(1)  Thirty of the fifty students who took an exam received a grade of 90%  or greater.  What percentage of those fifty students received a grade of less than 90%?

(A)  70  (B)  35  (C)  40  (D)  30  (E)  10


(2)  Let n be a number from -3 to 4 inclusive.  What is the range of values of n2?

(A)  -9 ≤ n2 ≤ 16  (B)   9 ≤ n2 ≤ 16  (C)  3 ≤ n2 ≤ 4 

(D)  0 ≤ n2 ≤ 2  (E)  0 ≤ n2 ≤ 16


(3)  A is 3 times C.  B is 8 less than C.  For what value of C does A = B?

(A)  -4  (B)  0  (C)  1  (D)  2  (E)  5/2


(4)  In a class of 28 students, everyone likes math, English, or both.  If 17 like math and 19 like English, how many like both?

 (A)  2  (B)  8  (C)  16  (D)  20  (E)  28


(5)  Let x = 32·53·74 and y = 23·3·52.  What is the greatest common factor of and y?

(A)  2· 3 · 5 · 7  (B)  2· 3· 5· 74  (C)  3 · 5 

(D)  3 · 52  (E)  32·53


(6)  The equation 2(3x + 8) = 3(2x + 4) is satisfied by

(A)  no value of x.  (B)  only negative values of x 

(C)  only x = 0.  (D)  only positive values of x. 

(E)  all values of x.


(7)  In the formula V = s2h, if s is doubled and h is tripled, then V is multiplied by

 (A)  5  (B)  6  (C)  12  (D)  18   (E)  36


(8)  You have 10 large boxes that can each hold 8 soccer balls, and 10 small boxes that can each hold 5 of the same soccer balls.  If you have 99 soccer balls, what is the greatest number of boxes you can completely fill? 

(A)  13  (B)  14  (C)  15  (D)  16  (E)  19



The straight line graph shows the relationship between number of hours worked and amount earned.  How much would be earned for 50 hours of work?

(A)  $50  (B)  $83  (C)  $120  (D)  $150  (E)  $300


(10)  The perimeter of a triangle, all of whose sides have integer length, is 19.  A possible length for the largest side is

(A)  6  (B)  8  (C)  10  (D)  15  (E)  17


(11)  A value of x that satisfies the inequality 2x – 10 > 3x is

(A)  -11  (B)  -10  (C)  -1  (D)  0  (E)  12



The midpoints of the four sides of square ABCD are joined to form square WXYZ as shown.  The area of square WXYZ is 16.  The area of triangle YCX is

(A)  4  (B)  2  (C)  1.5  (D)  1  (E)  none of these


(13)  The mean of 3 numbers is 7.  The mean of 4 other numbers is 8.  The mean of 5 other numbers is 11.  What is the mean of all 12 numbers?

(A)  4  (B)  4(2/13)  (C)  8(2/3)  (D)  9  (E)  36


(14)  There were 20 socks in a drawer.  Of these, 8 were blue, 10 were black, and 2 were white.  Someone then removed 4 blue socks.  If one sock is now drawn at random, what is the probability that it is not white?

(A)  1/10  (B)  9/10  (C)  1/8  (D)  7/8

(E)  None of these


(15)  Two sides of a right triangle are 3 and 4.  The third side is

(A)  1  (B)  3  (C)  5  (D)  7  (E)  not uniquely determined


(16)  A cube 3 by 3 by 3 is painted red on all six faces and then cut into 27 smaller 1 by 1 by 1 cubes.  How many of these new smaller cubes have exactly two faces that are painted red?

 (A)  6  (B)  8  (C)  12  (D)  21  (E)  27


(17)  If 2 blobs = 3 glops and 3 blobs = 2 chunks, then 1 chunk =

(A)  1 glop  (B)  2/3 glop  (C)  3/2 glops 

(D)  4/9 glop  (E)  9/4 glops


(18) and (19)  The two pie charts show the ice cream flavor preferences of the students at two high schools.

(18)  The ratio of Montague students who prefer vanilla to Montague students who prefer chocolate is

         (A)  10:9  (B)  4:3  (C)  3:10  (D)  3:4  (E)  2:5


(19)  If the number of Montague students who prefer vanilla is M and the number of Capulet students who prefer vanilla is C, then

(A)  M > 2C  (B) M = 2C  (C)  M = C  (D)  M < C 

(E) The relationship cannot be determined from the given information


(20)  If x is an integer, which one of the following must be odd?

(A)  3x + 1  (B)  3x + 2  (C)  4x - 1 

(D)  4x - 2  (E)  5x – 2x


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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


Quantitative aptitude

Multiplication tricks


Aptitude test online


Test - I

Test - II


Horizontal translation

Vertical translation

Reflection through x -axis

Reflection through y -axis

Horizontal expansion and compression

Vertical  expansion and compression

Rotation transformation

Geometry transformation

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Transformations using matrices





Converting customary units worksheet

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Mensuration worksheets

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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



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 formulas

Area and perimeter



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


Coordinate geometry formulas

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Different forms equations of straight lines

Point of intersection

Slope of the line 

Perpendicular distance


Area of triangle

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Matrix Calculators

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Missing addend 

Double facts 

Doubles word problems


Direct proportion and inverse proportion

Constant of proportionality 

Unitary method direct variation

Unitary method inverse variation

Unitary method time and work


Order of rotational symmetry

Order of rotational symmetry of a circle

Order of rotational symmetry of a square

Lines of symmetry


Converting metric units

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HCF and LCM  word problems

Word problems on simple equations 

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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

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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


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

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