Welcome to your Mathematics national exam 2014

Choose the best answer from given

alternatives

1.

what are the quotient and remainder respectively, when 75 divided by 20 ?

4 and 5

15 and 3

3 and 15

2 and 19

2.

Which of the following is the measure of an exterior angle of a 10 sided regular polygons?

180º

144º

72º

36º

3.

The radian measure of an angle of 120º is equal to:

π

π/8

π/4

2π/3

π/2

4.

(-7,3)

(3,1)

(-3,1)

(7,-3)

5.

What is the dot (scalar) product of the vectors

6

-8

7

5

6.

-2

-3

2

3

7.

item Which one of the following quantities represents a vector?

Weight of an object

Speed of a motorbike

Volume of a box

The width of your bedroom

8.

What is the surface area of a sphere with radius 6 cm ?

36π cm²

48π cm²

144π cm²

24π con

9.

If the volume of a right circular cone is 64π cm² and the diameter of ii base is 8 cm, what is the height of the cone?

4cm

3cm

8cm

12cm

10.

11.

what is the image of the circle with equation (x+2)² +(y-2)²=1, when it is rotated through π/6about the origin?

12.

Which one of the following is the derivative of ƒ(x)tan x+3^x

13.

Which one of the following is true?

π∞

The range of arctangent function is [-π,π]

The range of arcsine function is (-∞,∞)

the domain of arcsine function is[0,π]

the domain of arccosine function is [-1,1]

14.

In rolling a fair die, what is the probability of obtaining 3 or 5 ?

1/3

1/4

1/6

1/2

15.

what is the locus all points in the plane in which the sum of the distances from two fixed points is constant?

Circle

Ellipse

Hyperbola

Parabola

16.

The simplified form of the expression

√5

1/5

5

√15/15

17.

In ∆ ABC, if AB=10 units, BC=14 units and AC—8 units, then the area of the triangle is

16 √3 square unit

16 √ 2 square unit

10 √6 square unit

16 √6 square unit

18.

Which one of the following sets is the symmetric difference, A∆ Bof the sets A={1,3,5,6,8,10} B={2,5,8,11}?

{1,3,6,10}

{1,2,3,5,6,8,10,11}

{2,11}

{1,2,3,6,10,11}

19.

Which one of the following gives the polar form of the complex number

20.

The solution set of the equation given by long (x²-3)=2 log (x-1)is:

∅

{4}

{1/2}

{2}

21.

which one of the following is the simplified form

-4(x+2)(x²+4)

4(x-2)(x²-4)

4(x+2)(x²+4)

-4(x-2)(x²+4)

22.

What is the product of the two complex number z=2 -i and w=5+2i ?

29

16+11i

4-11i

16-11i

23.

Which one of the following is an onto functional from on to [0,∞] ?

ƒ²

ƒ(x)=√x²

ƒ(x)=2x

ƒ(x)=|x|+2

ƒ(x)=x²+1

24.

The graph of a certain relation fi is represented by the shaded region shown on the figure below.

Which one of the following pairs of sets respectively gives the domain and range of this relation?≤

R and R

{x| x ≤ 2}and R

R and {y |y≤2}

{x| x ≤ 2} and R

25.

which one of the following interval is the solution set of the inequality x² -5x+6≤0 ?

∞

[-∞,2]

[2,3]

[0,2]

[infty,3]

26.

The angle of depression of the top of a flag pole from the top of a building is 40 √3in away from the flag pole is 30 . If the height of thing that is pole is 10m, what is the height of the building?

20√3m

40 m

50 m

10(4√3+1)m

27.

What is the seventh term of an arithmetic sequence whose third term is -4 and common difference is 5 ?

16

-16

15

-15

28.

which one of the following trigonometric values is correct?

º

tan (-120º)=-1

cos (-120º)=-0.5

sin(-120º)=0.5

cos (-60º)=√3/2

29.

The sum of the first 8 terms of a geometric sequence with first term 0.3 and common ratio 1 /10 is equal to:

30.

What are the coordinates of a point that divides the line segment with end points P (0, 1) and Q(5. 6) in the ratio 2 :3 from P

(2,3)

(0,2)

(0,3)

(3,2)

31.

The distance from the point P (3, 4 ) to the line L with equation: 3x+4y-5+0 is

4 units

6 units

5 units

7 units

32.

Which of the following is true about the trigonometric values of the given of angles?

sin(120º)=sin(60º)

sin(75º)=cos(105º)

cos (120º)=cos (60º)

tan(75º)=tan(105º)

33.

A line segment chord in an ellipse which passes through the center and perpendicular to

latus rectum

Semi major axis

Minor axis

Eccentricity

34.

which of the following is true about bounded sequence?

Every monotone hounded sequence converges.

Every bounded sequence is convergent.

every increasing hounded sequence converges to the greatest lower hound of the sequence.

Every decreasing bounded sequence converges to the least upper bound of the sequence.

35.

3

-3

-15

15

36.

