basic-algebra-q2-for-student.pptx lesson

algebra lessons

1. 0.25

2. 6: 2 etutorworld” ALGEBRA
バト レッ) Learning by Design

What is Algebra? - is a way of expressing mathematical ideas
that use variables, constants, numerical coefficients, and
mathematical operations.

What is a Variable?

It is a letter that represents an unknown value or a changing value.

all letters like x, y, a, z, m
What is a Constant?

A quantity which is not changed.

all numbers like 3, -6, 14, 23, 100

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3. Ed etutorworld” ALGEBRA
レプ) Learning by Design

What is a Term?

It is made up of a number and a variable put together by multiplication
and separated by addition or subtraction. There can be two or more
terms in an expression.

5y has one term, 5x + 3y has two terms, 3x? - Zab + 2er
has three terms and so on

What is an Algebraic Expression?

A mathematical statement that contains terms (numbers and
variables) and at least one operation ( +, -, +, x)

ㆍ “7

Examples of Algebraic Expression: x?, 2y?, 3x? - 5, 4xy + 7

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4. eS etutorworld" ALGEBRA

What is a Coefficient?

Coefficient of x? in 3x? is 3

Coefficient of y? in 0.25y? is 0.25

Coefficient of m in -25m is -25

Coefficient of xy in 7x2y is 7

It is the number part of the terms that multiply a variable or powers

of a variable . In simple terms, it is the number before a variable in
an expression

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What is a Monomial?

An algebraic expression which consists of one non-zero term only is
called a monomial.

Examples of a monomial: x, 10ab?, 5m?n, -16b?

What is a Binomial?

An algebraic expression which consists of two non-zero terms is
called a binomial.

Examples of a binomial: m + n, a? + 3b, 5x3 - 9y?, 5m?n? + 1/7

What is a Trinomial?

An algebraic expression of three non-zero terms only is called a trinomial
Examples of a trinomial: x + y + z, 2a2 + 5a + 7, 5abc - Zab + 9ac

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6. (な Sa etutorworld" ALGEBRA
21 Learning by Design

What is a Polynomial?

An algebraic expression which consists of more than two terms is
called a polynomial.

Examples of polynomial: 2a + 5b, 3xy + 5x + 1, 3y4 + 2y3 + 7y? - 9y - 17

What should a polynomial not contain?
Polynomials should not contain any term whose degree is a negative

number and or a radical.

How can we identify a Polynomial?
(i) 3xy? is not, because the exponent is "-2" (exponents can only

0,12...)

(ii) 2/(x+2) is not, because dividing by a variable is not allowed

(iii) 1/x is not either

(iv) /x is not, because the variable has a radical sign or exponent is

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2
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ur) Learning by Design

What is difference between a polynomial and an algebraic expression?

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8. 6: 2 etutorworld” ALGEBRA
ar.) Learning by Design

How can we identify the Degree of an Algebraic Expression
or Polynomial?

The degree of the expression 2x? - 3x5 + 5x has the highest power
and hence the degree is

The degree of the expression 2x? - 3x + 5 has the highest power
and hence the degree is

The degree of the expression 2xy - 3a - 5b + 7 has the highest

power and hence the degree is
2x? - 3x5 + 5x5 :6
2x? - 3x+5 12
2xy - 3a - 5b+7 2

The degree of the polynomial is the greatest of the exponents
(powers) of ¡ts various terms. If there are two variables together,
we add the powers and consider the degree.

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ES

What are Like terms?
x? and -5x?, 3x4 and -9x*, 6xy and 13xy

Two or more terms are called like terms if they have same variable
with same power

What are Unlike terms?

Two or more terms are called unlike terms if they have one of the
following:

(i) same variable with different power : x? and 3x

(ii) different variable with same power : y? and x
(iii) different variable with different power : a3 and b?

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10. fs ALGEBRA

“2.4 etutorworld”
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aq

What are Factors of an Algebraic Expression?

