SHSAT MATH MIXED PRACTICE QUESTIONS

Question 1 :

 (3 + 4)² =

(A)  13  (B)  14  (C)  19  (D)  25  (E)  49

Solution :

  =   (3 + 4)²

  =   7²

  =  49

Hence the answer is 49.

Question 2 :

The exact value of √49 - √24 is

(A)  2  (B)  between 2 and 5  (C)  5 (D)  more than 5

(E)  The expression does not have an exact value.

Solution :

=   √49 - √24 

=  7 - √(2⋅2⋅2⋅3)

=  7 - 2√6

The answer is between 2 and 5.

Question 3 : 

200% of 7 is

(A)  .14  (B)  7  (C)  14  (D)  21  (E)  1,400

Solution :

  =  200% of 7  

  =  (200/100) ⋅ 7 

  =  14

Hence the answer is 14.

Question 4 :

(All line segments are either horizontal or vertical, as shown.)  The perimeter of the figure is

(A)  5  (B)  6  (C)  7  (D)  12  (E)  14

Solution :

The two unmarked vertical side must add upto 3, and two unmarked horizontal sides must add upto 4.

Perimeter  =  3. + 4 + 3 + 4  =  14

Hence the perimeter is 14.

Question 5 :

What is the value of N if (1/5) – (1/6) = 1/N?

(A)  7  (B)  30  (C)  1/30  (D)  -30  (E)  -1/30

Solution :

  =  (1/5) – (1/6)

Since the denominators are not same, we have to take L.C.M.

  =  (6 - 5)/30

  =  1/30

Hence the value of N is 30.

Question 6 :

Find the value of (2⁴ – 4²) + (2³ – 3²)

(A)  -11  (B)  -8  (C)  -1  (D)  0  (E)  1

Solution :

=  (2⁴ – 4²) + (2³ – 3²)

=  (16 - 16) + (8 - 9)

=  0 + (-1)

  =  -1

Hence the answer is -1.

Question 7 :

On the number line shown, Q (not shown) is the midpoint of PR.  What is the midpoint of QS?

(A)  -5  (B)  -4  (C)  0  (D)  1  (E)  8

Solution :

Midpoint of PR  =  Q

Distance between PR :

-8 to -6  =  -2 units, -6 to -4 = -2 units, -4 to -2 = -2 units,

-2 to 0 = -2 units, 0 to 2 = 2 units.

Midpoint of PR, Q = -6/2  =  -3

S is located on 5.

Q is located on -3

Midpoint of QS  =  (-3 + 5)/2  =  2/2  =  1

Question 8 :

The ratio of boys to girls at a dance was 2 to 3.  If 45 girls attended, what is the number of boys who attended?

(A)  9  (B)  18  (C)  27  (D)  30  (E)  45

Solution :

Ratio of boys to girls  =  2 : 3

Number of girls attended  =  45

2x + 3x  =  5x 

5x  =  45

x  =  9

Number of boys attended = 2(9)  =  18

Hence the number of boys is 18.

Question 9 :

If the measure of angle A is 40°, then x + y =

(A)  80°  (B)  120°  (C)  180°  (D)  220°  (E)  360°

Solution :

Let the other interior angles of triangle be "p" and "q"

x + p  =  180

y + q  =  180

x + p + y + q  =  180 + 180

x + y + (p + q)  =  360  ---(1)

p + q + 40  =  180

p + q  =  180 - 40  =  140  

Applying the value of p + q in (1), we get

x + y + 140  =  360

 x + y  =  360 - 140

x + y  =  220

Hence the answer is 220.

Question 10 :

If 6x is increased by 4y, and the sum is divided by 2, the result is equivalent to

(A)  3x + 4y  (B)  6x + 2y  (C)  3x + 2y

(D)  (10x + y)/2  (E)  5(x + y)

Solution :

By converting the given statement "6x is increased by 4y, and the sum is divided by 2" into expression. We get

  =  (6x + 4y) / 2

  =  2(3x + 2y) / 2

  =  3x + 2y

Hence the answer is 3x + 2y.

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