SHSAT FREE MATH PRACTICE WORKSHEET FREE

(1)  For how many positive integer values of N will the expression 18/(N + 2) be and integer?

        (A)  1  (B)  2  (C)  3  (D)  4  (E)  5

(2)  In the figure, numbers are to be placed in each of the nine small squares such that the sum of the numbers in any row, column, or diagonal must be the same.  The number x

(A)  will be 1.  (B)  will be 7.  (C)  will be 9. 

(D)  will be 11. 

(E)  cannot be determined from the given information

(3)  The two straight line graphs indicate the change in the price per pound of coffee and the change in the price per pound of sugar during part of a year.  The initials on the horizontal axis represent January, February, March, and so on, and the vertical lines indicate the start of each month.  During which month did it occur that the price per pound of coffee was twice the price per pound of sugar?

(A)  March  (B)  April  (C)  May  (D)  June  (E)  July

(34)  The pie chart shows the yearly expenses of the Jones family.  Each expense is indicated as a percent of the total money they spent.  Which one of the following bar charts, which indicate actual money spent in each area, best represents the data in the pie chart?

(35)  A fence encloses a triangular field.  There is a vertical wooden fence post at each corner (vertex) of the field, and vertical posts all along the fence, placed 5 feet apart.  If the sides of the field measure 20 feet by 35 feet by 25 feet, how many posts are there altogether?

         (A)  13  (B)  14  (C)  15  (D)  6  (E)  17

(36)  The longest side in the figure (which need not be drawn to scale) must be

        (A)  BC  (B)  BD  (C)  CD  (D)  AB  (E)  AD

(37)  (x²y³)(xy²) =

        (A)  x²y⁶ (B)  x³y⁶ (C)  2 x³y⁶  (D)  x³y⁵ (E)  2 x³y⁵

(38)  The smallest positive integer value of n that will make 12n exactly divisible by 56 is

          (A)  7  (B)  12  (C)  14  (D)  21  (E)  24

(39)  If 2x + 2y + 2z = 110 and x + y = 11, then z =

        (A)  99  (B)  50  (C)  49(1/2)  (D)  49  (E)  44

(40)  Suppose a  b means a2 – ab (For example, 3 2 = 9 – 6 = 3 and 5 3 = 10)  Which of the following has the smallest value?

        (A)         (B)      (C)    (D)     (E) 

(41)  Box A contains exactly four cards, numbered 3,5,6, and 9.  Box B contains exactly three cards, numbered 1, 4, and 7.  One card is selected at random form Box A, and one card is selected at random from Box B.  What is the probability that the sum of the numbers on the two selected cards is even?

        (A)  1/4  (B)  1/3  (C)  5/12  (D)  1/2   (E)  7/12

(42)  Gil is now 80 miles ahead of Larry.  Gil is traveling at a constant rate.  Larry is travelling in the same direction, at a rate 5 miles per hour faster than Gil.  In how many hours will Larry catch up to Gil?

        (A)  16  (B)  15  (C)  12  (D)  10  (E)  Larry cannot catch up to Gil

(43)  If (3x + 3) / 3 = 2.5, then x =

        (A)  -.5  (B)  .5  (C)  .75  (D)  1  (E)  1.5

(44)  On Thursday, the ABC Company stock lost 60% of its value.  On Friday it lost another 10% of its remaining value.  The total loss for the two days would have been the same if the stock had x% of its value the first day and x% of its remaining value the second day.  Then x =

        (A)  30  (B)  35  (C)  38  (D)  40  (E)  64

(45)  The area of triangle AOE

        (A)  is 1.  (B)  is 2.  (C)  is 2.5.  (D)  is 4  (E)  cannot be determined from the given information

(46)  Given triangles ABC and DEB as shown, the value of y in terms of x is

        (A)  y = x + 120  (B)  y = x – 120  (C)  y = 100 – x  (D)  y = 80 – x  (E)  y = x – 80

(47)  Here are two sequences. 

          Sequence F:  2, 7, 12, 17, 22, . . . .

         Sequence S:  3, 10, 17, 24, 31, . . . .

        The numbers in sequence F increase by fives.  The numbers in sequence S increase by sevens.  The first number that occurs in both sequences is 17.  What is the next number that occurs in both sequences?

        (A)  87  (B)  85  (C)  72  (D)  65  (E)  52

(48)  A certain type of drinking glass holds exactly 5/8 liter of water.  How many of those glasses can be filled if you have 40 liters of water?

        (A)  72  (B)  64  (C)  30  (D)  25  (E)  24

(49)  5⁴ + 5⁴  + 5⁴ + 5⁴ + 5⁴ =

        (A) 5⁵  (B)  5²⁰  (C)  25²⁰  (D)  25⁴  (E)  10⁴

(50)  Points C, D, E, and H lie on the sides of rectangle ABFG as shown.  AB = 8 and AG = 15.  What is the mean of the areas of the three triangles ACG, ADH, and HEG?

        (A)  120  (B)  60  (C)  40  (D)  30  (E)  There is more than one possible answer.

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