SHSAT PRACTICE QUESTIONS ONLINE FREE

About "SHSAT Practice Questions Online Free"

SHSAT Practice Questions Online Free :

Here we are going to see some practice worksheets for SHSAT exams. Each question paper consists of 20 question. For each questions, you can find solution with detailed explanation. 

SHSAT Practice Questions Online Free - Practice questions

Question 1 :

4/9 is the square root of what number ?

Solution :

From the given option, by taking square of 16/81 we get 4/9.

Hence the answer is 16/81.

Question 2 :

In the following system of equations

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

Solution :

Let us solve the given system of equations by elimination method.

3x + 7y = 24  -----(1) 

9x + 4y  =  21  -----(2) 

(1) ⋅ 4  ==>  12x + 28y  =  96

(2) ⋅ 7  ==>  63x + 28y  =  147

                   (-)    (-)       (-)

                ---------------------

                 -51x  =  -51

                     x  =  1

By applying x = 1 in (1), we get

3(1) + 7y  =  24

3 + 7y  =  24

7y  =  24 - 3 

7y  =  21

y  =  3

Hence the solution is (1, 3).

Question 3 :

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

Solution :

√abcd  =  √1(3) (12)(4)  

  =  √144

  =  12

Question 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)

Solution :

To find the which term is greater, we must know the values of X and Y.

Hence the given information is not enough to find answer.

Question 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 ?

Solution :

Area of triangle  =  20

Let "x be the base of the triangle

  (1/2) ⋅ ⋅ 5  =  20

x  =  20(2/5)

x  =  8 inches.

Perimeter of the triangle  =  AB + BC + CA 

=  6 + 4 + 8

Perimeter of triangle  =  Perimeter of square  =  18

4a  =  18

a  =  18/4  =  9/2

Area of square  =  (4.5)2

=  20.25 square inches.

Question 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 :

69, 71, 74, 74, 83, 84, 89, 91, 92

n = 9 (odd)

Middle term  =  Median  =  83

Hence the Median is 83.

Question 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 ?

Solution :

To find the number of revolutions made by the wheel, we have to divide speed of the car by the area covered by 1 revolution.

Area covered in 1 revolution  =  2πr

  =  π(2r)

  =  10 π

Number of revolutions  =  50/10 π

  =  5/π

Question 8 :

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

Solution :

Let "r" be the radius of the circle.

2r  =  side length of square

Area of circle  =  πr2

Area of square = a2 =  (2r)2  =  4r2

Area of shaded region  =  4rπr2

   =  r2(4 - π)

Probability of penny will fall on the shaded region 

=  r2(4 - π)/4r2

=  (4r2/4r2) - πr2/4r2

=  1 - π/4

Question 9 :

What is 10% (10%)/100% ?

Solution :

10% (10%)/100%  =  (10/100)(10/100)/(100/100)

  =  (100/100) / (100/100)

  =  1

Hence the answer is 1.

Question 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 ?

Solution :

10% means = 10/100  =  0.1

⌊0.1⌋  =  0.0

⌊10%⌋ + 1  =  0 + 1  =  1

Hence the answer is 1.

Question 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 ?

Solution :

Area of the circular field  =  100 square meter

 πr=  100

r2  =  100/π

r  =  √(100/π)  

Diameter of the circular path  =  2√(100/π)  

Time  =  Distance / Speed 

2√(100/π) / 10

=  0.2 √(100/π)

Question 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?

Solution :

Required Fibonnaci sequence 

0, 1, 1, 2, 3

Mean  =  (0 + 1 + 1 + 2 + 3)/5

  =  7/5

Question 13 :

If 1 slack  =  x vaks

9 vaks  =  12 hips

How many slack are in 24 hips?