Example:

The factors of 4m? is

The factors of 270° is
The factors of 10p? is

The factors of 60m?n*yis2x2x3x5xmxmxnxnxnxy.

The letter and/or numbers multiplied together are factors of the term.

Standard form of expression
Example: 3x? - 7 + 4x3 + x® is written in standard form as

x + 4x3 + 3x? - 7
A way of writing a polynomial with terms having highest degree first,

then next degree and so on and constant in the last.

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Evaluating Algebraic expressions

(i) The value of the expression x? - 6xy + 9y? when x = 2 and
y = -1 is (2)? - 6(2)(-1) + 9-1)? = 4 + 12 + 9 = 25

(ii) The value of the expression (6 + h? - j) + 2 when h = 6 and
j= 4 is [6+ (6)?-4)+2=38+2=19

To evaluate an algebraic expression means to replace(substitute) the
variables in the expression with numeric values that are assigned to
them and perform operations in the expression.

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12. Ed etutorworld" ALGEBRA
ベッ /) Learning by Design

How can you convert a word phrase into an algebraic
expression?

Phrases used:

Addition : added to, sum, total, more than, increased by
Subtraction : subtracted from, take away, less than, decreased by,
difference

Multiplication : multiplied by, product of, times

Division : Divided by, quotient of

Examples:

(i) The equivalent algebraic expression for "6 less than 3 times a
number" is

(ii) The equivalent word phrase for "4p/5 + 3h/5 + 8" is

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What is a Simple/Linear equation?

Simple equation is an equation in which two algebraic expressions are

made equal to each other. The degree of the expression is always 1

Examples of Linear Equation:

Solve forx:
2x-19=5

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14. 700 etutorworld" CLASS VI - ALGEBRA
アガ Learning by Design

A
Practice questions

1) Coefficient of x in 25 x is
a) 5 b)25 c)0125 d)0.25

Mathematical reasoning

2) The equation representing the statement "The quotient of

fifty and
five more than a number is ten” is
a) 50 + 5/n = 10 b) 50/(n + 5) = 10
c) n= 50/5 + 10 d) 50 + n/5 = 10 Mathematical reasoning

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3) The value of the expression 7c + 2(-5f - 3) when f = -4 and
c=6

a) 19 b) 1 c) 34 d) 76

Mathematical reasoning

4) The value of m in the equation 16(m + 7) = 144 is
a) 2 b)1 c) 0 d) 3

Mathematical reasoning

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16. ~ etutorworld” CLASS VI - ALGEBRA

5) When Alex multiplies a certain number by 15 and
subtracts 4 from the product, he gets 326. Find the number,
a) 14 b) 15 c) 22 0) 60

Logical reasoning

6) 24a - [3(3a - 3) - 4(5a)] - 9 is equal to ?
a) 0 b) 1 c) 20a d) 35a

Mathematical reasoning

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17. CLASS VI - ALGEBRA

6: 2 etutorworld”
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7) I had Rs. 100. I gave Rs y to Abhishek, Rs y/2 to Praveen
and I am left with Rs. 55. How much did I give to Praveen?

a) Rs. 15 b) Rs. 35 c) Rs. 45 d) Rs. 55
Everyday Mathematics

8) The measure of second side of a triangle is twice the
first side and the third side of the triangle is thrice the
second side. The perimeter of the triangle is 72 cm. What is
the measure of the third side?

a) 20 b) 16 c) 48 d) 8 Logical reasoning

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18. a} etutorworid" CLASS VI - ALGEBRA
ar) Learning by Design

9) Ages of two persons are in the ratio 5: 2. If the sum of

their ages is 49, then their ages are respectively

a) 25 and 24 b)35and14 c)30.and 29 d) 31 and 18

Everyday Mathematics

10) Sum of three consecutive numbers is 126. Find the greatest
number
a) 41 b) 44 c) 42 d) 43

