# Sulvme!

### Unified Tertiary Matriculation Examination Mathematics 2011

1:

Which Mathematics Question Paper Type is given to you?

A:

Type A

B:

Type B

C:

Type C

D:

Type D

E:

No option

2:

If 2q35 = 778, Find q

A:

2

B:

1

C:

4

D:

0

E:

No option

3:

Simplify      $\frac{3\frac{2}{3}\times\frac{5}{6}\times\frac{2}{3}}{\frac{11}{15}\times\frac{3}{4}\times\frac{2}{27}}$

A:

$5\frac{2}{3}$

B:

$30$

C:

$4\frac{1}{3}$

D:

$50$

E:

No option

4:

A man invested #5,000 for 9 months at 4%. What is the simple interest?

A:

#150

B:

#220

C:

#130

D:

#250

E:

No option

5:

If the numbers M,N,Q are in the ratio 5:4:3, find the value of $\frac{2N - Q}{M}$

A:

2

B:

3

C:

1

D:

4

E:

No option

6:

Simplify $\left ( \frac{16}{81} \right )^{\frac{1}{4}} \div \left ( \frac{9}{16} \right )^{-\frac{1}{2}}$

A:

$\frac{2}{3}$

B:

$\frac{1}{2}$

C:

$\frac{8}{9}$

D:

$\frac{1}{3}$

E:

No option

7:

If log318 + log33 - log3x = 3, find x

A:

1

B:

2

C:

0

D:

3

E:

No option

8:

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

A:

$\frac{1 - \sqrt{5}}{2}$

B:

$\frac{1 - \sqrt{5}}{4}$

C:

$\frac{\sqrt{5} - 1}{2}$

D:

$\frac{1 + \sqrt{5}}{4}$

E:

No option

9:

Simplify   $\left [ \sqrt{2} + \frac{1}{\sqrt{3}} \right ]\left [ \sqrt{2} - \frac{1}{\sqrt{3}} \right ]$

A:

$\frac{7}{3}$

B:

$\frac{5}{3}$

C:

$\frac{5}{2}$

D:

$\frac{3}{2}$

E:

No option

10:

From the venn diagram below, the complement of the set $P \cap Q$ is given by

A:

{a, b, d, e}

B:

{b, d}

C:

{a, e}

D:

{c}

E:

No option

11:

Ralia has 7 different posters to be hung in her bedroom, living room and kitchen. Assuming she has plans to place, at least, a poster in each of the 3 rooms, how many choices does she have?

A:

49

B:

170

C:

21

D:

210

E:

No option

12:

Make R the subject of the formula if    $T = \frac{KR^{2} + M}{3}$

A:

$\frac{\sqrt{3T - K}}{M}$

B:

$\frac{\sqrt{3T + M}}{K}$

C:

$\frac{\sqrt{3T + K}}{M}$

D:

$\frac{\sqrt{3T - M}}{K}$

E:

No option

13:

Find the remainder when x3 - 2x2 + 3x - 3 is divided by x2 + 1

A:

2x - 1

B:

x + 3

C:

2x + 1

D:

x - 3

E:

No option

14:

Factorize completely 9y2 - 16x2

A:

(3y - 2x)(3y - 4x)

B:

(3y + 4x)(3y + 4x)

C:

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

D:

(3y + 4x)(3y - 4x)

E:

No option

15:

Solve for x and y respectively in the simultaneous equations -2x - 5y = 3, x + 3y = 0

A:

-3, -9

B:

9, -3

C:

-9, 3

D:

3, -9

E:

No option

16:

If x varies directly as square root of y and x = 81 when y = 9, find x when y = $1\frac{7}{9}$

A:

$20\frac{1}{4}$

B:

$27$

C:

$2\frac{1}{4}$

D:

$36$

E:

No option

17:

T varies inversely as the cube of R. When R = 3, T = $\frac{2}{81}$, find T when R = 2

A:

$\frac{1}{18}$

B:

$\frac{1}{12}$

C:

$\frac{1}{24}$

D:

$\frac{1}{6}$

E:

No option

18:

Which of the following diagrams represents the solution of the inequalities $y\leq x - 2$ and $y\geqslant x^{2} - 4$

A:

A

B:

B

C:

C

D:

D

E:

No option

19:

Solve the inequalities $-6(x + 3)\leq 4(x - 2)$

A:

$x\leq 2$

B:

$x\geq -1$

C:

$x\geq -2$

D:

$x\leq -1$

E:

No option

20:

Solve the inequalities $x^{2} + 2x > 15$

A:

x < -3 or x > 5

B:

-5 < x < 3

C:

x < 3 or x > 5

D:

x > 3 or x < -5

E:

No option

21:

Find the sum of the first 18 terms of the series 3, 6, 9, ......, 36

A:

505

B:

513

C:

433

D:

635

E:

No option

22:

The second term of a geometric series is 4 while the fourth term is 16. Find the sum of the first five terms.