Solution :

x vaks  =  1 slack 

1 vak  =  (1/x) slack  ---(1)

9 vaks  =  12 hips

1 vak  =  (12/9)  hips

1 vak  =  (4/3) hips  ----(2)

(1)  =  (2)

(1/x) slack  =  (4/3) hips

(3/x) slack  =  4 hips

Multiply by 6 on both sides

(18/x) slack  =  24 hips

Question 14 :

What is the value of 112/102 ?

Solution :

112  =  11 ⋅ 11  =  121

102 =  10 ⋅ 10  =  100

112/102  =  121/100

  =  1.21

Hence the answer is 1.21

Question 15 :

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

Solution :

(ab)  =  a + b - b2

  =  5 + 2 - 22

  =  7 - 4

  =  3

Hence the answer is 3.

Question 16 :

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

Solution :

Non positive integers stands for negative integers

-3, -2, -1, 0, 1, 2, 3, 4, 5

The negative integers are -3, -2 and -1.

Hence we have 3 negative integers.

Question 17 :

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

Solution :

"x" be the required number

The sum of square of the number and its reciprocal

  =  x2 + (1/x) 

Question 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.

Solution :

Initial size = 20

50% of 20  =  10

New size of ball =  20 + 10  =  30

50% of 30  =  15

New size of ball  =  30 + 15  =  45

Percentage of increase  =  (45 - 30)/30 ⋅ 100%

  =  (15/30) ⋅ 100%

  =  (1/2) ⋅ 100%

  =  50%

Question 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?

Solution :

Area of the given rectangle  =  440 square meter 

length ⋅ width  =  440

(l/2) ⋅ width  =  440/2

(l/2) ⋅ width  =  220

BC ⋅ CD  =  220

BC  =  base of the triangle and CD  = height of the triangle

(1/2) BC ⋅ CD  =  (1/2)  220

Area of the triangle  =  110

Hence the answer is 110.

Question 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 or by is the least common multiple of x and y.

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

Solution : 

Since √2 and π are both irrational, there are no integers, a and b that can satisfy the definition of LCM(x,y).

Hence the LCM does not exist.

(A)  π √2  (B)  2√2π  (C)  2π

(D)  2π2  (E)  Does not exist

After having gone through the stuff given above, we hope that the students would have understood, "SHSAT Practice Questions Online Free".

