FREE SHSAT MATH  PRACTICE TEST

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 :

The sum of three lengths is given as 19. If the longest side is 10, the sum of the other two sides would be 9, which is impossible.

Hence the longest side must be less than 10. If the longest side is only 6, then the perimeter cannot be more than 18.

So the answer is 8.

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 :

2x – 10 > 3x

Subtract 2x on both sides, we get

2x - 2x - 10 > 3x - 2x

-10 > x

Hence the answer is -10

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 :

Area of square WXXZ  =  16

a²  =  16

a  =  4

Base of YCX is = 2, height = 2

Area of triangle YCX  =  (1/2) ⋅ base ⋅ height

  =  (1/2) ⋅ 2 ⋅ 2

  =  2 square units

Hence the answer is 2 square units.

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 :

Mean of 3 numbers  =  7

Sum of 3 numbers/3  =  7

Sum of 3 numbers  =  21

Sum of 4 numbers/4  =  8

Sum of 4 numbers  =  32 

Sum of 5 numbers/5  =  11

Sum of 5 numbers  =  55

Mean of 12 numbers  =  Sum of 12 numbers / 12

=  (21 + 32 + 55) / 12

=  108/12

=  9

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 :

Number of socks  =  20

Number of blue socks  =  8 - 4  =  4

umber of black socks  =  10

Number of white socks  =  2

After removing 4 blue socks, we will have 16 socks.

Probability of getting other than white socks 

  =  (10 + 4)/16

  =  14/16

  =   7/8

Hence the answer is 7/8.

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 :

= x² + 10x + 24

= x² + 6x + 4x + 24

= x(x + 6) + 4(x + 6)

= (x + 4)(x + 6)

Comparing with (x + 4)(x + k), the value of k is 6.

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 :

Number of tickets sold on Thursday = 300

Number of tickets on Friday = 600

Revenue on Thursday was one of the ticket revenue on Friday. So, option B is correct.

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 :

Total number of marbles = 60

Probability of choosing blue marble = 0.35

Total number of blue marble/100 = 0.35

Total number of blue marble = 0.35(100)

= 35

So, option B is correct.

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 :

The ratio between the moment the person sees the lightning to the moment the person hears the thunder

m : k = 1 : 5

m : 25 = 1 : 5

m/25 = 1/5

m = 25/5

m = 5

So, the required number of miles is 5. Option D is correct.

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 :

= 2x² + ax

Factoring x, we get

= x(2x + a)

Comparing with x(2x + 7)

So, the value of a is 7.

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