SHSAT Math Sample Test with Answers :
Here we are going to see some practice questions questions for SHSAT exams. Each question paper consists of 20 question. For each questions, you can find solution with detailed explanation.
SHSAT Math Sample Test with Answers
Question 11 :
If a * b means a^{b}, then 2*(3*2) is
(A) 512 (B) 256 (C) 81 (D) 64 (E) 12
Solution :
a * b = a^{b}
2*(3*2)
First let us evaluate the statement in parenthesis
2*(3*2) = 2 * (3^{2})
= 2 * 9
= 2^{9}
Question 12 :
Let n be an integer from 9 to 38. For how many values of n will n/5 be a prime?
(A) 3 (B) 4 (C) 6 (D) 8 (E) 29
Solution :
9 to 38
Range 9 - 19(exclusive) 19 - 29(exclusive) 29 - 38 |
Number of terms 10 10 10 |
n = 10 + 10 + 10
n = 30
n/5 = 30/5 = 6
Question 13 :
|2 – 8| - |7 – 3| =
(A) -10 (B) -2 (C) 2 (D) 10 (E) none of these
Solution :
= |2 – 8| - |7 – 3|
= |-6| - |4|
= 6 - 4
= 2
Hence the answer is 2.
Question 14 :
Mary is m years old now. Joe is 3 years younger than Mary. Express Joe’s age 10 years from now in terms of m.
(A) 13 - m (B) m - 3 (C) m + 7
(D) m + 10 (E) m + 13
Solution :
Age of Mary = m
Age of Joe = m - 3
After 10 years :
Age of Joe = m - 3 + 10
= m + 7
Question 15 :
The smaller angle between the hands of a clock at 10:00 is
(A) 15° (B) 30° (C) 45° (D) 60° (E) 75°
Solution :
Angle between two consecutive numbers in a clock
= 360/12
= 30
Angle between the hands of a clock 10 : 00 is 2(30) = 60
Hence the angle at 10 : 00 is 60 degree.
Question 16 :
Find the smallest positive integer that is a multiple of both 21 and 77.
(A) 7 (B) 33 (C) 98 (D) 231 (E) 1,617
Solution :
7 is not a multiple of both 21 and 77.
The number 231 is divisible by 21 and 77.
Hence 231 is the least number which is divisible by both 21 and 77.
Question 17 :
Over which interval was the growth in the value of the stock of the ABC Company most rapid?
(A) March to April (B) April to May (C) May to June
(D) June to July (E) July to August
Solution :
We must find the one one month interval, where the graph rises most quickly.
This is between March and April.
Question 18 :
Express the sum of 1.2 x 10^{2} and 1.2 x 10^{3 }in scientific notation.
(A) 0.144 x 10^{8 }(B) 1.32 x 10^{3} (C) 1.44 x 10^{5 }
(D) 2.4 x 10^{5 }(E) 2.4 x 10^{6}
Solution :
= (1.2 x 10^{2}) + (1.2 x 10^{3})
= 1.2 x 100 + 1.2 x 1000
= 120 + 1200
= 1320
By writing 1320 in scientific notation, we get
= 1.32 x 10^{3 }
Question 19 :
Today is Saturday. What day of the week will it be 65 days from today?
(A) Sunday (B) Monday (C) Tuesday
(D) Wednesday (E) Thursday
Solution :
By dividing 65 by 7, we get
According to days arithmetic 0 stands for "Sunday"
1 - Monday
2 - Tuesday .............. 6 - Saturday
63^{rd} day is Saturday, 64^{th} day is Sunday and 65^{th} day is Monday.
Question 20 :
The circles are “tangent” to the rectangle and to each other, as shown. If the area of each circle is 16π, then the area of the rectangle is
(A) 32 (B) 48 (C) 96 (D) 128 (E) 512
Solution :
Area of circle = 16π
πr^{2} = 16π
r^{2} = 16 ==> r = 4
Diameter of the circle = 8 units (width of rectangle)
diameter of 2 circles = 2 (8) = 16 (length of rectangle)
Area of rectangle = length (width)
= 16 (8)
= 128 square units
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Word problems on simple equations
Word problems on linear equations
Word problems on quadratic equations
Area and perimeter word problems
Word problems on direct variation and inverse variation
Word problems on comparing rates
Converting customary units word problems
Converting metric units word problems
Word problems on simple interest
Word problems on compound interest
Word problems on types of angles
Complementary and supplementary angles word problems
Markup and markdown word problems
Word problems on mixed fractrions
One step equation word problems
Linear inequalities word problems
Ratio and proportion word problems
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Pythagorean theorem word problems
Percent of a number word problems
Word problems on constant speed
Word problems on average speed
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OTHER TOPICS
Time, speed and distance shortcuts
Ratio and proportion shortcuts
Domain and range of rational functions
Domain and range of rational functions with holes
Graphing rational functions with holes
Converting repeating decimals in to fractions
Decimal representation of rational numbers
Finding square root using long division
L.C.M method to solve time and work problems
Translating the word problems in to algebraic expressions
Remainder when 2 power 256 is divided by 17
Remainder when 17 power 23 is divided by 16
Sum of all three digit numbers divisible by 6
Sum of all three digit numbers divisible by 7
Sum of all three digit numbers divisible by 8
Sum of all three digit numbers formed using 1, 3, 4
Sum of all three four digit numbers formed with non zero digits
Sum of all three four digit numbers formed using 0, 1, 2, 3
Sum of all three four digit numbers formed using 1, 2, 5, 6