3\sqrt{15} - 11$

D:

$3\sqrt{15} + 11$

E:

No option

10:

Express the product of 0.21 and 0.34 in standard form

A:

$7.14\times10^{-3}$

B:

$7.14\times10^{-1}$

C:

$7.14\times10^{-2}$

D:

$7.14\times10^{-4}$

E:

No option

11:

Which of the venn diagrams below represents  $P'\cap Q\cap R'$

A:

A

B:

B

C:

C

D:

D

E:

No option

12:

A:

15

B:

5

C:

10

D:

20

E:

No option

13:

Make Q the subject of the formula if   $P = \frac{M}{5}(X + Q) + 1$

A:

$\frac{5P + MX - 5}{M}$

B:

$\frac{5P - MX - 5}{M}$

C:

$\frac{5P - MX + 5}{M}$

D:

$\frac{5P + MX + 5}{M}$

E:

No option

14:

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

A:

3x - 2y

B:

2y - 3x

C:

2y + 3x

D:

3x + 2y

E:

No option

15:

Factorize completely  $\frac{x^{3} + 3x^{2} - 10x}{2x^{2} - 8}$

A:

$\frac{x^{2} + 5}{2x + 4}$

B:

$\frac{x(x + 5)}{2(x + 2)}$

C:

$\frac{x(x - 5)}{2(x + 2)}$

D:

$\frac{x(x - 5)}{2(x - 2)}$

E:

No option

16:

Solve for x and y if x - y = 2 and x2 - y2 = 8

A:

(1,3)

B:

(3,1)

C:

(-1,3)

D:

(-3,1)

E:

No option

17:

If y varies directly as the square root of x and y = 3 when x = 16, Calculate y when x = 64

A:

5

B:

12

C:

6

D:

3

E:

No option

18:

If x is inversely proportional to y and $x = 2\frac{1}{2}$  when y = 2, find x if  y = 4

A:

$2\frac{1}{4}$

B:

$5$

C:

$4$

D:

$1\frac{1}{4}$

E:

No option

19:

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:

$x< -\frac{3}{2}$

E:

No option

20:

Solve the inequalities $-6 \leq 4-2x < 5-x$

A:

$-1\leq x< 6$

B:

$-1 < x \leq 5$

C:

$-1< x< 5$

D:

$-1\leq x\leq 6$

E:

No option

21:

Find the sum to 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:

$\frac{5}{11}$

E:

No option

22:

The 3rd term of an arithmetic progression is -9 and the 7th term is -29. Find the 10th term of the progression.

A:

44

B:

-165

C:

-44

D:

165

E:

No option

23:

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

A:

36

B:

11

C:

25

D:

55

E:

No option

24:

If p and q are two non zero numbers and 18(p+q) = (18+p)q, which of the following must be true?

A:

q = 18

B:

p = 18

C:

p<1

D:

q<1

E:

No option

25:

If   $\begin{vmatrix} x & 3\\ 2 & 7 \end{vmatrix} = 15$ , find the value of x

A:

3

B:

5

C:

4

D:

2

E:

No option

26:

Evaluate   $\begin{vmatrix} 2 & 0 & 5\\ 4 & 6 & 3\\ 8 & 9 & 1 \end{vmatrix}$

A:

-42

B:

102

C:

18

D:

-102

E:

No option

27:

If   $P = \begin{pmatrix} 2 & -3\\ 1 & 1 \end{pmatrix}$ , what is P-1

A:

$\begin{pmatrix} \frac{1}{5} & \frac{3}{5}\\ \frac{1}{5} & \frac{2}{5} \end{pmatrix}$

B:

$\begin{pmatrix} \frac{1}{5} & \frac{3}{5}\\ -\frac{1}{5} & \frac{2}{5} \end{pmatrix}$

C:

$\begin{pmatrix} -\frac{1}{5} & \frac{3}{5}\\ -\frac{1}{5} & \frac{2}{5} \end{pmatrix}$

D:

