mathematics Social national exam 2014 – SMART ETHIO E-Learning

Welcome to your mathematics Social national exam 2014

Choose the best answer from the given

Alternatives

1.

Consider ΔABC with right angle at C and in(∠ ABC)=55º. If the length of AC is 10 units, then what is the area of the triangle? T (Given tan35º =0.7 and tan55º =1.43)

tan 85 = 0.7 and tan 55 1. 43 )

. If the length of AC is 10 units, then what is the area of the triangle? T (Given

tan 85 = 0.7 and tan 55 1. 43 )

70 sq. units

35 sq.units

2.

The base of a right prism is a rectangle with sides 3 cm and 4 cm and the altitude of the prism is 5 cm. What is the total surface area of the prism?

94 cm²

82 cm²

70 cm²

102 cm²

3.

3cm in the direction East 60º North

3cm in the direction East 30º North

6cm in the direction East 30º North

6cm in the direction East 60º North

4.

5.

Below is a histogram showing the time taken to complete a test.

Based on the above histogram, which of the following is true?

30% of the students completed the test with less than 40 minutes.

40% students completed the test with more than 40 minutes

50% of the students completed the test with less than 50 minutes

25% of the students completed the test with more than 50 minutes

6.

what is the solution set of the equation of 3^=x2=1/9?

{-1,2}

{1,-2}

{0,1}

{-1,0}

7.

Which one of the following is true about the trigonometric values of 855º

cos 855º=-√2/2

tan855º=1

sin 855º=√3/2

cot855º=-√

8.

which of the following true about the function y=sinx?

∞

its domain is(0,∞)

its period is π

its range is[-1,1]

its domain is[-1,1]

9.

The lower and upper bases of the frustum of a regular pyramid are equilateral triangles of side 3 cm long and 2 cm long respectively. If its slant height is 4 cm, then what is the lateral surface area of the frustum?

72cm²

30cm²

48cm²

96cm²

10.

which one of the following is true about the signum function ,f(x)=sgnx

its domain{-1,0,1}

Its range is[0,∞]

Its range is the set of real numbers.

Its domain is the set of real numbers.

11.

Which one of the following is the equation of a circle with center ( 2, - 1) and radius 3 units?

x²+y² +2x+2y- 4-0

x²+y² +4x-2y-5=0

x²+y² -4x+2y- 4-0

x²+y² -4x+2y-5=0

12.

Consider the ellipse given by the equation

4(x+1)²+(y-1)²=16. Which one of the following is the standard form of equation of the ellipse?

13.

120º

90º

105º

150º

14.

Which one of the following is the inverse of f ?

15.

Consider the rational function Which one of following is true about the

graph of f ?

It's intercept is -1

It has no x intercept

It is symmetrical about the y axis.

It is symmetrical about the origin.

16.

Consider the grouped frequency table for students' weight in a certain school.

What is the mean weight of the students?

43.8 kg

41.5 kg

43 kg

45 kg

17.

Let A={0, 2, 4, 6, 8, 9, 10} and B={1, 3, 5, 7, 9} . Which one of the following is true?

B-A -B

A- B —-A

A -B ={0, 2, 4, 6, 8, 10}

B -A={1, 3, 5, 7}

18.

Consider the polynomial function f(x) =ax⁴- b

, where a and b are real numbers. Which one

of the following is true about f ?

The graph of f opens downward for any b≤ 0.

he graph of f opens upward for any b<0.

The graph of f opens downward for any a≤ 0.

The graph of f opens upward for any a> 0.

19.

The solution set of inequality 3x² +35x -12 < 0 is.

(-12,1)

(-∞,1/3)

(-12,1/3)

(-∞,-12)

20.

A closed right circular cone has a base radius 2 cm and slant height 3√2 cm What is the total surface area of the cone?

2π(1 +3√2)cm ²

2π(2 +3√2 )cm²

6π√14cm²

2π√14cm²

21.

Which of the following is true? A hyperbola is a locus of points in the plane so that

the sum of the distance from two fixed points is constant.

the points have the same distance from a given point and a given line.

the difference between the distances from two fixed points is constant.

the points have the same distance any given two points.

22.

Which of the following is the converse of; "If wages increase, then inflation decreases."?

If inflation increases, then wages decrease.

If inflation increases, then wages increase.

If inflation decreases, then wages decrease.

If inflation decreases, then wages increase.

23.

24.

You happened to notice that the 8% sales tax that your paid on the new Television Set came to Birr 3,800. How much did the Television fog cost him?

Birr 47,500

Birr 35, 400

Birr 45,800

Birr 30,600

25.

Voter turnout in the local school board elections declined 40% from law year. This year only 3600 eligible voters went to the polls. How many people voted in last years school board elections?

4,500

6,000

5,000

5,500

26.

Which one of the following statements is NOT true about the graph of the given linear inequality?

