mathematics Social national exam 2012 – SMART ETHIO E-Learning

Welcome to your mathematics Social national exam 2012

choose the best answer from the given

alternatives

1.

A system of linear equations is given as:

Which one of the following is the augmented matrix for the above system?

2.

Which one of the following is true about E and F ?

F=2E

F=1/2E

F=-1/2 E

F=-1/2E

3.

What is the range of function ƒ given by ƒ(x)|x-1/2|+3

4.

Which are of the following is equivalent to

5.

If z1 and z2 are complex numbers, then which one of the following statement is NOT true about them?

z1 + z2 is complex number.

z1 + z2, can be real number

z1 + z2 is a complex number .

z1 - z2 is always a real number

6.

7.

A function ƒ is continuous on an interval if and only if

≠

it is continuous at every point of the interval

for some point c interval ƒ (x)≠ ƒ (c).

for some point c in interval limƒ(x)=0

For exactly one point C is the interval ƒ (x)≠ ƒ (c).

8.

Which one of the following is NOT principle of taxation?

Compliance costs to business and administration cots for government should be minimized as far as possible.

Tax rules should be clear and simple to understand so that taxpayers know where they stand.

Exemption of taxes are made to ensure revenue to cover government cost of administration.

Taxation should seek to be neutral and equitable between forms of business activities.

9.

Lat A and B be two sets and ƒ be a function from A in to B(f :A →B). In order to say ƒ is

an on-to function which one of the following condition said be fulfilled?

If you can find two distinct elements in A that range pre-image of exactly one elements of B, then / cannot be onto function.

If any two elements in B are the images of exactly one element of A, then ƒ is onto function.

If you find an element y in B that is not an A image of any one of the elements of A, then ƒ is not onto function.

If each element x in A is the pre-image of at D least one element y in & under ƒ , then / is onto function.

10.

The frequency distribution table of a grouped data X is given as shown below.

Which one of the following is true about this

data?

The lower class limit of the 4th class is 24.5

class is22.5

The class mid-point of the Parser Error: Expected '}', got 'EOF'

The class mark of the 2nut class is 17

the upper class boundary of the 3rd class is 24

11.

Which one of the following is a discrete variable?

The temperature of an object.

Number of road accidents in Ethiopia.

Profit earned by a company.

The speed of a moving object.

12.

Which one is the standard form of the equation of the parabola with vertex (- 2. 3) and focus (2, 3)?

²

(y-3)²=-16(x+2)

(x+2)²=-16(y-3)

(x+2)²=16(y-3)

(y-3)²=16(x+2)

13.

for a given ellipse, what do you call the ratio of the distance between the two foci to the length of the major axis?

Eccentricity

Length of minor axis

Latus rectum

DirectriX

14.

When 3.125 is written in the form of d/b , it is equal to

3094/990

3090/1009

3100/900

3094/1000

15.

503

508

500

498

16.

2(n-1)!

(2n)!

2n!

2(n+1)!

17.

If fourth term of a geometric sequence with positive term is 125 . If the tenth term is 125 /64then which one of the following is the first term this sequence?

500

1000

250

750

18.

Consider the function ƒ(x)=x³ +x²-4x-3 whose graph is shown

Which one of the following is the slope of the

tangent line at (— 2 1)

4

-4

3

-3

19.

Which of the following is an equation of the line tangent to the graph of y=x²+e× at ×=0 ?

y=x

y=2x

y=x+1

y=-1

20.

If ƒ ( x )= 4 —x² sin x, then which of the following expressions describes ƒ'(x) ?

1-cos x-2 sin x

1+cos x+2 sin x

x (x cos x-2 sin x)

-x (x cos x+2 sin x)

21.

A sum on money is invested at a compound interest calculated annually which amounts to 21,632 Birr at the end of the second year and to 22,497.28 Birr at the end of the third year. Which one of the following pairs of values gives the rate of interest and the principal, respectively?

0.05 and 21, 000 Birr

0.06 and 21,550 Birr

0.03 and 18,550Birr

0.04 and 20,000 Birr

22.

If 20,000 Birr is divided among three persons in the ratio 5:2:3, the which one of the following is the maximum share?

3,000 Birr

4,000 Birr

6, 000Birr

10,000 Birr

23.

120πcm³

150πcm³

210πcm³

270πcm³

24.

Which one of the following pairs contains the modulus and argument of the contains number 1+√3i respectively?

