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Present value, P = Rs.31250 Interest rate, R = 8% per annum Time, n = (3/2) years ∵ Compounded halfyearly. ∴ Amount (A) = P [1 + (R/2)/100]2n [Where, P = Present value R = Annual interest rate n = Time in years] ∴ A = 31250 [1 + (8/2)/100]3 [2n = 2 × 3/2] ⇒ A = 31250 [1 + 4/100]3 ⇒ A = 31250 [1 + 1/25]3 ⇒ A = 31250 [26/25]3 ⇒ A = 31250 × 17576/15625 ⇒ A = 2 × 17576 ⇒ A = 35152 ∴ Amount = Rs.35152 ∴ Compound interest = Rs.(35152 – 31250) [∵CI = A – P] = Rs.3902
1. Find the amount of $ 8000 for 3 years, compounded annually at 5% per annum. Also, find the compound interest.Solution: Here, P = $ 8000, R = 5 % per annum and n = 3 years. Using the formula A = $ P(1 + R/ 100)ⁿ amount after 3 years = $ {8000 × (1 + 5/100)³} = $ (8000 × 21/20 × 21/20 × 21/20) = $ 9261. Thus, amount after 3 years = $ 9261. And, compound interest = $ (9261  8000) Therefore, compound interest = $ 1261. 2. Find the compound interest on $ 6400 for 2 years, compounded annually at 7¹/₂ % per annum.Solution: Here, P = $ 6400, R % p. a. and n = 2 years. Using the formula A = P (1 + R/100)ⁿ Amount after 2 years = [6400 × {1 + 15/(2 × 100)}²] = $ (6400 × 43/40 × 43/40) =$ 7396. Thus, amount = $ 7396 and compound interest = $ (7396  6400) Therefore, compound interest = $ 996. Case 2: Let principal = $ P, time = 2 years, and let the rates of interest be p % p.a. during the first year and q % p.a. during the second year. Then, amount after 2 years = $ {P × (1 + P/100) × (1 + q/100)}. This formula may similarly be extended for any number of years.1. Find the amount of $ 12000 after 2 years, compounded annually; the rate of interest being 5 % p.a. during the first year and 6 % p.a. during the second year. Also, find the compound interest.Solution: Here, P = $12000, p = 5 % p.a. and q = 6 % p.a. Using the formula A = {P × (1 + P/100) × (1 + q/100)} amount after 2 years = $ {12000 × (1 + 5/100) × (1 + 6/100)} = $ (12000 × 21/20 × 53/50) =$ 13356 Thus, amount after 2 years = $ 13356 And, compound interest = $ (13356 – 12000) Therefore, compound interest = $ 1356. Case 3: For example suppose time is 2³/₅ years then, Amount = P × (1 + R/100)² × [1 + (3/5 × R)/100]1. Find the compound interest on $ 31250 at 8 % per annum for 2 years. Solution Amount after 2³/₄ yearsSolution: Amount after 2³/₄ years = $ [31250 × (1 + 8/100)² × (1 + (3/4 × 8)/100)] = ${31250 × (27/25)² × (53/50)} = $ (31250 × 27/25 × 27/25 × 53/50) = $ 38637. Therefore, Amount = $ 38637, Hence, compound interest = $ (38637  31250) = $ 7387. Let principal = $ P, rate = R% per annum, time = a years. Suppose that the interest is compounded half yearly.Then, rate = (R/2) % per halfyear, time = (2n) halfyears, and amount = P × (1 + R/(2 × 100))²ⁿ Compound interest = (amount)  (principal). 1. Find the compound interest on $ 15625 for 1¹/₂ years at 8 % per annum when compounded halfyearly.Solution: Here, principal = $ 15625, rate = 8 % per annum = 4% per halfyear, time = 1¹/₂ years = 3 halfyears. Amount = $ [15625 × (1 + 4/100)³] =$ (15625 × 26/25 × 26/25 × 26/25)= $ 17576. Compound interest = $ (17576  15625) = $ 1951. 2. Find the compound interest on $ 160000 for 2 years at 10% per annum when compounded semiannually.Solution: Here, principal = $ 160000, rate = 10 % per annum = 5% per halfyear, time = 2 years = 4 halfyears. Amount = $ {160000 × (1 + 5/100)⁴} =$ (160000 × 21/20 × 21/20 × 21/20 × 21/20) compound interest = $ (194481 160000) = $ 34481. Compound Interest by Using Formula, when it is calculated QuarterlyInterest Compounded QuarterlyThen, rate = (R/4) % Per quarter, time = (4n) quarters, and amount = P × (1 + R/(4 × 100))⁴ⁿ Compound interest = (amount)  (principal). Page 2
