SHSAT MATH PRACTICE TEST QUESTIONS

Question 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 :

Total number of students  =  50

Number of students scored 90% or

more than 90% marks   =  30

Percentage of students who score

more than 90% of marks  =  (30/50) ⋅ 100%

  =  60%

So, 60% of students are scoring 90% or more than 90% of marks.

Hence 40% students are getting lesser than 90% marks.

Question 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

Solution :

The range of n² lies between 9 to 16 (inclusive).

Question 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

Solution :

Given that :

A  =  3 C

B  =  C - 8

A  =  B

3 C   =  C - 8

3C - C  =  -8

2C  =  -8

C  =  -4

Hence the answer is -4.

Question 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

Solution :

Number of students in a class  =  28

Number of students who like math  =  17

Number of students who like English  =  19

Number of students who like at least one  =  28

17 - x + x + 19 - x  =  28

36 + x  =  28

x  =  28 - 36

x  =  8

Hence the number of students who like both subject is 8.

Question 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)  2³ · 3² · 5³ · 7⁴  (C)  3 · 5 

(D)  3 · 5²  (E)  3²·5³

Solution :

x = 3²·5³·7⁴ and y = 2³·3·5²

Common factors are 3 · 5².

Question 6 :

The population density of Cedar County is 230 people per square mile. The county has a population of 85,100 people. What is the area, in square miles, of Cedar County?

Solution :

Total population of the country = 85100

Density per square mile = 230 people

Area of the country = 85100/230

= 370

So, the required area of the country is 370 square miles.

Question 7 :

For the function f, the graph of y = f(x) in the xy-plane has slope of 3 and passes through the point (0, -8). Which equation defines f ?

a) y = 3x     b) y = 3x - 8      c) y = 3x + 5    d) y = 3x + 11

Solution :

Slope = 3

One of the points on the line is (0, -8)

Equation of the line :

(y - y₁) = m(x - x₁)

(y + 8) = 3(x - 0)

y + 8 = 3x

y = 3x - 8

So, option b is correct.

Question 8 :

The y-intercept of the graph of 

12x + 2y = 18

in the xy-plane (0, y). What is the value of y ?

Solution :

Applying the point (0, y) in the given linear equation, we get

12(0) + 2y = 18

2y = 18

y = 18/2

y = 9

Question 9 :

If quotient = 3x² – 2x + 1, remainder = 2x - 5 and divisor = x + 2, then the dividend is:

A) 3x³ - 4x² + x - 3       B) 3x³ - 4x ² - x + 3

C) 3x³ + 4x ² -x + 3       D) 3x³ + 4x ² - x - 3

Solution :

Dividend = ?

divisor = x + 2

Quotient = 3x² – 2x + 1

Remainder = 2x - 5

Using division algorithm :

Dividend = divisor x quotient + remainder

= (x + 2)(3x² – 2x + 1) + 2x - 5

Using distributive property, we get

= 3x³ - 2x² + x + 6x² - 4x + 2 + 2x - 5

= 3x³ + 4x² - x - 3

So, option D is correct.

Question 10 :

Factor it completely 

2k³ + 6k² + 5k + 15

Solution :

2k³ + 6k² + 5k + 15

Factoring 2k² from the first two terms,

= 2k²(k + 3) + 5(k + 3)

= (2k² + 5) (k + 3)

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