1 and π/3 rad

2 and π/3 rad

2 and π/6 rad

1and π/6 rad

25.

if Z₁=5 -3i and Z₂=3-4i, then Z₁/Z₂is equal to

27/25+29/25i

27/25+11/25i

3/25+11/25i

27/25-11/25i

26.

if f(x)=x+³ log₁₀x, then which one of the following is equal to f'(x)?

x² /log10x-3x²Inx

x³ /log10x-3x²Inx

x² /ln10x-3x²log10x

x³ /In103x²log10x

27.

Which one of the following events explains the meaning of derivative?

It is the slope of secant line to graph of a function f where this secant line passes B through two distinct points (x0,y0) and (x1,y1) of f

It gives the position of an that is moving along a coordinate line at a certain given time t.

It gives the amount of money at the end of n years, if someone deposit P birr in a bank that pays r annual interest compound monthly.

It is the marginal cost of a product which is the rate of change of cost with respect to the level of production.

28.

Which one of the following is the set of all critical numbers of f(x)=+ x3 —2x² well on the interval |—1, 3] ?

{1}

29.

Which is of the following statements gives the geometric interpretation of the Rolle’s theorem stated for a continuous function f on [a,b] that ls differentiable in (o, 1) ?

At every point within the interval , it is possible to draw a tangent line to the graph of f which is parallel to the x-axis

there is a point on the graph of f where the tangent line through this point is not parallel to a secant line joining any two points of he graph

there is a point c in the interval (a,b) where a tangent line to the graph of the function through this point is parallel to the x-axis

the exists at most one tangent line to the graph of the function which is parallel to the y-axis

30.

What is then value of k so that f(x)=x/x²+k has a relative extremum at x=2

0

4

2

8

31.

What is the 3rd decile (D) of the data 2, 5, 3, 4, 4, 11, 9, 8, 7,12, 19 ?

4.5

4

5

5.5

32.

A committee of three members with position the of Chairman, Vice-chairman and Secretary is to be from 10 candidates. If every candidate has equal chance to be selected and to take any of three positions, in how many ways an the committee with specified positions be formed?

120

360

720

840

33.

if f(x)= In(2 + sinx ), then f'(x) is equal to

-cosx/1 + sin x

cscx/1 + sin x

cosx/2 + sinx

sec/1 + sin x

34.

35.

Which one of the following is the contra positive of the statement: "If 9 is divisible by 2 , then 5 is an even number"?

If 9 is not divisible by 2 , then 5 is not an even number.

If 5 is not an even number, the 9 is not divisible by 2 .

If 5 is an even number, then 9 is divisible by 2 .

If 5 is not an even number, then 9 is divisible by 2 .

36.

If P⇒¬q is False, then for any proposition which one of the following statements is True?

37.

A textile factory produces shirts and

calculates the revenue r, cost c and profit P

as functions of the number of shirts. The

functions are as follows:

r(x) =the revenue from selling x shirts,
c(x) =the cost of producing the x shirts,

p(x)=r(x)-c(x)=the profit from producing

and selling x shirts.

If r(x)=9x and c(x)—x ³—6x ²+15x, where x

represents thousands of shirts produced, then which one of the following statements is correct about the loss or profit gained at the given production level?

Maximum profit occurs at about x= 3414

Maximum loss occurs at about x=2510

Maximum profit occurs at about x=6828

Maximum loss occurs at about x=1586

38.

Let a function f be continuous on [a,b]and differentiable in (a,b). Which one of the following is correct about f ?

≤

if f (a)=f(b) and f (x)>f(a)for all x∈ (a,b),then f has got a minimum value at c ∈ (a,b) where f' (c)=.

f(x)=0 for all x ∈ (a,b) then f is a constant on (a,b)

If f”(c)=0 and f” is continuous at C such A that f”(C ) >0, then f has a local maximum at c

if f (x)≤0 for all x ∈ (a,b) then f is increasing on (a,b).

39.

Which one of the following is a possible solution for

2

1/2

0

1

40.

Which of the following is true the graph of the function given by f(x)=-8/x²-4

its vertical asymptote is x=4

(2,0) is the x-intercept

it is symmetric about the orign.

its horizontal asymptote is y=0

41.

Which one of the following functions is NOT invertible?

