# SHSAT MATH PRACTICE TEST FOR 9th GRADERS

(1)  Thirty of the fifty students who took an exam received a grade of 90%  or greater.  What percentage of those fifty students received a grade of less than 90%?

(A)  70  (B)  35  (C)  40  (D)  30  (E)  10

Solution

(2)  Let n be a number from -3 to 4 inclusive.  What is the range of values of n2?

(A)  -9 ≤ n2 ≤ 16  (B)   9 ≤ n2 ≤ 16  (C)  3 ≤ n2 ≤ 4

(D)  0 ≤ n2 ≤ 2  (E)  0 ≤ n2 ≤ 16

(3)  A is 3 times C.  B is 8 less than C.  For what value of C does A = B?

(A)  -4  (B)  0  (C)  1  (D)  2  (E)  5/2

(4)  In a class of 28 students, everyone likes math, English, or both.  If 17 like math and 19 like English, how many like both?

(A)  2  (B)  8  (C)  16  (D)  20  (E)  28

(5)  Let x = 32·53·74 and y = 23·3·52.  What is the greatest common factor of and y?

(A)  2· 3 · 5 · 7  (B)  2· 3· 5· 74  (C)  3 · 5

(D)  3 · 52  (E)  32·53

(6)  The equation 2(3x + 8) = 3(2x + 4) is satisfied by

(A)  no value of x.  (B)  only negative values of x

(C)  only x = 0.  (D)  only positive values of x.

(E)  all values of x.

Solution

(7)  In the formula V = s2h, if s is doubled and h is tripled, then V is multiplied by

(A)  5  (B)  6  (C)  12  (D)  18   (E)  36

(8)  You have 10 large boxes that can each hold 8 soccer balls, and 10 small boxes that can each hold 5 of the same soccer balls.  If you have 99 soccer balls, what is the greatest number of boxes you can completely fill?

(A)  13  (B)  14  (C)  15  (D)  16  (E)  19

(9) The straight line graph shows the relationship between number of hours worked and amount earned.  How much would be earned for 50 hours of work?

(A)  \$50  (B)  \$83  (C)  \$120  (D)  \$150  (E)  \$300

(10)  The perimeter of a triangle, all of whose sides have integer length, is 19.  A possible length for the largest side is

(A)  6  (B)  8  (C)  10  (D)  15  (E)  17

(11)  A value of x that satisfies the inequality 2x – 10 > 3x is

(A)  -11  (B)  -10  (C)  -1  (D)  0  (E)  12

Solution

(12) The midpoints of the four sides of square ABCD are joined to form square WXYZ as shown.  The area of square WXYZ is 16.  The area of triangle YCX is

(A)  4  (B)  2  (C)  1.5  (D)  1  (E)  none of these

Solution

(13)  The mean of 3 numbers is 7.  The mean of 4 other numbers is 8.  The mean of 5 other numbers is 11.  What is the mean of all 12 numbers?

(A)  4  (B)  4(2/13)  (C)  8(2/3)  (D)  9  (E)  36

Solution

(14)  There were 20 socks in a drawer.  Of these, 8 were blue, 10 were black, and 2 were white.  Someone then removed 4 blue socks.  If one sock is now drawn at random, what is the probability that it is not white?

(A)  1/10  (B)  9/10  (C)  1/8  (D)  7/8

(E)  None of these

(15)  Two sides of a right triangle are 3 and 4.  The third side is

(A)  1  (B)  3  (C)  5  (D)  7  (E)  not uniquely determined

(16)  A cube 3 by 3 by 3 is painted red on all six faces and then cut into 27 smaller 1 by 1 by 1 cubes.  How many of these new smaller cubes have exactly two faces that are painted red?

(A)  6  (B)  8  (C)  12  (D)  21  (E)  27

(17)  If 2 blobs = 3 glops and 3 blobs = 2 chunks, then 1 chunk =

(A)  1 glop  (B)  2/3 glop  (C)  3/2 glops

(D)  4/9 glop  (E)  9/4 glops

(18) and (19)  The two pie charts show the ice cream flavor preferences of the students at two high schools.  (18)  The ratio of Montague students who prefer vanilla to Montague students who prefer chocolate is

(A)  10:9  (B)  4:3  (C)  3:10  (D)  3:4  (E)  2:5

(19)  If the number of Montague students who prefer vanilla is M and the number of Capulet students who prefer vanilla is C, then

(A)  M > 2C  (B) M = 2C  (C)  M = C  (D)  M < C

(E) The relationship cannot be determined from the given information

(20)  If x is an integer, which one of the following must be odd?

(A)  3x + 1  (B)  3x + 2  (C)  4x - 1

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