9TH GRADE SHSAT PRACTICE QUESTIONS

Question 1:

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

Solution

Question 2 :

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

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

Solution

Question 3 :

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

Question 4:

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

Question 5 :

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

Solution

Question 6 :

x² + 10x + 24

When the given expression is rewritten in the form (x + 4) (x + k), where k is constant, what is the value of k ?

Solution

Question 7 :

The ticket revenue of a movie theater is proportional to the number of tickets the theater sells. The theater sold 300 tickets on Thursday and 600 tickets on Friday. Which of the following is true ?

A) The ticket revenue on Thursday was one quarter the ticket revenue on Friday.

B) The ticket revenue on Thursday was one half the ticket revenue on Friday

C)  The ticket revenue on Thursday was twice as great as the ticket revenue on Friday.

D) The ticket revenue on Thursday was four times as great as the ticket revenue on Friday.

Solution

Question 8 :

A bag contains a total of 60 marbles. a marble is to chosen at random from the bag. If the probability that a blue marble will be chosen is 0.35, how many marbles in the bag are blue ?

A) 21    B)  35   C)  25    D) 39

Solution

Question 9 :

For a reason m miles from a flash of lightning, the length of the time interval from the moment the person sees the lightning to the moment the person hears the thunder is k seconds. The ratio of m to k can be estimated to be 1 to 5. According to this estimate, the person is how many miles from a flash of lightning if the time interval is 25 seconds ?

A)  10    B)  9     C)  6    D)  5.

Solution

Question 10 :

The expression 2x² + ax is equivalent to x(2x + 7) for some constant a, what is the value of a ?

A) 2     B)  3    C) 4     D)  7

Solution

Question 1 :

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

Solution

Question 2 :

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

Solution

Question 3 :

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

(4) and (5)  The two pie charts show the ice cream flavor preferences of the students at two high schools.

Solution

Question 4 :

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

Solution

Question 5 :

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

Solution

Question 6 :

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

(A)  3x + 1  (B)  3x + 2  (C)  4x - 1 

(D)  4x - 2  (E)  5x – 2x

Solution

Question 7 :

In DXYZ above, what is the value of y?

(A) 24   (B) 28    (C) 48    (D) 72   (E) 78

Solution

Question 8 :

In a bowl of fruit there are 4 apples, 3 oranges, 5 bananas, 2 plums, and 6 peaches. What is the probability that a piece of fruit chosen at random from the bowl is not a peach?

(A) 3/10    (B) 2/5   (C) 1/2    (D) 7/10    (E) 8/9

Solution

Question 9 :

Five more than one-third of a certain number is 3 less than the number. What is the number?

(A) 3   (B) 5  1/3   (C) 6    (D) 7  2/3    (E) 12

Solution

Question 10 :

If m = 4n + 5 and p = 3n + 6, which of the following expresses n in terms of m and p ?

A) m + 2p - 3   B) m - p + 1

C) 3m - 2p  + 4    D) 4m + p + 1   E) 2m - 5p

Solution