MATHEMATICS SOCIAL ENTRANCE 2015 – SMART ETHIO E-Learning

Welcome to your MATHEMATICS SOCIAL ENTRANCE 2015

MATHEMATICS SOCIAL ENTRANCE 2015

1.

Consider the functions f, g, h and m defined by f(x)=√(x−7), g(x)=log₃x, h(x)=2^(x+1), and m(x)=(x+1)². Which one of the following is true?

The range of the function h∘m is {y∈ℝ|y=(f∘g)(x)>7}.

The range of h∘m is {y∈ℝ|y=(h∘m)(x)>0}.

The domain of the function h∘m is {x∈ℝ|x≥0}.

The domain of the function f∘g is {x∈ℝ|x≥√7}.

2.

Which one of the following is the slope of a line passing through the points P(1/2, -2) and Q(-5, √3)?

(-2-√3)/(1/2+5)

(√3+2)/(-5-1/2)

(-2-√3)/(1/2-5)

(2+√3)/(-5-1/2)

3.

Which one of the following is true for the values of the trigonometric functions for the indicated angles?

csc(π/4)=√2

cos(3π/2)=0

sin(5π/6)=-1/2

tan(π/3)=-√3

4.

Which one of the following is true about the function f(x)=cosx?

Domain of f is [-1,1].

It is periodic with period 2π.

The difference between its maximum and minimum values is 2.

Range of f is {y: y∈ℝ}.

5.

In △ABC shown below, the medians BD and AE of △ABC are concurrent at O. If BD=15 cm, OD=5 cm and AO=BO, then which one of the following is NOT true?

OE=5 cm

AO=5 cm

BO=10 cm

AE=15 cm

6.

Which one of the following statements defines frustum of a pyramid?

It is a part of the pyramid included between the base and the cross-section made by a plane parallel to the base.

It is a part of the pyramid included between the vertex and a cross-section made by a plane parallel to one of its lateral surface.

It is a part of the pyramid included between the vertex and the cross-section made by a plane parallel to the base.

It is a part of the pyramid included between the base and a cross-section made by a plane parallel to one of its lateral surface.

7.

8.

A frustum of a cone is formed from a right circular cone of height 15 cm. If the base radii of the frustum are 2 cm and 3 cm, where the height from the smaller base to the vertex is 4 cm, what is the volume of the frustum of the cone?

(285/3)π cm³

(195/3)π cm³

(119/3)π cm³

(2.09/3)π cm³

9.

Which one of the following is the converse of the conditional statement "If life in Ethiopia was simpler, then people in Ethiopia would not go to other nations."?

If life in Ethiopia was simpler, then people in Ethiopia would go to other nations.

If people of Ethiopia would go to other nations, then life in Ethiopia was not simpler

If life in Ethiopia was not simpler, then people in Ethiopia would go to other nations.

If people of Ethiopia would not go to other nations, then life in Ethiopia was simpler.

10.

Which one of the following pairs of functions, f and g, are inverse to each other?

f(x)=5ˣ and g(x)=log₅ x

f(x)=x+11 and g(x)=x-11

f(x)=(2x-1)/(x+3) and g(x)=(3x+1)/(2-x)

f(x)=(x-13)² and g(x)=x+√13

11.

Which one of the following is equation of the tangent line to the circle (x-2)²+y²=10 at (5,1)?

3x+y-16=0

x+3y-16=0

-x+3y+14=0

-3x+y-14=0

12.

Which of the following is the possible standard form of equation of an ellipse whose center is at (-1,0), length of major axis is 3 and that of the minor axis is 2?

x²/9 + y-²/4 = 1

(x+1)²/9 + y²/4 = 1

(x-2)²/9 + y²/4 = 1

(x+1)²/9 + (y+1)²/4 = 1

13.

The foci of a hyperbola are (-2,4) and (8,4), and the length of its conjugate axis is 8. Which one of the following is the standard equation of the hyperbola?

(x-3)²/25 - (y-4)²/16 = 1

(x-3)²/16 - (y-4)²/9 = 1

(y-4)²/9 - (x-3)²/16 = 1

(y-4)²/16 - (x-3)²/25 = 1

14.

If a regular polygon circumscribes a circle and the sides of the polygon touch the circle at exactly seven points, what is the maximum number of lines of symmetry of the polygon?

Six

Eight

Five

Seven

15.

Which of the following defines a prime number?

It is a natural number that has exactly two distinct factors.

It is a natural number where one of its factors is 3.

It is an odd natural number that has only factors.

It is a natural number that has odd number of factors.

16.

Which one of the following statements is true?

It is not possible to find a point on a number line corresponding to an irrational number.

For every real number there is exactly one point corresponding to it on a number line.

The set of integers has a one-to-one correspondence with the set of all points on a number line.