∞

g={(x,y)}: y= x²+ 1}, where g :R→R

h= {(x,y)}: y= log3 2x}, where h:(0,∞)→R

k= {(x,y)}: y =e²x}, where k: R →(0,∞)

f= {(x,y)}: y = 4x -3 }, where f: R→R

42.

a² - a

a³-1

a(a²-1)

a³- a

43.

minor of a 23 =-38

cofactor of a13 =8

minor of a 13 = cofactor of a31

cofactor of a23 = 38

44.

Which one of the following sequence has no upper bound?

{1-n}

(2n -1)

{(4n -1)}/2n}

{(-1) n/n}

45.

Which one of the following matrices is the inverse of

46.

if two e1=2x+3y-5=0 and e2 : lax +2y + p=0, are perpendic ular at point (-2,3),then which one pf the following pairs gives the correct values of k and p?

k=3 and p=15

k=- and p=9

k=-3 and p=- 12

k=3 and p=-6

47.

which one of the following is the value of

2

1/2

4

1/4

48.

for all n ∈ Ν which one of the following sequences is a null sequence ?

49.

It coverages to its least upper bound 0

It is unbounded sequence and hence diverges.

All its terms of positive numbers and hence diverges.

It is a monotonic sequence and converges to -1

50.

3/2

5/2

1

7/2

51.

52.

Consider the following linear programming

model: objective function Z-3 x+5 y

3 x+y 1 x+2 y< 6

x> 0, y>0

Which one of the following the minimum value of Z ?

5

3

0

It's his no minimum value

53.

problem to be solved using linear programming is given as follows: ”A coffce packer blends coffee from Harar and from Sidama to prepare two kinds products, viz, ' Super' and ”Deluxe brands. Each kilogram of Super coffee contains 0.5 kg of Harar coffee and 0.5 kg of Sidama coffee, whereas Deluxe coffee contains 0.25 kfi of Harar coffec and 0.75 kg of Sidama coffee. The packer has 120 kg of Harar coffee and 160 kg Silyna cuffee in the store. Moreover, the plan is to get 20 Birr profft each kilogram of Supper coffee and a profit of 30 Birr on each kilogrem of Delure coffee. In arder to maximize profit the packer needs to kaion the amount (in kg ) of each brand of coffee that should be blendec. If o the amount of Super coffee in kilogram and P the amount of Deluxe coffee in kilograms, then which one of the following standard forms of linear programming models should be used to solve the above problem?

54.

A person has 2 parents, 4 grandparents, 8 great grandparents and so on. What is the total number of his ancestors during the ten generations preceding his own?

5048

1024

2064

4092

55.

Assuming that the population of Ethiopia increases at the rate of 3% per year and the current population is 102 million, which one of the following is the best approximate of the population of Ethiopia 10 years from now?

133 million

125 million

137 million

141 million

56.

What is the number that satisfies the
conclusion of the Mean Value Theorem for f(x)=x³ -1 on the interval [0,2] ?

√(2/3)

2/3

√2/3

2√3√3

57.

A water tank is m the form of a right circular cylinder with base radius 2m and height 3m . If water is pumped into the tank at the rate of 0.5 m³/min, what is the rate at which the water level is rising?

4π/3 m/min

8/π m/min

3π/8 m/min

1/8π m/min

58.

What is the tangent of the angle formed by the lines 2x+3 y=5 and x-2 y=4

2/3

-7/4

-1/4

1/3

59.

If the line y= 2x+1 is tangent to a circle centered at (4, 0), then what are the coordinates for the intersection point of the line and the circle?

(4/5,8/5)

(2/5,8/5)

(3/4,5/2)

(2/5,9/5)

60.

Which one of the following triplets of values of x,y and z contains all solutions for

4 x—y + z=- 5

2 x+2 y+3z=10 ?

5x-2y+6z=1

x=2 ,y =-2, =3

x=3,y=-1,z=2

x=-1, y=3,z=2

x=3, y= 2,z=-1

61.

4/3

2/3

0

1/3

62.

What is the maximum possible interval on which f continuous?

(-∞.∞)

(-∞,-2)

(-∞,-2)u(-2,∞)

(-2,∞)

63.

Among a group of 200 students who are asked whether or not they like Mathematics and/or History, it is found that 80 of them like Mathematics only, 20 like History and 40 like both. If a student is randomly selected from the group, what is the probability that the likes neither Mathematics nor History?

0.8

0.5

0.3

0.7

64.

what is the six term in the expanded form of (x+2y)8 ?

what is the six term in the expanded form of (x+2y)⁸?