In 8th grade math practice you will get all types of examples on different topics along with the solutions. 8th grade math worksheets are arranged in such a way that students can learn math while practicing it step by step. Keeping in mind the mental level of child in 8th grade, every efforts has been made to introduce new concepts in a simple language, so that the child understands them easily. The difficulty level of the problems has been reduced and mathematical concepts have been explained in the simplest possible way. Each topic contains a large number of examples to understand the applications of concepts. In 8th grade math test we need to learn Rational Numbers, Exponents, Square and Square Roots, Cubes and Cube roots, Operations on Algebraic Expressions, Factorization, Linear Equations, Profit and Loss, Compound Interest, Ratio and Proportion, Time and Work and in geometry we learn Quadrilaterals, Parallelograms, Construction of Quadrilaterals, ThreeDimensional Figures, Area of a Trapezium and a Polygon, Volume and Surface Area of Solids, Data Handling, Constructing and Interpreting Bar Graphs, Pie Charts, Probability, Graphs, etc…… If student follow mathonlymath they can improve their knowledge by practicing the worksheets for 8th graders which will them to score in their exam. ● Set Theory Sets Theory: Brief description on set theory and the important sets used in mathematics. Representation of a Set: Definition with examples of statement form, roster form or tabular form, set builder form cardinal number of a set and the standard sets of numbers. Types of Sets: Definition with examples of empty set or null set, singleton set, finite set, infinite set, cardinal number of a set, equivalent set and equal sets. Finite Sets and Infinite Sets: Learn how to distinguish between finite set and infinite set with examples. Power Set: Explanation on power sets will help us to get the basic concepts if sets with examples. Problems on Union of Sets: Learn how to find the union of two or more sets and workedout examples of operations on union of sets. Problems on Intersection of Sets: Learn how to find the intersection of two or more sets and workedout examples of operations on intersection of sets. Difference of two Sets: Learn how to find the difference between the two sets and workedout examples. Complement of a Set: Definition of complement of a set and their properties with some workedout examples. Problems on Complement of a Set: Learn how to find the complement of two or more sets and workedout examples of operations on complement of sets. Problems on Operation on Sets: Learn how to find the union and intersection of two or more sets and workedout examples of the two basic operations of sets. Word Problems on Sets: Apply set operations to solve word problems involving the properties of union and intersection of sets. Venn Diagrams in Different Situations: Learn how to use the Venn diagrams in different situations to find the different sets. Relationship in Sets using Venn Diagram: Learn how to find the relationship of the union, intersection and difference of the two sets using Venndiagram. Union of Sets using Venn Diagram: Diagrammatic representation to find the union of two sets and their properties, workedout examples. Intersection of Sets using Venn Diagram: Diagrammatic representation to find the intersection of two sets and their properties, workedout examples. Disjoint of Sets using Venn Diagram: Learn how to represent the disjoint sets of union and intersection using VennDiagram. Difference of Sets using Venn Diagram: Learn how to represent the difference between two sets using VennDiagram. Examples on Venn Diagram: Learn how to use the basic concepts of sets for solving the different types of problems on Venn diagram. ● Relations and Mapping Ordered Pair Cartesian Product of Two Sets Relation Domain and Range of a Relation Practice Test on Math Relation Functions or Mapping Domain Codomain and Range of Function Math Practice Test on Function ● Relations and Mapping  Worksheets Worksheet on Math Relation Worksheet on Functions or Mapping ● Cube and Cube Roots Cube To Find if the Given Number is a Perfect Cube Cube Root Method for Finding the Cube of a TwoDigit Number Table of Cube Roots ● Cube and Cube Roots  Worksheets Worksheet on Cube Worksheet on Cube and Cube Root Worksheet on Cube Root ● Rational Numbers Introduction of Rational Numbers What is Rational Numbers? Is Every Rational Number a Natural Number? Is Zero a Rational Number? Is Every Rational Number an Integer? Is Every Rational Number a