Conversion of Measurement Grade 7 Mathematics

Measurement

1. December 5, 2022 Algebra/Polynomials Mathematics 7

2. Mathematics 7 Class - Algebra/Polynomials –December 5, 2022

3. ALGEBRA The word algebra comes from the Arabic: الجبر ‎ : al- jabr , which means 'reunion of broken parts’. This is based from the title of the early 9th century book "The Science of Restoring and Balancing" by the Persian mathematician and astronomer al- Khwarizmi . It is the branch of mathematics in which letters and other general symbols are used to represent numbers and quantities in formulae and equations. Mathematics 7 Class - Algebra/Polynomials –December 5, 2022

4. ALGEBRA Definition of Terms ALGEBRAIC EXPRESSION It is a mathematical phrase which is composed of variables and constants along with mathematical operations (addition, subtraction, multiplication, division). Example: 3x – 2, 4m 2 + 7m – 4, b + 3 Mathematics 7 Class - Algebra/Polynomials –December 5, 2022

5. ALGEBRA Definition of Terms POLYNOMIAL It is a kind of algebraic expression where each term is a constant, a variable or a product of a constant and variable in which the variable has a whole number (non-negative number) exponent . An algebraic expression is NOT a polynomial if 1) the exponent of the variable is NOT a whole number {0, 1, 2, 3 ...}. 2) the variable is inside the radical sign. 3) the variable is in the denominator. Mathematics 7 Class - Algebra/Polynomials –December 5, 2022

6. ACTIVITY 2 Which of the following algebraic expressions is a polynomial? Mathematics 7 Class - Algebra/Polynomials –December 5, 2022

7. ALGEBRA Definition of Terms VARIABLE It is a symbol or letters that may take one or more than one value. Example: x, a, b, m, n CONSTANT It is a number on its own and never changes its value. Example: 1, - 2, 4, 0, ½ , ¾ Mathematics 7 Class - Algebra/Polynomials –December 5, 2022

8. ALGEBRA Definition of Terms TERM It can be a constant, a variable, or a constant and a variable multiplied together or divided by another. Terms are separated by “+” and “-”. Example: x 2x – 3y 2m 5xy - 4 1 2x 2 - x Mathematics 7 Class - Algebra/Polynomials –December 5, 2022

9. ACTIVITY 3 Identify the variable used in the expression and the constant if there’s any. x - 2 2ab m 2 + 5m – 2 Identify the terms in the given algebraic expressions. x - 2 2ab m 2 + 5m – 2 x a and b m x - 2 There are 2 terms. 2ab There is only 1 term. m 2 5 m - 2 There are 3 terms. Mathematics 7 Class - Algebra/Polynomials –December 5, 2022

10. POLYNOMIALS Kinds of Polynomials According to Number of Terms MONOMIAL – A polynomial with one term. BINOMIAL – A polynomial with two terms. TRINOMIAL – A polynomial with three term. MULTINOMIAL – A polynomial with more than three terms. Mathematics 7 Class - Algebra/Polynomials –December 5, 2022

11. ACTIVITY 4 Classify the given polynomials according to number of terms. x - 2 2ab m 2 + 5m – 2 x + 2y – 3x 2 + 1 There are 2 terms. BINOMIAL There is only 1 term. MONOMIAL There are 3 terms. TRINOMIAL There are 4 terms. MULTI NOMIAL Mathematics 7 Class - Algebra/Polynomials –December 5, 2022

12. NUMERICAL COEFFICIENT The number that comes before the variable. LITERAL COEFFICIENT The variable together with the exponent 4 x 2 NUMERICAL COEFFICIENT LITERAL COEFFICIENT In 4x 2 + 5x – 2, the first term is 4x 2 , the second term is 5x and the third term is – 2 . Mathematics 7 Class - Algebra/Polynomials –December 5, 2022

13. ACTIVITY 5 Identify the terms of the given expression then list down the numerical coefficient and literal coefficient of each term. Given Expression TERMS NUMERICAL COEFFICIENT LITERAL COEFFICIENT 1. x - 2 2. 2ab 3. m 2 + 5m – 2 x - 2 1 x - 2 none 2ab 2 ab m 2 1 + 5m m 2 + 5 m - 2 - 2 none Mathematics 7 Class - Algebra/Polynomials –December 5, 2022

14. BASE AND EXPONENT Definition of Terms BASE It is a number or a quantity that will be multiplied to itself. EXPONENT It tells how many times the base is multiplied to itself. x 2 BASE EXPONENT Mathematics 7 Class - Algebra/Polynomials –December 5, 2022

15. ACTIVITY 6 Identify the base and exponent. TERMS LITERAL COEFFICIENT BASE EXPONENT x 2ab m 2 5m 3x 3 3a 3 b 6 c 4 x ab x 1 a 1 b 1 m 2 m m 2 m 1 x 3 x 3 a 3 b 6 c 4 a 3 b 6 c 4 Mathematics 7 Class - Algebra/Polynomials –December 5, 2022

16. POLYNOMIALS Definition of Terms STANDARD FORM A polynomial is in standard form if the terms are arranged from the highest exponent of the variable to the lowest exponent. Example: 2x 2 – x + 1 4x 3 – 6x 2 + x - 3 LEADING TERM – the first term in a polynomial in standard form. LEADING COEFFICIENT – the numerical coefficient of the leading term. Mathematics 7 Class - Algebra/Polynomials –December 5, 2022

17. POLYNOMIALS Definition of Terms DEGREE It is the highest exponent in a polynomial. Example: 2x 2 – 3x + 5 – The highest exponent is 2, the degree is 2 . 4y + 5y 4 – 3y 2 + 1 – The highest exponent is 4, the degree is 4. If there are two or more variables, the degree is the sum of the exponents in the leading term. Example: 2x 3 y 4 – 3xy 2 + xy - The leading term is 2x 3 y 4 , the sum of the exponents of x and y is 7. Mathematics 7 Class - Algebra/Polynomials –December 5, 2022

18. POLYNOMIALS Kinds of Polynomials According to Degree QUADRATIC – A polynomial with degree 2. CUBIC – A polynomial with degree 3. QUARTIC – A polynomial with degree 4. QUINTIC– A polynomial with degree 5. LINEAR – A polynomial with degree 1. Mathematics 7 Class - Algebra/Polynomials –December 5, 2022

19. ACTIVITY 7 Identify the degree and classify the given polynomials. POLYNOMIAL STANDARD FORM LEADING TERM DEGREE CLASSIFICATION ACC. TO DEGREE 1. x 2 – 3x + 1 2. 5a – 4a 3 – a 5 + a 2 3. 3xy 2 4. 4x – x 2 + 3x 3 5. 10a – 12 x 2 – 3x + 1 5 quadratic quintic cubic 3 x 2 2 – a 5 – 4a 3 + a 2 + 5a - a 5 3xy 2 3xy 2 cubic 3 3x 3 – x 2 + 4x 3x 3 linear 1 10a – 12 10a Mathematics 7 Class - Algebra/Polynomials –December 5, 2022

20. Thank you! Mathematics 7 Class - Algebra/Polynomials –December 5, 2022