Mathematics national exam 2012 – SMART ETHIO E-Learning

Welcome to your Mathematics national exam 2012

choose the best answer from the given

alternative

1.

Which of the following statements is NOT true?

When the variance of a data is close to zero, the data shows less variability.

If two data have equal mean, the data with less variance shows less variability.

A large value of variance shows that the data values are closer to the mean.

Variance indicates the variability of a set of numerical data items.

2.

The following is the frequency distribution of a group data.

Class interval and Frequency (f)

what is the mean of data?

13

14

12.5

15

3.

4.

5.

R\{1}

R\{-1,1}

R\{-1}

R

6.

What is the set of parabola is given by y2 +6y+8x +25= 0. Which one of the following NOT true about this parabola?

Its vertex is {- 2, -3)

It is directrix is the y-axis

Its focus lies at (-4, -3)

It is opens to the right

7.

8.

9.

If P : "the rainy season is very good this year" and q : "river are rising", then the statement "It is not true that neither the rainy season is very good this year nor rivers are rising" denoted by

10.

the distance between point (2,-3)and the line e: x+y -7=0 is

11.

0 is one of it terms

it terms are odd numbers

it terms are non-positive

it terms are natural numbers

12.

Let {a_n }be a sequence of real numbers,
Then which of the following is true about the sequence?

13.

Which of the following is an upper bound for the sequence

0

2

1

4/3

14.

Which of the following is the lower bound for the sequence

1

5/3

9/5

7/4

15.

√2

√5

2

5

16.

-1/3

-1

1/3

1

17.

18.

19.

7/4

7/2

4

2

20.

What is the slope of the line tangent to the graph of f (x)=x²+tan x at (π, f(π)) ?
π

2π

2

2π+1

2π-1

21.

2

-6

6

-2

22.

The product of two positive real numbers is 100 , such that the sum of two times the first number and eight times the second number is minimum. Which of the following pairs of numbers are the first and the second numbers respectively?

1 and 99

50 and 2

20 and 5

25 and 4

23.

Which of the following is a zero for the function f(x)=x3 – 3x2 +3x - 1 ?

1

-1

0

-2

24.

25.

24

6

2/3

3/2

26.

27.

28.

29.

The amplitude is 1

The range is [-5,1]

The period is 2 π

The base shift is 6

30.

If the 1^st and 4^th terms of a geometric progression are 3 and 81 respectively,
what is common ration for this progression?

1/3

1/9

9

3

31.

-6 and -3

10 and 0

6 and 3

-1 and 3

32.

33.

The volume of a cube is increasing at a rate of 9 cm² / sec. How fast is the surface area increasing when the length of an edge is 10cm?

3.6cm² /sec

36cm² /sec

90cm² /sec

6 cm² /sec

34.

The maximum profit that a company can make if the profit function is given by P (x )= 36+72x —18x² is

31

108

124

2232

35.

36.

Which of the following is NOT true about the scalar product of vectors?

The scalar product is distributive over addition of vectors.

The scalar product of perpendicular vectors is zero.

The scalar product is commutative.

The scalar product of non -zero parallel vectors is zero.

37.

Which one of the following is NOT true about transformation?

Translations move angles to congruent angles.

Reflection is not a rigid motion.

Rotation move triangles in to congruent triangles.

Rotation is a rigid motion.

38.

39.

Areal number o is the limit of a sequence {a_n} if

40.

Which one of the following is the standard form of the equation of the ellipse with vertices: (3, 1), (3, 9); and minor axis of length 6

41.

42.

Let P and q propositions with truth value True and false respectively. Then which of the following is correct?

43.

44.

x-intercept at (-4,0)

a vertical asymptote , x=1.

y-intercept (0,-4)

a horizontal asymptote , y=2

45.

46.

1/3

-1

1

-1/3

47.

48.

1

-1/2

2

1/2

49.

50.

Which one of the following is a row reduced electron form of the matrix

51.

5+4i

4+5i

4i

5i

52.

Consider the experiment of rotting a die whose sample space is (1, 2, 3, 4, 5,6). If two dice are rolled simultaneously, what is the probability that a prime number turns up on one of the dice and a composite number on the other?

1/3

5/6

2/3

1/6

53.

Consider the following frequency distribution of grouped data.

Values & frequency

Which of the following statements is true this
frequency distribution?