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ALGEBRA

Variables and constants

Writing and evaluating expressions

Solving linear equations using elimination method

Solving linear equations using substitution method

Solving linear equations using cross multiplication method

Solving one step equations

Solving quadratic equations by factoring

Solving quadratic equations by quadratic formula

Solving quadratic equations by completing square

Nature of the roots of a quadratic equations

Sum and product of the roots of a quadratic equations 

Algebraic identities

Solving absolute value equations 

Solving Absolute value inequalities

Graphing absolute value equations  

Combining like terms

Square root of polynomials 

HCF and LCM 

Remainder theorem

Synthetic division

Logarithmic problems

Simplifying radical expression

Comparing surds

Simplifying logarithmic expressions

Negative exponents rules

Scientific notations

Exponents and power

COMPETITIVE EXAMS

Quantitative aptitude

Multiplication tricks

APTITUDE TESTS ONLINE

Aptitude test online

ACT MATH ONLINE TEST

Test - I

Test - II

TRANSFORMATIONS OF FUNCTIONS

Horizontal translation

Vertical translation

Reflection through x -axis

Reflection through y -axis

Horizontal expansion and compression

Vertical  expansion and compression

Rotation transformation

Geometry transformation

Translation transformation

Dilation transformation matrix

Transformations using matrices

ORDER OF OPERATIONS

BODMAS Rule

PEMDAS Rule

WORKSHEETS

Converting customary units worksheet

Converting metric units worksheet

Decimal representation worksheets

Double facts worksheets

Missing addend worksheets

Mensuration worksheets

Geometry worksheets

Comparing  rates worksheet

Customary units worksheet

Metric units worksheet

Complementary and supplementary worksheet

Complementary and supplementary word problems worksheet

Area and perimeter worksheets

Sum of the angles in a triangle is 180 degree worksheet

Types of angles worksheet

Properties of parallelogram worksheet

Proving triangle congruence worksheet

Special line segments in triangles worksheet

Proving trigonometric identities worksheet

Properties of triangle worksheet

Estimating percent worksheets

Quadratic equations word problems worksheet

Integers and absolute value worksheets

Decimal place value worksheets

Distributive property of multiplication worksheet - I

Distributive property of multiplication worksheet - II

Writing and evaluating expressions worksheet

Nature of the roots of a quadratic equation worksheets

Determine if the relationship is proportional worksheet

TRIGONOMETRY

SOHCAHTOA

Trigonometric ratio table

Problems on trigonometric ratios

Trigonometric ratios of some specific angles

ASTC formula

All silver tea cups

All students take calculus 

All sin tan cos rule

Trigonometric ratios of some negative angles

Trigonometric ratios of 90 degree minus theta

Trigonometric ratios of 90 degree plus theta

Trigonometric ratios of 180 degree plus theta

Trigonometric ratios of 180 degree minus theta

Trigonometric ratios of 180 degree plus theta

Trigonometric ratios of 270 degree minus theta

Trigonometric ratios of 270 degree plus theta

Trigonometric ratios of angles greater than or equal to 360 degree

Trigonometric ratios of complementary angles

Trigonometric ratios of supplementary angles 

Trigonometric identities 

Problems on trigonometric identities 

Trigonometry heights and distances

Domain and range of trigonometric functions 

Domain and range of inverse  trigonometric functions

Solving word problems in trigonometry

Pythagorean theorem

MENSURATION

Mensuration formulas

Area and perimeter

Volume

GEOMETRY

Types of angles 

Types of triangles

Properties of triangle

Sum of the angle in a triangle is 180 degree

Properties of parallelogram

Construction of triangles - I 

Construction of triangles - II

Construction of triangles - III

Construction of angles - I 

Construction of angles - II

Construction angle bisector

Construction of perpendicular

Construction of perpendicular bisector

Geometry dictionary

Geometry questions 

Angle bisector theorem

Basic proportionality theorem

ANALYTICAL GEOMETRY

Analytical geometry formulas

Distance between two points

Different forms equations of straight lines

Point of intersection

Slope of the line 

Perpendicular distance

Midpoint

Area of triangle

Area of quadrilateral

Parabola

CALCULATORS

Matrix Calculators

Analytical geometry calculators

Statistics calculators

Mensuration calculators

Algebra calculators

Chemistry periodic calculator

MATH FOR KIDS

Missing addend 

Double facts 

Doubles word problems

LIFE MATHEMATICS

Direct proportion and inverse proportion

Constant of proportionality 

Unitary method direct variation

Unitary method inverse variation

Unitary method time and work

SYMMETRY

Order of rotational symmetry

Order of rotational symmetry of a circle

Order of rotational symmetry of a square

Lines of symmetry

CONVERSIONS

Converting metric units

Converting customary units

WORD PROBLEMS

HCF and LCM  word problems

Word problems on simple equations 

Word problems on linear equations 

Word problems on quadratic equations

Algebra word problems

Word problems on trains

Area and perimeter word problems

Word problems on direct variation and inverse variation 

Word problems on unit price

Word problems on unit rate 

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

Double facts word problems

Trigonometry word problems

Percentage word problems 

Profit and loss word problems 

Markup and markdown word problems 

Decimal word problems

Word problems on fractions

Word problems on mixed fractrions

One step equation word problems

Linear inequalities word problems

Ratio and proportion word problems

Time and work word problems

Word problems on sets and venn diagrams

Word problems on ages

Pythagorean theorem word problems

Percent of a number word problems

Word problems on constant speed

Word problems on average speed 

Word problems on sum of the angles of a triangle is 180 degree

OTHER TOPICS 

Profit and loss shortcuts

Percentage shortcuts

Times table shortcuts

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

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