A:

60

B:

62

C:

54

D:

64

E:

No option

23:

A binary operation $\oplus$ on real numbers is defined by x $\oplus$ y = xy + x + y for two real numbers x and y. Find the value of $3 \oplus -\frac{2}{3}$

A:

$-\frac{1}{2}$

B:

$\frac{1}{3}$

C:

$-1$

D:

$2$

E:

No option

24:

If    $\begin{vmatrix} 2 & 3\\ 5 & 3x \end{vmatrix}$ $= \begin{vmatrix} 4 & 1\\ 3 & 2x \end{vmatrix}$, find the value of x

A:

-6

B:

6

C:

-12

D:

12

E:

No option

25:

Evaluate     $\begin{vmatrix} 4 & 2 & -1\\ 2 & 3 & -1 \\ -1 & 1 & 3 \end{vmatrix}$

A:

25

B:

45

C:

15

D:

55

E:

No option

26:

The inverse of matrix N = $\begin{bmatrix} 2 & 3\\ 1 & 4 \end{bmatrix}$

A:

$\frac{1}{5}\begin{bmatrix} 2 & 1\\ 3 & 4 \end{bmatrix}$

B:

$\frac{1}{5}\begin{bmatrix} 4 & -3\\ -1 & 2 \end{bmatrix}$

C:

$\frac{1}{5}\begin{bmatrix} 2 & -1\\ -3 & 4 \end{bmatrix}$

D:

$\frac{1}{5}\begin{bmatrix} 4 & 1\\ 3 & 2 \end{bmatrix}$

E:

No option

27:

What is the size of each interior angle of a 12-sided regular polygon?

A:

120o

B:

150o

C:

30o

D:

180o

E:

No option

28:

A circle of perimeter 28cm is opened to form a square. What is the maximum possible area of the square?

A:

56cm2

B:

49cm2

C:

98cm2

D:

28cm2

E:

No option

29:

A chord of a circle of radius 7cm is 5cm from the center of the circle. What is the length of the chord?

A:

$4\sqrt{6}cm$

B:

$3\sqrt{6} cm$

C:

$6\sqrt{6}cm$

D:

$2\sqrt{6}cm$

E:

No option

30:

A solid metal cube of side 3cm is placed in a rectangular tank of dimensions 3, 4 and 5cm. What volume of water can the tank now hold?

A:

48cm3

B:

33cm3

C:

60cm3

D:

27cm3

E:

No option

31:

The perpendicular bisector of a line XY is the locus of a point

A:

whose distance from X is always twice its distance from Y

B:

whose distance from Y is always twice its distance from X

C:

which moves on the line XY

D:

which is equidistant from the points X and Y

E:

No option

32:

The midpoint of P(x,y) and Q(8,6) is (5,8). Find x and y

A:

(2,10)

B:

(2,8)

C:

(2,12)

D:

(2,6)

E:

No option

33:

Find the equation of a line perpendicular to line 2y = 5x + 4 which passes through (4,2)

A:

5y - 2x - 18 = 0

B:

5y + 2x - 18 = 0

C:

5y - 2x + 18 = 0

D:

5y + 2x - 2 = 0

E:

No option

34:

In a right angled triangle, if   $tan\Theta = \frac{3}{4}$ . What is $cos\Theta - sin\Theta$?

A:

$\frac{2}{5}$

B:

$\frac{3}{5}$

C:

$\frac{1}{5}$

D:

$\frac{4}{5}$

E:

No option

35:

A man walks 100m due West from a point X to Y, he then walks 100m due North to a point Z. Find the bearing of X to Z

A:

195o

B:

135o

C:

225o

D:

045o

E:

No option

36:

The derivative of (2x + 1)(3x + 1) is

A:

12x + 1

B:

6x + 5

C:

6x + 1

D:

12x + 5

E:

No option

37:

Find the derivative of   $\frac{sin\Theta }{cos\Theta }$

A:

$sec^{2}\Theta$

B:

$tan\Theta cosec\Theta$

C:

$cosec\Theta sec\Theta$

D:

$cosec^{2}\Theta$

E:

No option

38:

Find the value of x at the minimum point of the curve y = x3 + x2 - x + 1

A:

$\frac{1}{3}$

B:

$-\frac{1}{3}$

C:

$1$

D:

$-1$

E:

No option

39:

Evaluate   $\int_{0}^{1}(3 - 2x)dx$

A:

3

B:

5

C:

2

D:

6

E:

No option

40:

Find    $\int cos 4x dx$

A:

$\frac{3}{4}sin4x + k$

B:

$-\frac{1}{4}sin4x + k$

C:

$-\frac{3}{4}sin4x + k$

D:

$\frac{1}{4}sin4x + k$

E:

No option

41:

The pie chart shows the distribution of courses offered by students. What percentage of the students offer English?

A:

30%

B:

25%

C:

35%

D:

20%

E:

No option

42:

The bar chart below shows the distribution of SS2 students in a school. Find the total number of students

A:

180

B:

135

C:

210

D:

105

E:

No option

43:

The sum of four consecutive integers is 34. Find the least of these numbers

A:

7

B:

6

C:

8

D:

5

E:

No option

44:

From the table below, find the median and range of the data respectively

A:

(8,5)

B:

(3,5)

C:

(5,8)

D:

(5,3)

E:

No option

45:

Find the mode of the distribution below

A:

9

B:

8

C:

10

D:

7

E:

No option

46:

Find the standard deviation of the distribution below

A:

$\sqrt{5}$

B:

$\sqrt{3}$

C:

$\sqrt{7}$

D:

$\sqrt{2}$

E:

No option

47:

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

A:

6!

B:

7!

C:

5!

D:

8!

E:

No option

48:

In how many ways can five people sit round a circular table?

A:

24

B:

60

C:

12

D:

120

E:

No option

49:

Find the probability that a number picked at random from the set {43, 44, 45,...... 60} is a prime number.

A:

$\frac{2}{3}$

B:

$\frac{1}{3}$

C:

$\frac{2}{9}$

D:

$\frac{7}{9}$

E:

No option

50:

In a class of 60 students, 30 offer physics and 40 offer chemistry. If a student is picked at random from the class, what is the probability that the students offers both physics and chemistry?

A:

$\frac{1}{3}$

B:

$\frac{1}{4}$

C:

$\frac{1}{2}$

D:

$\frac{1}{6}$

E:

No option