FREE SHSAT MOCK TEST

(1)  For how many values of x is the function is not equal to 1 ?

f(x)  =  (x - 3)/(x - 3)

(A)  0    (B)  1    (C)  2    (D)  3    (E)  undefined

Solution

(2)  If today is Monday, what day will it be in 49² from now?

(A)  Tuesday  (B)  Wednesday  (C)  Thursday 

(D)  Monday  (E)  Sunday

Solution

(3)  If f(x)  =  x³, then how many times greater is f(4) then f(2) ?

(A)  2  (B)  3  (C)  4  (D)  8  (E)  10

Solution

(4)  Convert 3/40 to a decimal.

(A)  0.0075  (B)  0.075   (C)  0.06  (D)  0.75 (E)  7.5

Solution

(5)  How many prime numbers are between 4 and 16 inclusive ?

(A)  2  (B)  3  (C)  4  (D)  5  (E)  6

Solution

(6)  How many perfect squares are between 9 and 25 exclusive.

(A)  0  (B)  1  (C)  2  (D)  3  (E)  4

Solution

(7)  An octagon, a triangle and a circle all have same perimeter (circumference for the circle). Which is true of the areas of these shapes? (O=area of octagon, T= area of triangle and C = area of circle)

(A)  O < T < C  (B)  O < C < T  (C)  O = T = C

(D)  C > T = O  (E)  C > O > T

Solution

(8)  If (x/y) = x², then what is (x/y) - (x/y)² ?

(A)  x²  (B)  x² y  (C)  x⁴  (D) x²(1-x²)  (E) x²(1+x²)

Solution

(9)  In scaled drawing, 1 millimeter represents 150 meters. How many square millimeters on the drawing represent 1 square meter ?

(A)  1/150  (B)  1/22500  (C)  150/22500 

(D)  120  (E) 22500

Solution

(10)  A rectangle is drawn on the coordinate plane. If the coordinates of one corner of the rectangle is (0, -5) and the coordinates of the opposite corner is (7, 3), then what is the area of the rectangle ?

(A)  -56  (B)  -21  (C)  21  (D)  56  (E)  105

Solution

(11)  (60 ⋅ 30) / (60 + 30)  =  

(A)  2  (B)  20  (C)  200  (D)  2000  (E)  None of these

Solution

(12)  Which of the following is closest in value to 0.213 ?

(A)  1/2  (B)  1/3  (C)  1/4  (D)  1/5  (E)  1/6

Solution

(13)  In a triangle ABC, CD bisects angle ACB. Compute the value of x + y, in degrees.

(A)  45   (B)  70  (C)  80  (D)  110  (E)  135

Solution

(14)  The consecutive odd primes, such as 11 and 13 are, are called a pair of "twin primes". How many pairs of twin primes are there between 15 and 45.

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

Solution

(15)  For any number x, the symbol ⌈x⌉ means the smallest integer that is greater than or equal to x. For examples ⌈3.2⌉ is 4. what is √156.3

(A)  11  (B)  12  (C)  13   (D)  156  (E)  157

Solution

(16)  Eight years from now, Oana will be twice as old as her brother is now. Oana is now 12 years old. How old is her brother now ?

(A)  2  (B)  4  (C)  6  (D)  10  (E)  16

Solution

(17)  Suppose a snail crawls 2/5 inch per second. At this rate, what is the total number of inches the snail crawls in 2 minutes ?

(A)  48  (B)  30  (C)  24  (D)  5  (E)  4/5

Solution

(18)  The straight line graph shows the relationship between the number of tickets sold and amount of money in the cash register if the register contained $150 before any tickets were sold. What is the price of 1 ticket.

(A)  $100  (B)  $20  (C)  $15  (D)  12.50  (E)  $10.

Solution

(19)  If 15 - 2x <7, then for all possible values of x that make the inequality true.

(A)  x < 8  (B)  x > 8  (C)  x > 4  (D)  x < 4  (E)  x > 1/4

Solution

(20)  Four congruent circles are enclosed in a square as shown. The perimeter of the square is 64. What is the circumference of one of the circles (in terms of π)

(A)  4π  (B)  8π  (C)  16π  (D)  32 π   (E)  64π

Solution