Fraction? Positive Rational Number Negative Rational Number Equivalent Rational Numbers Equivalent form of Rational Numbers Rational Number in Different Forms Properties of Rational Numbers Lowest form of a Rational Number Standard form of a Rational Number Equality of Rational Numbers using Standard Form Equality of Rational Numbers with Common Denominator Equality of Rational Numbers using Cross Multiplication Comparison of Rational Numbers Rational Numbers in Ascending Order Rational Numbers in Descending Order Representation of Rational Numbers on the Number Line Rational Numbers on the Number Line Addition of Rational Number with Same Denominator Addition of Rational Number with Different Denominator Addition of Rational Numbers Properties of Addition of Rational Numbers Subtraction of Rational Number with Same Denominator Subtraction of Rational Number with Different Denominator Subtraction of Rational Numbers Properties of Subtraction of Rational Numbers Rational Expressions Involving Addition and Subtraction Simplify Rational Expressions Involving the Sum or Difference Multiplication of Rational Numbers Product of Rational Numbers Properties of Multiplication of Rational Numbers Rational Expressions Involving Addition, Subtraction and Multiplication Reciprocal of a Rational Number Division of Rational Numbers Rational Expressions Involving Division Properties of Division of Rational Numbers Rational Numbers between Two Rational Numbers To Find Rational Numbers ● Rational Numbers  Worksheets Worksheet on Rational Numbers Worksheet on Equivalent Rational Numbers Worksheet on Lowest form of a Rational Number Worksheet on Standard form of a Rational Number Worksheet on Equality of Rational Numbers Worksheet on Comparison of Rational Numbers Worksheet on Representation of Rational Number on a Number Line Worksheet on Adding Rational Numbers Worksheet on Properties of Addition of Rational Numbers Worksheet on Subtracting Rational Numbers Worksheet on Addition and
Subtraction of Rational Number Worksheet on Rational Expressions Involving Sum and Difference Worksheet on Multiplication of Rational Number Worksheet on Properties of Multiplication of Rational Numbers Worksheet on Division of Rational Numbers Worksheet on Properties of Division of Rational Numbers Worksheet on Finding Rational Numbers between Two Rational Numbers Worksheet on Word Problems on Rational Numbers Worksheet on Operations on Rational Expressions Objective Questions on Rational Numbers ● Ratio and Proportion What is Ratio and Proportion? Practice Test on Ratio and Proportion Worked out Problems on Ratio and Proportion ● Ratio and Proportion  Worksheets Worksheet on Ratio and Proportion ● Significant Figures Significant Figures ● Significant Figures  Worksheets Worksheet on Significant Figures ● Fun with Numbers Playing with Numbers Test of Divisibility Number Puzzles and Games ● Fun with Numbers  Worksheets Worksheet on Number Puzzles and Games ● Exponents Exponents Laws of Exponents Rational Exponent Integral Exponents of a Rational Numbers Solved Examples on Exponents Practice Test on Exponents ● Exponents  Worksheets Worksheet on Exponents ● Square Square Perfect Square or Square Number Properties of Perfect Squares ● Square  Worksheets Worksheet on Squares ● Square Root Square Root Square Root of a Perfect Square by using the Prime Factorization Method Square Root of a Perfect Square by Using the Long Division Method Square Root of Numbers in the Decimal Form Square Root of Number in the Fraction Form Square Root of Numbers that are Not Perfect Squares Table of Square Roots Practice Test on Square and Square Roots ● Square Root Worksheets Worksheet on Square Root using Prime Factorization Method Worksheet on Square Root using Long Division Method Worksheet on Square Root of Numbers in Decimal and Fraction Form ● Algebraic Expression Algebraic Expression Addition of Algebraic Expressions Subtraction of Algebraic Expressions Multiplication of Algebraic Expression Division of Algebraic Expressions ● Formula Formula and Framing the Formula Change the Subject of a Formula Changing the Subject in an Equation or Formula