10th GRADE MATH PRACTICE QUESTIONS

Problem 1 :

The ratio of incomes of two persons is 9 : 7 and the ratio of their expenditures is 4 : 3. If each of them manages to save $2000 per month, find their monthly incomes.

Solution :

Let 9x, 7x be incomes of two persons.

Let 4y and 3y are expenditure of two persons.

9x - 4y  =  2000 ----(1)

7x - 3y  =  2000 ----(2)

(1) ⋅ 3 ==>    27x - 12y  =  6000

(2) ⋅ 4 ==>  -28x + 12y  =  -8000

(3) - (4)   ------------------------

                   -x  =  -2000

By applying the value of x  =  2000 in (1), we get

9(2000) - 4y  =  2000

4y  =  16000

y  =  4000

9x  =  18000 and 7x  =  14000

So, the incomes of two persons are 18000 and 14000 respectively.

Problem 2 :

Solve the following pair of linear equations by the elimination method 3x + 4y = 10 and 2x – 2y = 2.

Solution :

3x + 4y  =  10 ----(1)

2x – 2y  =  2 ----(2)

                    3x + 4y  =  10

(2) ⋅ 2 ==>    4x - 4y  =  4

                   ----------------

                     x  =  14

By applying the value of x in (2), we get

28 - 2y  =  2

2y  =  26

y  =  13

So, the solution is (14, 13).

Problem 3 :

Two players, Jessy and mark, play a tennis match. It is known that the probability of Jessy winning the match is 0.62. What is the probability of Mark winning the match ?

Solution :

Probability of Jessy is winning the match  =  0.62

Probability of Mark is winning the match  =  1 - 0.62

  =  0.38

Problem 4 :

Two dice, one blue and one red, are thrown at the same time. Write down all the possible outcomes. What will be  the probability that the sum of the two numbers appearing on the top of the dice is 8?

Solution :

Sample space  =  

{(1, 1) (1, 2) (1, 3) (1, 4) (1, 5) (1, 6) (2, 1) (2, 2) (2, 3) (2, 4) (2, 5) (2, 6) (3, 1) (3, 2) (3, 3) (3, 4) (3, 5) (3, 6) (4, 1) (4, 2) (4, 3) (4, 4) (4, 5) (4, 6) (5, 1) (5, 2) (5, 3) (5, 4) (5, 5) (5, 6) 6 (6, 1) (6, 2) (6, 3) (6, 4) (6, 5) (6, 6) }

n(s)  =  36

Let A be the event of sum as 8.

A  =  {(2, 6) (3, 5) (4, 4) (5, 3) (6, 2)} 

n(A)  =  5

p(A)  =  n(A)/n(S)

p(A)  =  5/36

Problem 5 :

James buys a fish from a shop for his aquarium. The salesman takes out one fish at random from a tank containing 5 male fish and 8 female fish. What will be the probability that the fish taken out would be  male fish?

Solution :

Sample space  =  Total number of fishes

n(S)  =  5 male + 8 female

n(S)  =  13 fishes

Let A be the event of getting male fish.

n(A)  =  5

p(A)  =  n(A)/n(S)

p(A)  =  5/13

So, the probability of getting male fish is 5/13.

Problem 6 :

If the points A (6, 1), B (8, 2), C (9, 4) and D (t, 3) are the vertices of a parallelogram, taken in order, find the value of t.

Solution :

Midpoint of diagonal AC  =  Midpoint of diagonal BD

Midpoint  =  (x1 + x2)/2, (y1 + y2)/2

(4 + 9)/2, (1 + 4)/2  =  (8 + t)/2, (2 + 3)/2

13/2, 5/2  =  (8 + t)/2, 5/2

Equating x coordinates, we get

8 + t  =  13

t  =  13 - 8

t  =  5

Problem 7 :

Find the ratio in which the line segment joining the points A (– 3, 10) and B (6, – 8) is divided by the point  P (– 1, 6).

Solution :

[l(6) + m(-3)]/(l + m), [l(-8) + m(10)]/(l + m)  =  (-1, 6)

(6l - 3m)/(l + m),  (-8l + 10m)/(l + m)  =  (-1, 6)

Equating the x coordinates, we get

6l - 3m  =  -1(l + m)

6l + l  =  -m + 3m

7l  =  2m

l/m  =  2/7

l : m  =  2 : 7

So, the required ratio is 2 : 7.

Problem 8 :

Find the coordinates of point A, where AB is the diameter of a circle with center is (2, – 3) and the coordinate of  B is (1, 4).

Solution :

Center is (2, -3). Let A(a, b) the required point.

Midpoint of diameter  =  Center

Midpoint  =  (x1 + x2)/2, (y1 + y2)/2

(1 + a)/2, (-3 + b)/2  =  (2, -3)

By equating x and y coordinate, we get

1 + a  =  4

a  =  1

-3 + b  =  -6

b  =  -6 + 3

b  =  -3

So, the required point is (1, -3).

Problem 9 :

Find the area of the triangle whose vertices are 

(1,–1), (–4, 6) and (–3, –5)

Solution :

Area of triangle ABC

  =  (1/2)[(6 + 20 + 3) - (4 - 18 - 5)]

  =  (1/2)[29 - (-19)]

  =  (1/2)[29 + 19]

  =  (1/2) 48

  =  24 square units

Problem 10 :

Find the equation of the straight line through (1, 3) and parallel to the straight line 5x - 3y + 1 = 0.

Solution :

Equation of the line parallel to the given line :

Slope of the required line  =  Slope of the given line

m  =  -coefficient of x/coefficient of y

m  =  5/3

(y - y1)  =  m(x - x1)

(y - 3)  =  (5/3)(x - 1)

3y - 9  =  5x - 5

5x - 3y  - 5 + 9  =  0

5x - 3y + 4  =  0  

Apart from the stuff given above, if you need any other stuff in math, please use our google custom search here.

If you have any feedback about our math content, please mail us : 

v4formath@gmail.com

We always appreciate your feedback. 

You can also visit the following web pages on different stuff in math. 

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