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1) What is the unit digit of the following products? 

  a.  6 ²⁺ⁿ  (n is +ive)

  b.  11³⁵ x 456 

  c.  4²⁰⁵

  d.  4²¹²

  e.  7² x 5⁹⁴

2) In a barber shop the number of customers come at least 10 more than 0.25 of this number come in video shop. Determine an inequality supposing b customers for barber and v for video shop.

3) If 0 < a ,  b < 0, then what is true?

   a) a + b = 0             c) a + b < 0                

   b) a / b < 0               d) a + b > 0

   e) ab > 0

4) If x is less than zero and y is less than zero, then:

  a.  x(y) = 0  False/True        c. y _ x > 0 False/True

  b. x + y < 0 False/True     d. y + x > 0 False/True

        xy

5) If f(x) = x/2 _ 5, c = ?                     f(x)         x  

   (see the chart)                                0         10

                                                             9           d

                           d            c

6) If (x) = 1 + 2x, find variables

f(x)         x

3            1

a           0.5

13          b

1            c

7) Radius and height of a circular cylinder are decreased by 20% and 50% respectively. What percent the volume be decreased?

8) Side of a square is increased by 30%. What percent its area be increased?         

9) Two points M and N have the following coordinates M(b, -b),  N(5a, 5a), find the distance from A to B.

10) A(1, 0), B(8, 0) and C(1, -4) are three vertices of a Rt triangle. Determine the hypotenuse.

 11) AB is a diameter of a circle where A(d, 0) and B(d, 4c). Area of the circle would be:

a) 0.5 pc²       b) pc²        c) 2 pc²          d) 4 pc²

12) Radius of a wheel is 2.5 ft. The wheel rolls along with ground at a rate of 352 revolutions per min. Find the wheel speed miles per hour.

14) 5^{11 - a}  = 625, find a

15) What is the rule of sequence?

            1, 3, 7, 15, ____

  A)2^n-1            B)3^n-1              C)4^n-1              D)2^n-1

16) What is the rule of sequence?

            12, 24, 72, 264, ____

  A)12n            B)n¹²               C)12ⁿ              D)4ⁿ⁺⁸

17) What is the rule of sequence?

            3, 5, 7, 9, ____

    A)2ⁿ            B)2n+1           C)2n         D)n² + 1

18) Find the 10^th term of the above sequence

19) Find 31^st term: 3, 7, 11, 15, ____

20) What is the median of the following ten numbers which are in ascending order:

x,  y,  z,  24,  36,  42,  60,  72,  x+72

21) The average (mean) of three even integers a, b, c is 8. What is the median of a, b, c, 20?

22) Find the mean of the following three terms:

15x² + 9,  3x _ 5,  1 _ 3x

A) 5x² + 1.7     B) 15x² + 5        C) 5 + 3x

23) Average score of my sister after 5^th examination is 58. How many minimum marks must she obtain in her last 6^th exam to reach the average 70?

24) A number is divisible by 6 and 15. It could also be divisible by:

a) 45               b) 30               c) 20               d) 12

25) If x + y < 10, and x - y > 12, which of the following pairs could be the values of x and y?

a.(-9, 9)           b.(10, -2)          c.(9, -1)

26) A special lottery is to be held to select the student. There are 100 seniors, 150 juniors, and 200 sophomores who applied. Each senior's name is placed in the lottery 3 times; each junior's name, 2 times; and each sophomore's name, 1 time. What is the probability that a senior's name will be chosen?

27) 4^-(x+2)  = 4^-3       find x

28) b and r are positive integers and b² = r + 12, is r supposed to be equal to 2, 3 4, 5 or 6?

29) a³ = b²_ 2, find the value of a and b  if a = b < 0

 A) 1                B) -1                C) 2                 E) -2

30) If x = -ive and y = +ive, then:

A) x + y > 0

B) x² + y² < 0

C) xy > 0

D) x divided y < 0

E) x _ y > 0

31) A rectangular solid has a length = 8, width = 8, height = 12. It is divided into 12 equal cubes. What is the edge of each cube?

32) Each side of a cube is 2.5 units, Its volume?

33) What is the perimeter of a square ABCD having diagonal 6?

34) According to an entry-record total 300 people came in an amusement park. One person could choose his/her one favorite ride. Entry of 10 persons was not made (undecided). What would be the most possible entry of Ride F while x and y both are positive?

                        RIDE           NUMBER OF PEOPLE

                        Ride A            90

                        Ride B            71

                        Ride C            19

                        Ride D            45

                        Ride E            x

                        Ride F             y

35) XY is the diameter of a circle; X(d, 0),  Y(d, 4c); Area of the circle would be:

  A) 0.5 pc²                   B) pc²

  C) 2pc²                     D) 4pc²           E) 16pc²

36) Three vertices of a triangle are M(0,5), P(2,-7) and R(-3,8); which side is the biggest?

A) RM                         B) RP                          C) PM

37) When 80 divided by 9, remainder is r

      When r divided by 3, remainder is n;  find  r n

Questions 38 thru 41; determine the rule of sequence:-

38) 12, 24, 72, 264, ___

A) 12n             B) n¹²              C) 12ⁿ            

D) 4ⁿ⁺¹            E) 4ⁿ + 8

39) 1, 3, 7, 15,  ____

A) 2^n-1             B) 3 ^n-1            C) 4 ^n-1          D) 2 ^n-1            E) n ²⁺¹

40) 2, 5, 7, 9, ____

A) 2 ⁿ               B) 2n+1          C) 2n           D) n ² + 1        E) n ² + 1

41) Find the 11^th term of the above seq.

42) The average (mean) of three even integers a, b, c is 8. What is the median of a, b, c, 20?

43) Average of four odd numbers is 16, find them.

44) What is the average (arithmetic mean) of all the multiples of ten from 10 to 190 inclusive?

45) A cubical block of metal weighs 5 pounds. How much will another cube of the same metal weigh if its sides are twice as long?

46) Solve: (*5 -  *6) ²      Note: Consider * the sign of square root.

47) Simplify: 2¹⁰ + 2¹⁰ + 2¹⁰ + 2¹⁰

A) 2⁴⁰              B) 8¹⁰              C) 2¹²

48) Helpers are needed in a bakery for a special order of 24 large cakes and 420 small cakes. One helper can prepare 2 large cakes and 35 small cakes in an hour. How many helpers are needed if kitchen is available for only 3 hours?

49) Ratio between the ages Ali and Jeo is 2:3 and between Jeo and Sam is 6:1. What is the ratio between the ages of Ali and Sam?

50) A rectangle measuring 3 x 4 inches is inscribed in a circle. Area of the circle=?

51) Two sets of 4 consecutive positive integers have exactly one integer in common. The sum of the integers in the set with greater numbers is how much greater than the sum of the integers in the other set?

52) After being dropped a certain ball always bounces back to 2/5 of the height of its previous bounce. After the first bounce it reaches a height of 125 inches. How high (in inches) will it reach after its fourth bounce?

53) n and m are positive. 2n is the square of a number and 9nm is the cube of a number. The smallest value for n + m is:

A) 13         B) 11         C) 8          E) 7

54) a = x + y   and b = x, then what is the ratio a to b?

                 y

55) You have a hundred dollars in dollar bills. You are going to divide it up (unequally)among four people. You want everyone to get a whole number of dollars and you don’t want any money left over. To fulfill these  conditions, you can divide the money according to which of the following ratios?

I. 4 : 3 : 2 : 1

II. 10 : 5 : 2 : 1

III. 9 : 7 : 3 : 1

(A) I, only

(B) II, only

(C) I and II, only

(D) I and III, only

(E) II and III, only