SHSAT MATH FREE TEST ONLINE

Question 1 :

One-half of one-sixth is equal to

(A)  one-third of one-fourth  (B)  one-third 

(C)  one  (D)  two  (E)  three

Solution :

Given that :

One-half of one-sixth is equal to

  =  (1/2) ⋅ (1/6)

  =  1/12

One third of one fourth is the answer.

Question 2 :

The areas of triangles ABC and XYZ are each 10.  The area of the shaded region is 14.  Then the area of triangle XWC is

(A)  12  (B)  8  (C)  6  (D)  3  (E)  2

Solution :

Area of triangle ABC  =  10

Area of XYZ  =  10

Area of shaded region  =  14

Area of ABC + Area of XYZ  =  10 + 10  =  20

Overlapping area  =  20 - 14  =  6

Question 3 :

1  1/10  + 2  11/100 + 3  111/1000 (mixed fractions)  =

(A)  6.111  (B)  6.123  (C)  6.111111  (D)  6.321  (E)  6.6

Solution :

  =  11/10 +  211/100 + 3111/1000

  =  1.1 + 2.11 + 3.111

  =  6.321

Hence the answer is 6.321.

Question 4 :

If x is positive and x² + x = 50, then x is a number between

(A)  6 and 7  (B)  7 and 8  (C)  8 and 9 

(D)  9 and 10  (E)  10 and 11

Solution :

x² + x = 50

Let us apply the first option, in the question

6² + 6 = 42

7² + 7 = 56

50 lies between 42 and 56.

Hence the value of x lies between 6 and 7.

Question 5 :

In the figure, C is a point on line segment AE.  If AB = BC, what is the measure of angle DCE?

(A)  80°  (B)  75°  (C)  60°  (D)  25°  (E)  20°

Solution :

AB  =  BC  =  y

In triangle ABC,

<BAC + <ACB + <CBA  =  180

 y + y + 20  =  180

2y  =  160

y  =  80

<ACB + x + 3x  =  180

80 + 4x  =  180

4x  =  100

 x  =  25

Question 6 :

Which of the following is a solution to the equation 

2x² + 4x = 3 + 3x²

a) -1    b) 0     c) 3     d) 6

Solution :

2x² + 4x = 3 + 3x²

2x² - 3x² + 4x - 3 = 0

-x² + 4x - 3 = 0

Multiplying by negative, we get

x² - 4x + 3 = 0

(x - 1)(x - 3) = 0

x = 1 and x = 3

So, option c is correct.

Question 7 :

The equation y = 36 + 18x models the relationship between the height y, in inches, of a typical golden delicious apple tree and the number of years, x, after it was planted. If the equation is graphed in the xy-plane, what is indicated by the y-intercept of the graph?

A) The age, in years, of a typical apple tree when it is planted

B) The height, in inches, of a typical apple tree when it is planted

C) The number of years it takes a typical apple tree to grow

D) The number of inches a typical apple tree grows each year

Solution :

y = 36 + 18x

y-intercept = 36

A) The age, in years, of a typical apple tree when it is planted

Question 8 :

A line is graphed in the -plane. If the line has a positive slope and a negative y-intercept, which of the following points cannot lie on the line?

A)  (-3, -3)    B) (-3, 3)    C) (3, -3)    D) (3, 3)

Solution :

The points on the line must be in the quadrants I, III and IV. The points will not be in the second quadrant. So, (-3, 3) will be on the line. Option B is correct.

Question 9 :

A parachute design uses 18 separate pieces of rope. Each piece of rope must be at least 270 centimeters and no more than 280 centimeters long. What inequality represents all possible values of the total length of rope x, in centimeters, needed for the parachute?

A) 270 ≤ x ≤ 280           B) 4,860 ≤ x ≤ 4,870

C) 4,860 ≤ x ≤ 5,040     D) 5,030 ≤ x ≤ 5,040

Solution :

Minimum length of one piece of rope > 270

Maximum length of one piece of rope < 280

Minimum and maximum lengths of 18 pieces

270(18) ≤ x ≤ 280(18)

4860 ≤ x ≤ 5040

So, option C is correct.

Question 10 :

In the figure, which of the following ratios has the same value as AB/BC ?

A)  BD/DC    B) BC/AC     C) AD/BD     D) DC/BC

Solution :

In triangle ABC and BDC

<BAD = <DBC

<BCA = <BCD

Using AA, triangles ABC and BDC are similar.

BC/DC = AB/BD = AC/BC

Equating the first two,

BC/DC = AB/BD

BD/DC = AB/BC

So, option A is correct.

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