SHSAT PRACTICE QUESTION PAPER

(1)  4/9 is the square root of what number ?

(A)  1/2  (B)  2/3  (C)  8/18  (D)  16/81  (E)  3/2

Solution

(2)  In the following system of equations

3x + 7y = 24, 9x + 4y  =  21 what is (x, y)

(A)  (1, 1)   (B)  (1, 3)   (C)  (3, 1)   (D)  (2, 4)   (E)  (4, 2)

Solution

(3)  If the first picture means √abcd, then what is the value of second picture.

(A)  3    (B)  √12    (C)  √24    (D)  12    (E)  144

Solution

(4)  Which of the following is bigger, the first or second ? Assume X does not equal to Y

First : X/(X - Y)  Second :  Y/(Y-X)

(A)   They are equal  (B)  First  (C)  Second   (D)  Not enough information   (E)  One of these is undefined

Solution

(5)

In the figure above, the triangle ABC has an area of 20 square inches, where the height is 5 inches, if the square has the same perimeter as the triangle above, then what is the area of the square ?

(A)  8  sq.in  (B)  18 sq.in  (C)  20 sq.in 

(D)  20.25 sq.in  (E)  25.50 sq.in 

Solution

(6)  The following table shows the class test average score in Ms. Jones Biology class over the years she has been teaching for, what is the median class test score for the years shown ?

Solution

(7)  The wheels of a car have diameter of 10 meters. If the speed of the car is 50 meters per hour, how many revolutions does one wheel make in one hour ?

(A)  1/2π  (B)  5  (C)  50/π  (D)  10  (E)  5/π

Solution

(8)  A circle is inscribed in a square. What is the probability that a penny, if thrown, will fail in the shaded region below?

(A)  2π  (B)  1  (C)  π - 2  (D)  1 - π/4  (E)  π/2

Solution

(9)  What is 10% (10%)/100% ?

(A)  1%  (B)  10%  (C)  0.01  (D)  1  (E)  50%

Solution

(10)  The greatest integer function of x, gives the largest integer that is less than x and is represented by ⌊x⌋, what is  ⌊10%⌋ + 1 ?

(A)  0  (B)  1 (C) 1.1  (D)  11  (E)  11%

Solution

(11)  Sara is stuck in a circular field. She knows that the area of the circular field is 100 square meters. She walks at a speed of 10 meter per minute. How long will it take her to walk from one end of the circular field to the other end assuming she must cross through the center ?

(A)  100/π   (B)  √100/π  (C)  2 √(100/π)  

(D)  10 √100/π   (E)  0.2 √100/π

Solution

(12)  The Fibonacci sequence involves taking two previous numbers and adding them together to get the next. If the first two Fibonacci numbers are 0 and 1, what is the mean of the first 5 Fibonnaci numbers?

(A)  5/6  (B)  7/6   (C)  7/5  (D)  1  (E)  2

Solution

(13)  If 1 slack  =  x vaks

9 vaks  =  12 hips

How many slack are in 24 hips?

(A) 2  (B)  9/x  (C)  18/x  (D)  x/9  (E)  x/18

Solution

(14)  What is the value of 11²/12² ?

(A)  12.1  (B)  121  (C)  0.121  (D)  1.21  (E)  1.12

Solution

(15)  (ab)  =  a + b - b², then what is the value of this expression when a = 5 and b = 2 ?

(A)  2  (B)  3  (C)  4  (D)  5  (E)  7

Solution

(16)  How many non positive integers are between -3 and 5 ?

(A)  1  (B)  3  (C)  4  (D)  6  (E)  8

Solution

(17)  A number is squared and added to its reciprocal. If that number is represented by x, what is the expression ?

(A)  x² + 1  (B)  x² + (1/x)   (C)  x² + (1/x²) 

(D)  (x⁴ + 1)/x  (E)  x

Solution

(18)  If I increase the size of a ball by 50% two times in a row, what is the percent increase assuming that the initial size of the ball was 20.

(A)  10%  (B)  25 %  (C)  50%  (D)  75 %  (E)  125%

Solution

(19)  

In the figure above, the rectangle ACDE has an area of 440 square meters. the points B and F area the midpoints of the sides AC and AE respectively. What is the area of the triangle BCD?

(A)  56   (B)  110  (C)  200 

(D)  220  (E)  Not enough information is given 

Solution

(20)  The least common multiple of two numbers, x and y can be represented by LCM  (x,y). The following is true for the concept of the least common multiple :

If we can find integers a and b both x and y respectively such that ax = by = LCM (x, y) then ax o r by is the least common multiple of x and y.

What is the least common multiple of √2 ⋅ π ?

(A)  π √2  (B)  2√2π  (C)  2π

(D)  2π²  (E)  Does not exist

Solution

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