# Sulvme!

### Unified Tertiary Matriculation Examination Mathematics 2007

1:

If 5, 8, 6 and 2 occur with frequencies 3, 2, 4 and 1 respectively, find the product of the modal and the median number.

A:

36

B:

48

C:

30

D:

40

E:

No option

2:

In a basket, there are 6 grapes, 11 bananas and 13 oranges. If one fruit is chosen at random, what is the probability that the fruit is either a grape or a banana?

A:

$\frac{6}{30}$

B:

$\frac{5}{30}$

C:

$\frac{17}{30}$

D:

$\frac{11}{30}$

E:

No option

3:

The histogam below represents the weights of students who travelled out of their school for an examination. How many people made the trip?

A:

78

B:

38

C:

29

D:

69

E:

No option

4:

A senatorial candidate has planned to visit seven cities prior to a primary election. However, he could only visit four of the cities. How many different itineraries could be considered?

A:

640

B:

840

C:

520

D:

720

E:

No option

5:

The pie chart below illustrates the amount of private time a student spends in a week studying various subjects. Find the value of k

A:

90o

B:

60o

C:

30o

D:

15o

E:

No option

6:

The table below shows the number of pupils in each age group in a class. What is the probability that a pupil chosen at random is at least 11 years old?

A:

$\frac{27}{40}$

B:

$\frac{17}{20}$

C:

$\frac{3}{30}$

D:

$\frac{33}{40}$

E:

No option

7:

What is the mean deviation of 3, 5, 8, 11, 12 and 21 ?

A:

4.7

B:

60

C:

3.7

D:

10

E:

No option

8:

The table below gives the frequency distribution of marks obtained by a group of students in a test. If the total mark scored is 200, caclulate the value of y

A:

15

B:

13

C:

11

D:

9

E:

No option

9:

In how many ways can 6 subjects be selected from 10 subjects for an examination

A:

218

B:

216

C:

215

D:

210

E:

No option

10:

The cummulative frequency for $5\leq x\leq12$ from the distribution above is

A:

40

B:

72

C:

22

D:

46

E:

No option

11:

Integrate $\frac{x^{2} - \sqrt{x}}{x}$ with respect to x

A:

$\frac{x^{2}}{2} - 2 \sqrt{x} + k$

B:

$\frac{2(x^{2} - x)}{3x}+k$

C:

$\frac{x^{2}}{2}-\sqrt{x} + k$

D:

$\frac{x^{2} - \sqrt{x}}{x^{2}} + k$

E:

No option

12:

If y = x cos x, find 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

E:

No option

13:

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

A:

$\frac{2}{3}$

B:

$1$

C:

$-\frac{2}{3}$

D:

$-1$

E:

No option

14:

Determine the value of  $\int_{0}^{\frac{\pi}{2}}(-2cosx)dx$

A:

-2

B:

$-\frac{1}{2}$

C:

$-3$

D:

$-\frac{3}{2}$

E:

No option

15:

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

A:

2x - 1

B:

x - 1

C:

2 + 2x

D:

1 + 2x

E:

No option

16:

A binary operation $\oplus$ on real numbers is defined by $x\oplus y = xy + x + y$ for any two real numbers x and y. The value of $\left ( -\frac{3}{4} \right ) \oplus 6$ is?

A:

$\frac{3}{4}$

B:

$-\frac{9}{2}$

C:

$\frac{45}{4}$

D:

$-\frac{3}{4}$

E:

No option

17:

The graph below is represented by?

A:

y = x3 - 3x - 2

B:

y = x3 + 2x2 - x - 2

C:

y = x3 - 4x2 + 5x - 2

D:

y = x3 - 4x + 2

E:

No option

18:

Make L the subject of the formula if $d = \sqrt{\frac{42W}{5L}}$

A:

$\sqrt{\frac{42W}{5d}}$

B:

$\frac{42W}{5d^{2}}$

C:

$\frac{42}{5dW}$

D:

$\frac{1}{d}\sqrt{\frac{42W}{5}}$

E:

No option

19:

The solution of the quadratic inequality $(x^{2} + x - 12) \geq 0$ is

A:

$x \geq-3$ or $x \leq4$

B:

$x \geq3$ or $x \geq-4$

C:

$x \leq3$ or $x \leq-4$

D:

$x \geq3$ or $x \leq-4$

E:

No option

20:

Factorize 2t2 + t - 15

A:

(2t - 3)(t + 5)

B:

(t + 3)(2t - 5)

C:

(t + 3)(t - 5)

D:

(2t + 3)(t - 5)

E:

No option

21:

Solve the inequality -3(x - 2) < -2(x + 3)

A:

x > 12

B:

x < 12

C:

x > -12

D:

x < -12

E:

No option

22:

$W \aa L^{2}$ and W = 6 when L = 4. If $L = \sqrt{17}$, find W.

A:

$6\frac{7}{8}$

B:

$6\frac{5}{8}$

C:

$6\frac{3}{8}$

D:

$6\frac{1}{8}$

E:

No option

23:

A binary operation $\Delta$ is defined by $a\Delta b = a + b + 1$ for any real numbers a and b. Find the inverse of the real number 7 under the operation $\Delta$, if the identity element is -1

A:

-7

B:

-9

C:

5

D:

9

E:

No option

24:

The nth term of the sequence $\frac{3}{2},3,7,16,35,74,.....$ is

A:

5.2n - 2 - n

B:

$5.2^{n - 2} - \frac{n+1}{2}$

C:

3.2n - 2

D:

$\frac{3}{2}n$

E:

No option

25:

If f(x) = 3x - 2, $P = \begin{pmatrix} 2 & 1\\ -1 & 0 \end{pmatrix}$ and I is $2 \times 2$ identity matrix, evaluate f(P)