Practice Test on Framing the Formula ● Formula  Worksheets Worksheet on Framing the Formula Worksheet on Changing the Subject of a Formula Worksheet on Changing the Subject in an Equation or Formula ● Factorization Factorization Factors of Algebraic Expressions Monomial is a Common Factor Factorization when Monomial is Common Binomial is a Common Factor Factorization when Binomial is Common Factorization by Grouping Factorize by Grouping The Terms Factoring Terms by Grouping Factorization by Regrouping Factorize by Regrouping The Terms Factoring Terms by Regrouping Factorization by Using Identities Factorization of Perfect Square Factorization of Perfect Square Trinomials Difference of Two Squares Factoring Differences of Squares Factorize the Difference of Two Squares Evaluate the Difference of Two Squares Factorize the Trinomial x^2 + px + q Factorize the Trinomial ax^2 + bx + c Factorization of Quadratic Trinomials ● Factorization  Worksheet Worksheet on Factoring Algebraic Expression Worksheet on Factoring Binomials Worksheet on Factoring by Grouping Worksheet on Factorization by Regrouping Worksheet on Factoring out a Common Binomial Factor Worksheet on Factoring Identities Worksheet on Factoring the Differences of Two Squares Worksheet on Factorization using Formula Worksheet on Factoring Trinomials Worksheet on Factoring Simple Quadratics Worksheet on Factoring Quadratic Trinomials Worksheet on Factoring Trinomials by Substitution Worksheet on Factorization ● Simplification of Algebraic Fractions Algebraic Fractions Arithmetic Fraction and Algebraic Fraction Highest Common Factor of Monomials Highest Common Factor of Monomials by Factorization Lowest Common Multiple of Monomials Lowest Common Multiple of Monomials by Factorization Highest Common Factor of Polynomials Lowest Common Multiple of Polynomials H.C.F. of Polynomials by Factorization Highest Common Factor of Polynomials by Factorization L.C.M. of Polynomials by Factorization Lowest common multiple of Polynomials by Factorization H.C.F. of Polynomials by Division Method H.C.F. of Polynomials by Long Division Method Relation Between H.C.F. and L.C.M. of Two Polynomials Reduce Algebraic Fractions to its Lowest Term Simplification of Algebraic Fractions Rule of Separation of Division Sum and Difference of Algebraic Fractions Problems on Algebraic Fractions Solving Algebraic Fractions Multiplication of Algebraic Fractions Division of Algebraic Fractions ● Simplification of Algebraic Fractions  Worksheets Worksheet on H.C.F. of Monomials Worksheet on L.C.M. of Monomials Worksheet on H.C.F. and L.C.M. of Monomials Worksheet on H.C.F. of Polynomials Worksheet on L.C.M. of Polynomials Worksheet on H.C.F. and L.C.M. of Polynomials Worksheet on Reducing Algebraic Fractions Worksheet on Algebraic Expressions to the Lowest Terms Worksheet on Algebraic Fractions Worksheet on Simplifying Algebraic Fractions ● Equations What is an Equation? What is a Linear Equation? How to Solve Linear Equations? Solving Linear Equations Problems on Linear Equations in One Variable Word Problems on Linear Equations in One Variable Practice Test on Linear Equations Practice Test on Word Problems on Linear Equations ● Equations  Worksheets Worksheet on Linear Equations Worksheet on Word Problems on Linear Equation ● Simultaneous Linear Equations Simultaneous Linear Equations Comparison Method Elimination Method Substitution Method CrossMultiplication Method Solvability of Linear Simultaneous Equations Pairs of Equations Word Problems on Simultaneous Linear Equations Word Problems on Simultaneous Linear Equations Practice Test on Word Problems Involving Simultaneous Linear Equations ● Simultaneous Linear Equations  Worksheets Worksheet on Simultaneous Linear Equations Worksheet on Problems on Simultaneous Linear Equations ● Linear Inequations What are Linear Inequality? What are Linear Inequations? 