If f and g are contain functions may NOT he continuous at ?

ƒ

2f+3g

ƒ-2g

ƒ/g

ƒ,g

37.

4

3

1

-1

38.

In order to find point P in space one can start from the origin O(0. 0,0) move 5 units in the direction of negative x-axis, then move 5 units in the direction of positive y-axis and finally move 5 units in the direction of negative z-axis. Which one of the following is the ordered triple of numbers represented by point?

(-5,-5,5)

(-5,5,-5)

(5,-5,5)

(5,5,5)

39.

which of the following is the variance of the data given as: 2,3,4,5,6,7

3.06

2.96

2.46

3.70

40.

Which of the following is true about the Arithmetic Mean of a given data?

it can be obtained even in the absence of some of the values in the data

It can also be used for qualitative data

There can be two means for a given data

It is affected by extreme values

41.

Which of the following pairs of events are depend?

Drawing two cards one after the other from a well shuffled pack of cards without replacement.

Drawing two balls successively from a box containing balls having the same size and shape with replacement.

Any events obtaining from tossing a coin and rolling a die at the same time.

Tossing two coins simultaneously and obtaining head from one and tail from the other.

42.

What is the derivative of the function

0

-1

1

2

43.

Let f and g be two functions. Which one of the following statements is true about f or g)

ƒ

If f and g differentiable at a, then f/g is differentiable at a

The line y= 0 is the a tangent line graph of ƒ(x )=| x | at (0, 0).45

If f’(a ) = 0, then the tangent line to the graph of f at ( a,f(a)) is y=a.

If f differentiable at a, then it is continuous at a

44.

Suppose ƒ is a twice continuously differentiable function and ƒ''(3)=5. If g ( x) ƒ(2x+3), then the second derivative of g at 0 is equal to:

20

10

5

40

45.

46.

Let ƒ be a continuous function on [a,b]. Then which of the following is NOT true?

47.

What is the value of

-1

-e

e

1

48.

Let ƒ be a continuous function R and c be a number in the domain of ƒ. Which one of the following must be true about the function?

ƒ

If f(c) is a local maximum value of f, then C f(c)-0

If f”(c)= 0, then (, f(c)) is an inflection point of f.

An absolute maximum value ƒ of which is b attained at a critical number is also a local maximum value of f.

If c is a critical number of ƒ, then ƒ (c) is a local extreme value of f.

49.

If the perimeter of a rectangle is 120 m, what are the length ƒand width wo the rectangle that maximizes its area?

l =50 m and ω=10 m

l=40 m and ω=20 m

i =30 m and ω =30 m

i =35 m and ω =35 m

50.

Suppose ƒ is a continuous function on an interval [a,b] and differentiable on [a,b] with the property ƒ (a) =ƒ (b ). Which one of the following must be true?

the function has a zero in (a,b)

the function has maximum value in (a,b)

The graph of f has horizontal tangent line at ( c, f (c) for some c ∈ (a, b).

51.

If A is a 3 x 3 matrix with det (A)— 5, then what is the determinant of 2A t?

10

40

1/2

30

52.

Which one of the following is augmented matrix associated to the system

53.

Which one of the following compound statements has a converse with truth value False?

If 6 is a prime integer, then 4 is an even number.

If man is mortal, then the earth does not rotate around the sun.

If athlete Derartu Tulu was born October 21, 1971, then 6 is prime.

If man is immortal, then earth does not rotate around the sun.

54.

which one of the following points is, inside

the sphere with equation x²+y²+z²=5

(1,2,3)

(0, 2,3)

(1, —2, 2)

(1,1,1)

55.

If Birr 20,000 is deposited in a Bank at rate of 12% interest compounded monthly, how long will it take to double the amount?

5 years

7.59 years

6years

5.81 years

56.

what is the point of intersection of the medians of Δ ABC whose vertices are given

by A(0. 0), B(6, 0) and C(0. 4) ?

57.

The following is the marks of distribution of the students oblainod is. Mathematics test out of 50

What is the first quartile of the distribution?

27.50

26

28

26.50

58.

Which one of the following is NOT true about the graph of

ƒ

x=-1 is its vertical asymptote of ƒ.

y=6 is its horizontal asymptote of ƒ.

y=4 is its horizontal asymptote.

y=5+x is its oblique asymptote

59.

If r₁, and r₂, are the roots of the equation 3x²+9x+6=0 which one of the following is true?

60.

61.

let P and q be propositions. Which of the following statement is a tautology?

62.

which of the following is NOT true about argument and validity?

An argument which is not valid if fallacy

In a valid argument if all the premises are true then the conclusion must also be true.

In a valid argument, the conclusion may be true or false whenever all the premises are true.

The validity of an argument can be checked by using a truth table.

63.

Which one of the following is true about the matrix

the cofactor of the entry 1 is -14

the cofactor of the entry 5 is -6

the minor of the entry 3 is 18

the minor of the entry 0 is 14

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