Logical reasoning

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11) State which one of the following given in the brackets is a
solution to the given equation
a) 2n+ 12 = 19(n= 1) b) 4p - 3 = 13(p = -4)
c) 7n - 5 = -19(n = -2) d) 4p - 3 = 13(p = 0)

Mathematical reasoning

12) Find the measurement of the smallest angle

a) 45 b) 30 c) 20 d) 35

Logical reasoning

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20. Erd etutorworld” TSR SE ALS
ur) Learning by Design
13) Hardeep thinks of a number. If she adds 19 to it and divides
the sum by 5, she will get 8. What is the number?
a) 21 b) 33 c) 38 d) 42

Logical reasoning

14) Mr. Surendar sells mangoes in two types of boxes, one

small and one large. A large box contains as many as 8 small
boxes plus 4 loose mangoes. If the number of mangoes ina
large box is 100, how many mangoes are there in small box?
a) 6 b)8 c) 10 d) 12

Achiever's section

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21. “4 etutorworld" CLASS VI - ALGEBRA
2) Learning by Design

Explanation on examples (for tutors only)
Variables : all letters like x, y, a, z, m
Constants : all numbers like 3, -6, 14, 23, 100
Algebraic expression : x?, 2y?, 3x? - 5, 4xy + 7

Term : 5y has one term, 5x + 3y has two terms, 3x? - Zab + 2e/1
has three terms and so on

Coefficient :

Coefficient of x? in 3x? is 3
Coefficient of y? in 0.25y? is 0.9
Coefficient of m in -25m is -25
Coefficient of x?y in 7x?y is 7

Monomials : x, 10ab?, 5m?n, -16b3

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Explanation on examples (for tutors only)
Binomials : m + n, a? + 3b, 5x3 - 9y?, 5m?2n? + 1/7
Trinomials : x + y +z, 202 + 50 + 7, 5abc - Zab + 900
Polynomial : 2a + 5b, 3xy + 5x + 1, 3y4 + 2y3 + 7y? - 9y - 17

Polynomial should not contain the following :

Polynomials should not contain negative power and radicals

(i) 3xy is not, because the exponent is "-2" (exponents can only 0,1,2,...)
(ii) 2/(x+2) is not, because dividing by a variable is not allowed

(iii) 1/x is not either

(iv) /x is not, because the variable has a radical sign or exponent is "3"

Degree of the expression for the following expressions :
ax? - 3x5 + 5x6 :6
2x? - 3x+5 :2
2xy-3a-5b+7 :2

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23. (な Sa etutorworld" AL6EBRA
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a
Explanation on examples (for tutors only)

Like terms : x? and -5x?, 3x* and -9x*, 6xy and 13xy

Unlike terms :

(i) same variable with different power : x? and 3x

(ii) different variable with same power : y* and x*

(iii) different variable with different power : a? and bz

Factors of the term :
The factors of 60m2n3y is2x2x3x5xmxmxnxnxnxy

Standard form of expression 3x? - 7 + 4x3 + x® is xó + 4x3+ 3x? - 7

Evaluating algebraic expressions :

The value of the expression x? - 6xy + 9y? when x = 2 and y = -1
is (2)? - 6(2)(-1) + 9-1)? = + 12 + 9 = 25

The value of the expression (6 + hz - j) = 2 when h = 6 and j = 4
is [6 + (6)? - 4) = 2 = 38 - 2 = 19

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“ar,
Explanation on examples (for tutors only)

Converting word phrase into algebraic expression:

(i) The equivalent algebraic expression for "6 less than 3 times a number"
3x - 6

(ii) The equivalent word phrase for “4p/5 + 3h/5 + 8" is

The sum of four fifth of p, three fifth of h and 8

CLASS VI - ALGEBRA

Simple Linear equation :
2x-19=5

Add 19 to both sides, we get
2x-19+19=5+19

2x=24

Divide by 2 on both sides, we get
x=12

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