$\begin{pmatrix} -\frac{1}{5} & -\frac{3}{5}\\ -\frac{1}{5} & -\frac{2}{5} \end{pmatrix}$

E:

No option

28:

From the diagram below, find x

A:

65o

B:

50o

C:

55o

D:

75o

E:

No option

29:

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

A:

102o

B:

52o

C:

82o

D:

112o

E:

No option

30:

From the cyclic quadrilateral TUVW below, find the value of x

A:

23o

B:

26o

C:

24o

D:

20o

E:

No option

31:

If the two smaller sides of a right angled triangle are 4cm and 5cm, find its area

A:

10cm2

B:

6cm2

C:

8cm2

D:

24cm2

E:

No option

32:

An arc subtends an angle of 50o at the center of circle of radius 6cm. Calculate the area of the sector formed.

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

A:

$\frac{90}{7}cm^{2}$

B:

$\frac{110}{7}cm^{2}$

C:

$\frac{100}{7}cm^{2}$

D:

$\frac{80}{7}cm^{2}$

E:

No option

33:

A cylindrical pipe 50m long with radius 7m has one end open. What is the total surface area of the pipe?

A:

$700\pi m^{2}$

B:

$98\pi m^{2}$

C:

$350\pi m^{2}$

D:

$749 \pi m^{2}$

E:

No option

34:

What is the locus of point that is 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

E:

No option

35:

Find the distance between the points  $\left ( \frac{1}{2}, \frac{1}{2} \right )$ and  $\left ( -\frac{1}{2}, -\frac{1}{2} \right )$

A:

$\sqrt{2}$

B:

$0$

C:

$1$

D:

$\sqrt{3}$

E:

No option

36:

Find the gradient of the line passing through the points P(1,1) and Q(2,5)

A:

4

B:

2

C:

3

D:

5

E:

No option

37:

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

E:

No option

38:

If   $cot \theta = \frac{8}{15}$ , where $\theta$ is acute, find $sin \theta$

A:

$\frac{13}{15}$

B:

$\frac{15}{17}$

C:

$\frac{8}{17}$

D:

$\frac{16}{17}$

E:

No option

39:

If the area of triangle PQR below is $12\sqrt{3} cm^{2}$, find the value of q?

A:

6 cm

B:

8 cm

C:

7 cm

D:

5 cm

E:

No option

40:

If y = (2x + 1)3, find dy/dx

A:

3(2x + 1)2

B:

3(2x + 1)

C:

6(2x + 1)

D:

6(2x + 1)

E:

No option

41:

If y = xsinx, find dy/dx

A:

sinx + cosx

B:

sinx + xcosx

C:

sinx - xcosx

D:

sinx - cosx

E:

No option

42:

At what value of x does the function y = -3 - 2x + xattain a minimum value?

A:

1

B:

-4

C:

-1

D:

4

E:

No option

43:

Evaluate   $\int_{0}^{2}(x^{3} + x^{2})dx$

A:

$2\frac{5}{6}$

B:

$6\frac{2}{3}$

C:

$4\frac{5}{6}$

D:

$1\frac{5}{6}$

E:

No option

44:

Find  $\int (sin x + 2)dx$

A:

cosx + x2 + k

B:

cosx + 2x + k

C:

-cosx + 2x + k

D:

-cosx + x2 + k

E:

No option

45:

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

A:

7

B:

2

C:

6

D:

9

E:

No option

46:

Use the table below to answer question 46 and 47

The table below shows the marks obtained in a given test

How many students took the test?

A:

15

B:

20

C:

16

D:

13

E:

No option

47:

Find the mean mark

A:

3.2

B:

3.0

C:

3.1

D:

3.3

E:

No option

48:

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

A:

$\sqrt{\frac{5}{2}}$

B:

$\sqrt{10}$

C:

$\sqrt{6}$

D:

$\sqrt{\frac{2}{5}}$

E:

No option

49:

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

A:

50

B:

200

C:

100

D:

30

E:

No option

50:

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:

$\frac{1}{9}$

E:

No option