SHSAT PRACTICE MATH TEST

Question 1 :

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 :

2(3x + 8) = 3(2x + 4)

6x + 16  =  6x + 12

No value of x.

Question 2 :

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

Solution :

V = s²h  ---(1)

Since "s" is doubled, s = 2s, "h" is tripled h = 3h

By applying the new values of s and h in (1), we get

V = (2s)²(3h)

V  =  4s² (3h)

V  =  12s² h

Hence V is multiplied by 12.

Question 3 :

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

Solution :

Large box can hold 8 soccer balls each, small box can hold 5 soccer balls each.

By choosing 8 large box, we may place 8 soccer balls each. So, in large box we will have 64 balls.

99 - 64  =  35

Now we may place these 35 balls in 7 small boxes containing 5 balls each.

Number of boxes  =  8 + 7  =  15

Hence the total number of boxes is 15.

Question 4 :

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

Solution :

Let "x" be the number of hours worked 

"y" be the amount earned.

y = kx  --(1)

30  =  k(5)

k = 30/5  =  6

The equation y = 6x represents the above relation.

y = 6 (50)  =  300

Hence the cost earned for working 50 hours is $300.

Question 5 :

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 6 :

f(x) = (3x/4) - 2

Which of the following could be the graph in the xy-plane of the function above

Solution :

f(x) = (3x/4) - 2

Slope = 3/4 (positive)

y-intercept = -2

Since it has positive slope, the straight line must be a raising line and it has negative y-intercept at -2.

Comparing the options given, option A is correct.

Question 7 :

As a part of he role on a planning committee for high school prom, Keisha hired a DJ. The DJ charges $150 per hour for performing plus $100 flat fee for set up and takedown . The committee budgeted $700 for a DJ for the prom. Which of the following represents the number of preforming hours x, for which DJ could hired to stay within the committee budget ?

A) x ≥ 7     B) x ≤ 7      C) x ≥ 4     D) x ≤ 4

Solution :

Set up fee = $100

Charge per hour = $150

Let x be the number of hours.

150x + 100 ≤ 700

150x ≤ 700 - 100

150x ≤ 600

x  ≤ 600/150

x ≤ 4

So, option D is correct.

Question 8 :

y = x - 4

y = x² - 16

If (x, y) is the solution to the system of equations above, which of the following could be the value of x ?

A)  20     B)  12    C) -3    D) -4

Solution :

y = x - 4 -----(1)

y = x² - 16 -----(2)

(1) = (2)

x - 4 = x² - 16

x² - x - 16 + 4 = 0

x² - x - 12 = 0

(x - 4)(x + 3) = 0

x = 4 and x = -3

Applying the value of x,

When x = 4, y = 0

When x = -3, y = -7

So, option C is correct.

Question 9 :

To ship a parcel based on its weight, a certain mail shipping service charges $2.50 for the first pound and $0.50 for each additional pound. If the parcel weights w pounds where w is a positive integer, which of the following represents the shipping charge c in dollars in terms of w ?

A) c = 2.5 + 0.5 (w - 1)     B) c = 0.5 + 2.5(w - 1)

C) c = 2.5 + 0.5w       D)  c = 0.5 + 2.5 w

Solution :

Shipping charge = 2.50 for first pound.

For additional pounds, 0.50

Weight of parcel is w. So, the total cost is 

c = 2.50 + 0.5(w - 1)

Option A is correct.

Question 10 :

The equation y = 7^x - 1 is graphed in the xy-plane. What is the y-intercept of the graph ?

A)  (0, -1)   B) (0, 0)    C) (0, 6)    D) (0, 7)

Solution :

y = 7^x - 1

To find y-intercept, we apply x = 0

y = 7⁰ - 1

y = 1 - 1

y = 0

So, option B is correct.

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