mathematics

class VII

#### Key Concepts

Constants, variables, coefficients, monomials, binomials, trinomials, polynomials, factors, constant terms, operations of algebraic expressions

#### essential questions

1.How is thinking algebraically different from thinking arithmetically?
2. How do I use algebraic expressions to analyze or solve problems?
3. How do the properties contribute to algebraic understanding?
4.What is meant by equality?
5. How can we generate equivalent expressions?
6. How can we create expressions for given situations, using rational numbers?
7. How can we use properties to write equivalent expressions?
8. What does it mean to evaluate algebraic expressions?
9. How can we collect and combine rational number like terms?

#### Remembering:

1. How many terms are there in the expression 1.2ab – 2.4 b +3.6a : a) 1  b) 2  c) 3  d) 4
2. What is the co-efficient of x in the expression y² x  + y : a) y²  b) y   c)1   d) 0
3. Which of the following pairs of terms is a pair of unlike terms: a) 3x, 2 xy    b) -xy² , -2xy²  c) -6x², 20 x²y  d) 8x², 7y
4. Which of the following pairs of terms is a pair of unlike terms: a) -p² q² , 12 q² p²   b) 41, 100  c)qp² , 13 p² q  d) -4yx² ,- 4 xy²
5. A term of an expression having no literal factor is called a____ a) monomial  b) binomial  c) trinomial d) variable
6. What is the degree of the polynomial 9xy – 12x²y +5 -2x² y³: a) 1   b)2   c) 5   d) 3
7. Number of terms in the expression 3x² y – 2y² z – z²x +5 is : a) 2  b) 3  c) 4  d) 5
8. The term of the expression 4x² -3xy are: a) 4x² and -3xy  b)4x² and 3 xy  c) 4x² and – xy  d) x² and xy
9. Co-efficient of x in -9xy²z is: a) 9yz  b) -9yz  c) 9 y²z  d) -9y²z
10. Which of the following is a pair of like terms:  a) -7xy²z , -7 x²yz   b) -10 xyz² , 3 xyz²   c) 3xyz, 3x²y²z²             d) 4 xyz² , 4x²yz
11. Identify the binomial out of the following: a) 3xy ² + 5y – x²y   b) x²y – 5y -x²y  c) xy +yz +zx  d) 3xy² + 5y – xy²

#### understanding:

1. What is the sum of a + b- 1, b-a +1 and 1- 2 b? a) 1  b) -1  c) 2  d) -2
2. Simplify: p + (q-p) + q + (p-q)  a) p   b) q  c) p + q  d) p- q
3. The sum of  x4 – xy +2y ² and x4+ xy +2y2 : a) Monomial and polynomial   b) Binomial and Polynomial  c) Trinomial and Polynomial  d) Monomial and Polynomial
4. Factors of -5x²y² z are : a) -5 × x × y × z  b) -5 × x² × y× z   c) -5 × x × x × y× y× z   d) -5 × x × y × z²
5. 123x²y – 138x²y is a like term of: a) 10xy   b) -15xy  c) -15xy²   d) 10x²y

#### Application:

1. What should be added to x² +3 x y + y²  to get x² + y²: a) 2 x y  b) -2xy  c) 3xy  d) -3xy
2. What should be subtracted from 1 to get 1-x +2 x²: a) 2x² – 1  b) x-2x²  c) 1-x  d) 1+x
3. What should be added to x-y to get 2x: a) y   b) x  c) x + y  d) x-y
4. The subtraction of 5 times of y from x is a) 5x -y   b) y-5x   c) x-5y  d) 5y-x
5. -b -0 is equal to: a) -1× b    b) 1-b-0   c) 0 – (-1) × b  d) -b- 0- 1
6. The side length of the top of square table is x. The expression for perimeter a) 4+ x  b) 2x  c) 4x  d) 8x
7. The number of scarfs of length half meter that can be made from y meters of cloth is: a) 2 y  b) y/2   c) y+2  d) y+1/2
8.  The value of 3 x² -5x +3 when x=1 is a) 1  b) 0    c) -1  d) 11
9. The expression for the number of diagonals that we can make from one vertex of a n sided polygon is: a) 2n+1   b) n-2   c) 5n+2  d) n-3
10. The length of a side of square is given as 2x+ 3. Which expression represents the perimeter of the square: a) 2x+ 16    b) 6x+ 9  c) 8x+ 3  d) 8x+12
11. Find the values of the following polynomials at a = -2  and b=3

a) a² +2ab +b²

b) a² – 2ab + b²

c) a³ + 3a²b +b³

d) a³ – 3a²b +3 ab²- b³

e) a² + b²/ 3

f) a² – b²/3

g) a/b + b/a

f) a² +b² – ab -b² -a²

#### Analysis:

1. Each symbol given below represents an algebraic expressions: Δ= 2x² +3y    Ο= 5x² +3x  ◊= 8 y² -3x² +2x +3y The symbols are then represented in the expression: Δ + Ο =◊  Find the expression which is represented by the above symbols.
2. Arjun bought a rectangular plot with the length x and breadth y and then sold a triangular part of it whose base is y and height is z. Find the area of the remaining plot.
3. Sonu and Raj have to collect different kinds of leaves. They go to a park where Sonu collects 12 leaves and Raj collects 2 x leaves. Write the algebraic expression to find the total number of leaves collected by both of them.
4. A school has a rectangular play ground with length x and breadth y and a square lawn with side x as shown in the figure given below. What is the the total perimeter of both of them combined together?
5. The sum of first n natural numbers is given by ½n² +½ n. Find : a) The sum of first 5 natural numbers  b) The sum of first 11 natural numbers  c) The sum of natural numbers from 11 to 30
6. The sum o squares of first n natural numbers is given by 1/6 n (n+1) (2n+1) or 1/6 (2n³ +3n²+n). Find the sum of squares of the first 10 natural numbers.
7. The sum of multiplication table of natural number ‘n’ is given by 55× n. Find the sum of: a) Table of 7  b) Table of 10  c) Table of 19

#### Evaluation:

1. Write the two different algebraic expressions for the word phrase ” (1/4) of the sum of x and 7.” What the error? a student wrote an algebraic expression for  ” 5 less than a number n divided by 3″ as n/3 -5. What error did the students make?
2. Write an expression for the sum of 1 and twice a number n. If you let n be any odd number, will the result away be an odd number?
3. Will the value of 11x for x = -5 be greater than 11 or less than11? Explain