The graph of the linear inequality y ≤2x+1 is below the line y=yon the interval (-∞,-1)

The graph of the linear inequality y ≤x-1 is above the line y=2x on the interval (-∞,-1)

The graph of the linear inequality y >2x+1 contains no points of the line y=2x-3

The graph of the linear inequality y >2x-1 contains all points of the line y=2x

27.

Consider a line with equation y=mx+b Which of the following is true?

The line passes through the origin.

The line has no slope.

The line intersects the y axis, if m≠ 0 and b >0.

The line intersects the x axis, if m=0 and b >0.

28.

29.

Consider the function f(x)=x²-3x on[-1,2] What is the value x that satisfies the Mean Value Theorem?

3/2

1/2

1

0

30.

Hi carpenter wants to design a closed box that has a square base and total surface area of 54 cm² . What is the maximum volume that can be constructed with the given total surface area?

18 cm³

13.5 cm³

27 cm³

12 cm³

31.

What is the area of the region bounded by the line y=x and the parabola y =x² on the interval [0, 3]?

9 square units

3 square units

2 square units

9/2 square units

32.

Which of the following is NOT true?

Random sampling requires time to plan and implement.

There is no single rule for determining the size of a sample.

Random sampling is free from personal bias of the investigator.

Any person can implement random sampling from a given population.

33.

what is simplified form of ?

34.

Consider two firms with the given mean income and standard deviation

firm mean income standard deviation
(in birr) (in birr)

Firm I 1,500,000 300

Firm I I 1,500,000 350

which of the the following is true ?

The data set in firm I have greater variability than firm II

The data set in firm I have less variability than firm II

The two data sets have same consistency.

We cannot compare the two data sets.

35.

consider the following data 6, 6, 7,7,7,8,8, then which of the following is true

the mean deviation from the mean is 4/7

the mean deviation from the mean is 7/4

the mean deviation from the mean is 3/2

the mean deviation from the mean is 7/4?

36.

A painter buys 5 liters of paint for Birr 36 and 6 liters of the same brand paint for Birr 43 , Which of the following is true?

Buying 6 liters is more economical than buying 5 liters

both have the save economical purchase.

we can not compare

Buying 5liters is more economical than buying 6 liters

37.

One special perfume costs a cosmetic shop Birr 2,100. If the shop de sires a 25% markup rate based on the selling price, then which one of the following should be set as a selling price for this perfume?

birr 2,600

birr 2,800

birr 2,300

birr 2,400

38.

39.

40.

A line makes an angle of 145° with the positive x-axis. What is the slope of the line? (Given tan 35°-0.7)

0.7

-10/7

-0/7

10/7

41.

What is the solution set of

{4/11}

{11/4}

{5/4}

{4/5}

42.

3π/4

π/4

π/2

3π/2

43.

let p: 2 is prime number and q: 3 is an odd number. then the contrapositive and its truth value of the statement p⇒ q are respectively.

q ⇒ ¬p and false

¬ q ⇒ ¬p and false

¬p ⇒ q and true

¬q ⇒ ¬p and true

44.

The following table shows the test scores of 20 students in a class.

What is the variance of the given data?

18.45

19.45

17.2

16.2

45.

If two cards are drawn one after the other from a well shuffled pack of cards, then which one of the following is an independent event?

Drawing a king in the first draw and a queen in the second drawn by replacing the first.

Drawing a king in the first drawn and a queen in the second drawn without replacing the first.

Drawn queens in both draws without replacing the first.

Drawing kings in both draws without replacing the first.

46.

A bag contains 2 red, 3 white and 1 black balls. We drawn two balls one after the other without replacement. What is the probability that the first ball is red and the second ball is black?

1/15

1/18

1/10

1/12

47.

48.

49.

What is the solution of the system of linear

equations

50.

What is the area of an equilateral triangle inscribed in a circle radius 4 units?

12√3 sq.units

12sq.units

36sq.units

6√3sq.units

51.

Consider the sequence

Which one of the following is true about the sequence?

3/2 is its lower bound

6/5 is its upper bound

4 is its lower bound

2 is its lower bound

52.

which of the following is equal to

-1/2

0

-1

-2

53.

A couple own a house that value Birr 2,000,000 The house added Birr 10,000 in the first year, Birr 10,400 in the second year, Birr 10,800 the third year and so on. What is the value of the house at the end 6 years?

birr 2,012,000

birr 2,064,000

birr 2,060,000

birr 2,054,000

54.

Let f be a function defined on an open interval about a real number a, except possibly at a itself. Which one of the following is necessary for to exist?

55.

Let f be a function that is continuous at x_oWhich of the following is true about f ?

56.

57.

58.

what is the equation of the tangent line to the
graph of the function f(x)= e^x at (1,e)?

y=1/e x+1/e

y=x +1/e

y= ex + e

y= ex

59.

Water is flowing into a cylindrical water tank of radius 2 in and height 10m at a rate of 5m3/min . What is the rate change of the height when the water level is 6m?

2π m/min

5/4π m/min

2 m/min

5π/4m/min

60.

Which one of the following is equal to ∫(e^2x+cosx)dx?