If a point on a number line is represented by a rational number, then we can use the same point to represent an irrational number.

17.

Which one of the following is the solution set of:

{7/17}

{14/17}

{7/34}

{5/11}

18.

Which one of the following is the solution set of: |9x - (1 - x)| + 4x= 1?

{0, 1/6}

{0, 1/7}

{1/7, 1/6}

{-1/7, 0}

19.

20.

Which one of the following interval(s) is the solution set of the quadratic inequality 10x² - 4x - 6 < 8x² + 4x - 12?

(-∞, 1)

(1,3)

(3, ∞)

(-∞, 1) ∪ (3, ∞)

21.

For a parallelogram ABCD, the length of side AB is equal to the length of side of a square with area 64 cm². If the length of side BC of the parallelogram ABCD is 3cm and m (∠ABC) = 120°, what is the area of ABCD?

12√3 cm²

24√3 cm²

4√3 cm²

64 cm²

22.

Which one of the following is true about the function

Domain of f is {x ∈ ℝ : x ≥ 7/5}.

Domain of f is {x ∈ ℝ : x ≥ 7}.

Range of f is {f(x) ∈ ℝ : f(x) > 0}.

Range of f is {f(x) ∈ ℝ : f(x) ≥ 1}.

23.

A student took 5 Model Exams and scored 85,88,90 and 92 four subjects namely Engilsh, Geography, Economics and History exams respectively. she did not Know her score in Mathematics exam but she knew that her mean in all five exams is 90. What is here score in Mathematics?

89

95

93

90

24.

Which one of the following is a vector quantity?

Floor area of a classroom.

Tempreature of a room.

Speed of a motorbike

Force to push a car.

25.

If the polynomial f(x)=x⁴-9x²+22 is divided by x-2, wich one of the following are the quotient and remainder respectively?

x³+2x²-5x-10 and 2

x³+2x²-5x+10 and 2.

x³+2x²-5x-10 and -2.

x³+2x²-5x+10 and -2.

26.

Let x and y be real numbers and x >0. If y=

log√10 (1/x), which one of the following equations is true ?

x=10^{2 y}

x=10^{-1/2 y}

x=10^{-2 y}

x=10^{1/2 y}

27.

Consider the graph of f(x)=log (x+3) which is shown below

which one of the following is not true about the function ƒ ?

The function increases as the value of x increases.

The x- intercept of the graph of ƒ is-2.

the domain of ƒ is the set of real numbers greater than -3

the y-axis is a vertical asymptote of graph of ƒ.

28.

Let p,q and r propostions. if the truth value of the proposition [(p⇒ q)∧r]⇒q is False . Then ; the converse of which proposition has truth value True?

r⇒ q

q⇒ ¬p

p⇒ ¬q

p⇒ r

29.

Consider the system of equations . Which one of the following is the correct augmented matrix of the given system?

30.

The following table shows the age distribution of Grade 12 students in one section of a certain school.

Which one of the following is the mean age of in year?

23.2

21.2

22.2

20.2

31.

The following table shows the frequency distribution of scores of students in Mathematics Mid -Exam which was marked out of 50.

Which one of the following is true about the distribution of scores?

The third decile of the distribution lies in the first class

The eighth decile of the distribution lies in the fourth class.

The fourth decile of the distribution lies in the third class.

The fifth decile of the distribution lies in the third class.

32.

A committee of five members was formed from 6 female and 4 males. How many different committees can be formed that comsists 3 females and 2 males?

40

20

240

120

33.

Let M= and Q= be give matrices . which one of the following is true?

2Q =M

1/2 Q=2M

3M=3/2Q

2M=-Q

34.

if we toss a coin three times, what is the number of possible events of getting at least two heads?

6

4

5

3

35.

A woman wants to buy a new car that costs Birr 1,100,000. she paid Birr 870,000 and agreed with the seller to pay Birr 10,000 per month to cover the remaining amount at 0% interest rate. How many months will it take the woman to pay the remaining money ?

Thirteen months

Seventeen months

Twenty months

Seven months

36.

Which one of the following statements is true?

37.

Which are of the following geometric series is convergent?

38.

Which one of the following limit values is correct for the limit of the given function?

39.

Which one of the following is the correct definition of continuity of a function on the given interval?

if a function ^g is continuous on the interval (a,b], then ^g is continuous on (a,b) and continuous from the right of b,

if a function f is continuous on the interval (a,b] , then f is continuous for every point ^cin the inteval [a,b]

if a function ^his continuous on an open interval (a,b), then

if function ^mis continuous on the interval [a,∞) then ^mis continuous on [a,∞) and continuous from the right of a.

40.

The function fg is continuous on the interval (-∞,1]

The function f+g is continuous no [-1,1].

The function h-g is continuouson [-1,1].

The function 3g is continuous on the interval where g is continuous

41.