A:

h

B:

$\begin{pmatrix} 2 & 0\\ 0 & 2 \end{pmatrix}$

C:

dd

D:

d

E:

dsf

26:

Find the sum to infinity of the series $2 + \frac{3}{2} + \frac{9}{8} + \frac{27}{32} + ....$

A:

1

B:

2

C:

8

D:

4

E:

No option

27:

Evaluate $\begin{pmatrix} 3 & -2\\ -7 & 5 \end{pmatrix} + 2\begin{pmatrix} -2 & 4\\ 3 & -1 \end{pmatrix}$

A:

sdf

B:

df

C:

sdfs

D:

dfs

E:

dfs

28:

Find y, if  $\sqrt{12} - \sqrt{147} + y\sqrt{3} = 0$

A:

5

B:

1

C:

7

D:

3

E:

No option

29:

If x10 = 12145 find x.

A:

124

B:

121

C:

184

D:

180

E:

No option

30:

Evaluate $\frac{(0.5625)^{2} - (0.4375)^{2}}{0.04}$ correct to 3 significant figures

A:

3.11

B:

3.13

C:

0.313

D:

3.12

E:

No option

31:

Find the value of x for which 2(32x-1) = 162

A:

$\frac{5}{2}$

B:

$\frac{3}{2}$

C:

$\frac{2}{5}$

D:

$\frac{1}{2}$

E:

No option

32:

Simplify $\frac{3}{5}+(\frac{2}{7} \times \frac{4}{3} + \frac{4}{9})$

A:

$\frac{4}{5}$

B:

$\frac{7}{10}$

C:

$\frac{2}{5}$

D:

$\frac{1}{2}$

E:

No option

33:

If log102 = x, express log1012.5 in terms of x.

A:

2(1 + x)

B:

2 + 3x

C:

2(1 - x)

D:

2 - 3x

E:

No option

34:

A man made a profit of 5% when he sold an article for #60,000.00. How much would he have to sell the article to make a profit of 26%?

A:

#68 000

B:

#72 000

C:

#65 000

D:

#70 000

E:

No option

35:

Given:

P = {1, 3, 5, 7, 9, 11} and Q = {2, 4, 6, 8, 10, 12}.

Determine the relationship between P and Q

A:

$P \cap Q = \phi$

B:

coming

C:

coming

D:

coming

E:

No option

36:

Evaluate 101122 - 10122

A:

1100002

B:

1102

C:

11000002

D:

110002

E:

No option

37:

The sum of the ages of Musa and Lawal is 28 years. After sharing a certain sum of money in the ratio of their ages, Musa gets #600 and Lawal #800. How old is Lawal?

A:

20 years

B:

16 years

C:

14 years

D:

12 years

E:

No option

38:

If X = {all perfect squares less than 40} and

Y = {all odd numbers from 1 to 15}

Find $\mathbf{X} \cap \mathbf{Y}$

A:

{3, 9}

B:

{9}

C:

{9, 25}

D:

{1, 9}

E:

No option

39:

Calculate the length of an arc of a circle of diameter 14cm, which subtends an angle of 900 at the centre of the circle

A:

$\frac{7 \pi}{2}cm$

B:

$7 \pi cm$

C:

$14 \pi cm$

D:

$\frac{7 \pi}{4}cm$

E:

No option

40:

If the lines 3y = 4x - 1 and qy = x + 3 are parallel to each other, the value of q is

A:

$-\frac{4}{3}$

B:

$-\frac{3}{4}$

C:

$\frac{4}{3}$

D:

$\frac{3}{4}$

E:

No option

41:

In the parallelogram PQRS above, find angle SQR

A:

1000

B:

800

C:

500

D:

300

E:

No option

42:

The volume of a hemispherical bowl is $718\frac{2}{3}cm^{3}$. Find its radius

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

A:

4.0cm

B:

5.6cm

C:

7.0cm

D:

3.8cm

E:

No option

43:

A particle P moves between points S and T such that angle SPT is always constant. Find the locus of P.

A:

It is a semi-circle with ST as diameter

B:

It is a perpendicular bisector of ST

C:

It is a quadrant of a circle with ST as diameter

D:

It is a straight line perpendicular to ST

E:

No option

44:

If the lines 2y - kx + 2 = 0 and $y + x - \frac{k}{2} = 0$. Intersect at (1, -2), find the value of k

A:

-4

B:

-3

C:

-2

D:

-1

E:

No option

45:

A man 40m from the foot of a tower observes the angle of elevation of the tower to be 300. Determine the height of the tower.

A:

$\frac{40 \sqrt{3}}{3}m$

B:

$20m$

C:

$40 \sqrt{3}m$

D:

$40m$

E:

No option

46:

Find the locus of points equidistant from two straight lines y - 5 = 0 and y - 3 = 0

A:

y - 2 = 0

B:

y - 4 = 0

C:

y - 1  = 0

D:

y - 3 = 0

E:

No option

47:

What is the value of k if the mid-point of the line joining (1-k, -4) and (2, k+1) is (-k, k)?

A:

-3

B:

-1

C:

-4

D:

-2

E:

No option

48:

Find the size of each exterior angle of a regular octagon.

A:

510

B:

450

C:

400

D:

360

E:

No option

49:

Find the value of $\frac{tan 60^{0} - tan 30^{0}}{tan 60^{0} + tan 30^{0}}$

A:

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

B:

$\frac{2}{\sqrt{3}}$

C:

1

D:

$\frac{1}{2}$

E:

No option

50:

The area of a square is 144 sq cm. Find the length of the diagonal

A:

13cm

B:

$12 \sqrt{2}cm$

C:

12cm

D:

$11 \sqrt{3}cm$

E:

No option