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Percentage of a Number Increase Percentage Decrease Percentage Basic Problems on Percentage Solved Examples on Percentage Problems on Percentage Real Life Problems on Percentage Word Problems on Percentage Application of Percentage ● Percentage  Worksheets Worksheet on Fraction into Percentage Worksheet on Percentage into Fraction Worksheet on Percentage into Ratio Worksheet on Ratio into Percentage Worksheet on Percentage into Decimal Worksheet on Percentage of a Number Worksheet on Finding Percent Worksheet on Finding Value of a Percentage Worksheet on Percentage of a Given Quantity Worksheet on Word Problems on Percentage Worksheet on Increase Percentage Worksheet on Decrease Percentage Worksheet on increase and Decrease Percentage Worksheet on Expressing Percent Worksheet on Percent Problems Worksheet on Finding Percentage ● Profit, Loss and Discount Calculating Profit Percent and Loss Percent Word Problems on Profit and Loss Examples on Calculating Profit or Loss Practice Test on Profit and Loss Discount Practice Test on Profit Loss and Discount ● Profit, Loss and Discount  Worksheets Worksheet to Find Profit and Loss Worksheets on Profit and Loss Percentage Worksheet on Gain and Loss Percentage Worksheet on Discounts ● Time and Work Time and Work Pipes and Cistern Practice Test on Time and Work ● Time and Work  Worksheets Worksheet on Time and Work ● Time and Distance Speed of Train Relationship between Speed, Distance and Time Conversion of Units of Speed Problems on Calculating Speed Problems on Calculating Distance Problems on Calculating Time Two Objects Move in Same Direction Two Objects Move in Opposite Direction Train Passes a Moving Object in the Same Direction Train Passes a Moving Object in the Opposite Direction Train Passes through a Pole Train Passes through a Bridge Two Trains Passes in the Same Direction Two Trains Passes in the Opposite Direction ● Time and Distance  Worksheets Worksheet on Conversion of Units of Speed Worksheet on Calculating Time Worksheet on Calculating Speed Worksheet on Calculating Distance Worksheet on Train Passes through a Pole Worksheet on Train Passes through a Bridge Worksheet on Relative Speed Worksheet on Decimal into Percentage ● Simple Interest What is Simple Interest? Calculate Simple Interest Practice Test on Simple Interest ● Simple Interest  Worksheets Simple Interest Worksheet ● Compound Interest Compound Interest Compound Interest with Growing Principal Compound Interest with Periodic Deductions Compound Interest by Using Formula Compound Interest when Interest is Compounded Yearly Compound Interest when Interest is Compounded HalfYearly Compound Interest when Interest is Compounded Quarterly Problems on Compound Interest Variable Rate of Compound Interest Difference of Compound Interest and Simple Interest Practice Test on Compound Interest Uniform Rate of Growth Uniform Rate of Depreciation Uniform Rate of Growth and Depreciation ● Compound Interest  Worksheet Worksheet on Compound Interest Worksheet on Compound Interest when Interest is Compounded HalfYearly Worksheet on Compound Interest with Growing Principal Worksheet on Compound Interest with Periodic Deductions Worksheet on Variable Rate of Compound Interest Worksheet on Difference of Compound Interest and Simple Interest Worksheet on Uniform Rate of Growth Worksheet on Uniform Rate of Depreciation Worksheet on Uniform Rate of Growth and Depreciation ● Ratio and Proportion (Direct & Inverse Variation) Direct Variation Inverse Variation Practice Test on Direct Variation and Inverse Variation ● Ratio and Proportion  Worksheets Worksheet on Direct Variation Worksheet on Inverse Variation ● Probability Probability ● Probability  Worksheets Worksheet on Probability Geometry ● Lines and Angles Basic Geometrical Concepts Angles Classification of Angles Related Angles Some Geometric Terms and Results Complementary Angles Supplementary Angles Complementary and Supplementary Angles Adjacent Angles Linear Pair of Angles Vertically Opposite Angles Parallel Lines Transversal Line Parallel and Transversal Lines ● Parallelogram Parallelogram Properties of a Rectangle Rhombus and Square Problems on Parallelogram Practice Test on Parallelogram ● Parallelogram  Worksheet Worksheet on Parallelogram ● Quadrilateral What is Quadrilateral? 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