A man deposited Birr 5000 in a bank with annual interest rate of 14% compounded semi-annually. What is the total interest earned at the end of the second year approxmately?

Birr 1554

Birr 1654

Birr 6554

Birr 5554

42.

Which one of the following is true about the determinant of a matrix

The determinant of any two-by-two matrix is non -negative

43.

Which one of the following is true about addition of complex numbers?

44.

Which one of the following is true about the system of linear equations

45.

Which one of the following is true about the product of complex numbers?

46.

on the coordinate plane a graph is given as shown below.

Which one of the following system of linear equations has the above shaded region as its solution ?

47.

which one of the following is the minimum value of the objective function Z=2x-5y, subjected to the constraints:

-150/11

4

-10

0

48.

A man purchased a house from a Real estate for Birr 3,550,000 and made a down payment of 20% of the purchase price. The Real estate from which he purchased the house charges an annual interset rate 8% on his 15 years mortgage. Then what is the monthly mortgage payment?

Birr 5,134.72

Birr 7,094.32

Birr 8,414.92

Birr 10,383.04

49.

Which one of the following integrals of trigonometric functions is true

50.

What is the area (is square units) of the regions bounded by the graph of the equations f(x)=2x+1, y=0, x=-1 and x=4?

41

20.5

40

21.5

51.

What is the area (in square uints ) of the regions enclosed by the curve f (x)=x ²-4x+3, the x-axis the vertical lines x=-1 and x=3?

5

17

12

8

52.

Suppose the following data represents the weight in Kg of 10 students in a classroom.

61,49,52,68,61,55,64,63,67,60

Which one of the following is NOT true about the data?

Mean deviation about the mean of the data is 4.8

Mean deviation about the mean of the daa is 4.7

Mean deviation about the mode of the data is 4.6

Mean deviation about the median of the data is 4.6

53.

The following table shows the first quartile Q1 and the third quartile Q3 of two data sets X and Y.

Which if the following is true about the given data?

The inter quartile range of data x is 7.

Data Y possesses higher variability than data X.

Data X possesses higher variabiliy than data Y

The inter quartile range of data Y is 4.5.

54.

Students in class P, Q, R and S took similar test which is marked out of 20. The following table shows the mean score and the standard deviation of scores of the students in each class. Class Mean Standard Deviation

Which of the following statements is true about the these data?
Test result of class P students is more

Test result of class Q sudents is highly variable.

The most consistent test result is class P students' result.

Test result of class P students is more consistent than class R students.

Test result of class S students is more consistent than class R students.

55.

Which one of the following statements is true?

If a woman buys 20 Kg of sugar by Birr 2000.00, and she sells one kilogram of it by Birr 85.00, then she sells by 30% price decrease

A person earns Birr 175.00 commission per service he provides. If he provided 13 services and got Birr 2000.00, then the percent decrease of his income is approximately

If a shop owner offered 75 T-shirts by a price of Birr 325.00 for each and he bought all by Birr 25,000.00, then the percent decrease he had made for one T-shirt is 2.5%

If the price of an egg reduced from Birr 13.00 to 11.25, then the percent decrease is 0.142%.

56.

If ƒ and g are functions defined by f(x)= x⁷-10x⁵+x³ and g(x)=e ^-2xthen which one of the following is true?

57.

The following table is the distance traveled by a car in agiven times

Which of the following time interval has the maximum average rate of change of the distance with respect to time ?

t=4 hours and t=5 hours

t=1 hours and t=2 hours

t=3 hours and t=4 hours

t=2 hours and t=3 hours

58.

Which one of the following is true about the derivative of the given functions?

59.

Which one of the following is true about zero of a function?

60.

Which one of the following is NOT true about the derivative of a function?

The derivative of a function f at a point x is the slope of a line tangent to the graph of the function at apoint (x, f (x)).

The derivative of a function af a point is equal to the area of the region enclosed by the graph of the function and the coordinate axes.

The derivative of a function g at a point t equal to the limit of the ratio of the difference of functional values of g at x and at t to x minus t as x approaches t.

The derivative of a function at a point ^x0 is the instantaneous rate of change of f (x) at (^x0,f(^x0))

61.

Which one of the following is true about integration and differentiation ?

The process of finding f(x) from ∫ f(x)dx is called integration

integration is the reverse process of differentiation.

Any continuous function has only one anti-derivative

integral of a function is an anti-derivative of its dervative.

62.

if a rectangular region of length x and width y has an area of 64 m², what are the values of x and y such that its perimeter is minimum

x=8 and y=8

x=32 and y=2

x=16 and y=4

x=64 and y=1

63.

Which one of the following is an equation of the line tangent to the graph of f(x)= x³-3x²+x+1 at (1,0)?

y=2x-2

y=-2x+2

y=2x+2

y=-2x-2

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