Question 1:

Get the algebraic expressions in the following cases using variables, constants and arithmetic operations:

(i) Subtraction of z from y.

(ii) One-half of the sum of numbers x and y.

(iii) The number z multiplied by itself.

(iv) One-fourth of the product of numbers p and q.

(v) Numbers x and y both squared and added.

(vi) Number 5 added to three times the product of m and n.

(vii) Product of numbers y and z subtracted from 10.

(viii) Sum of numbers a and b subtracted from their product.

(i) Identify the terms and their factors in the following expressions, show the terms and factors by tree diagram:

(a) x – 3       

(b) 1 + x + x²        

(c) y – y³      

(d) 5xy² + 7x² y        

(e) –ab + 2b² – 3a²

(ii) Identify the terms and factors in the expressions given below:

(a) -4x + 5       

(b) -4x + 5y          

(c) 5y + 3y²            

(d) xy + 2x² y²         

(e) pq + q

(f) 1.2ab – 2.4b + 3.6a                 

(g)                

(h) 0.1p + 0.2q²

Identify the numerical coefficients of terms (other than constants) in the following expressions:

(i) 5 – 3t²         

(ii) 1 + t + t² + t³       

(iii) x + 2xy + 3y       

(iv) 100m + 1000n       

(v) –p² q² + 7pq          

 (vi) 1.2a + 0.8b          

(vii) 3.14r²           

(viii) 2(l + b)              

(ix) 0.1y + 0.01y²

(a) Identify terms which contain x and give the coefficient of x.

(i) y² x + y            

(ii) 13y² – 8xy            

(iii) x + y + 2        

(iv) 5 + z + zx           

(v) 1 + x + xy                 

(vi) 12xy² + 25            

(vii) 7x + xy²

(b) Identify terms which contain y² and give the coefficient of y².

(i) 8 - xy²  

(ii) 5y² + 7x  

(iii) 2x² y – 15 xy² + 7y³

Classify into monomials, binomials and trinomials:

(i) 4y – 7x           

(ii) y²          

(iii) x + y - xy         

(iv) 100          

(v) ab – a - b    

(vi) 5 – 3t          

(vii) 4p² q – 4pq²                      

(viii) 7mn       

(ix) z² – 3z + 8     

(x) a² + b²         

(xi) z² + z             

(xii) 1 + x + x²

State whether a given pair of terms is of like or unlike terms:

(i) 1, 100                     

(ii) -7x,                  

(iii) -29x, -29y             

(iv) 14xy, 42yx    

 (v) 4m² p, 4mp²       

(vi) 12xz, 12x² z²

Question 7:

Identify like terms in the following:

(a) –xy², -4yx², 8x², 2xy², 7y, -11x², -100x, -11yx, 20x² y, -6x², y, 2xy, 3x

(b) 10pq, 7p, 8q, -p²q², -7pq, -100q, -23, 12q²p², -5p², 41, 2405p, 78qp, 13p²q, qp², 701p²

Simplify combining like terms:

(i) 21b – 32 + 7b – 20b

(ii) –z² + 13z² – 5x + 7z³ – 15z

(iii) p – (p - q) – q – (q - p)

(iv) 3a – 2b – ab – (a – b + ab) + 3ab + b - a

(v) 5x² y – 5x² + 3yx² – 3y² + x² – y² + 8xy² – 3y²

(vi) (3y² + 5y - 4) – (8y – y² - 4)

Simplify combining like terms:

(i) 21b – 32 + 7b – 20b

(ii) –z² + 13z² – 5x + 7z³ – 15z

(iii) p – (p - q) – q – (q - p)

(iv) 3a – 2b – ab – (a – b + ab) + 3ab + b - a

(v) 5x² y – 5x² + 3yx² – 3y² + x² – y² + 8xy² – 3y²

(vi) (3y² + 5y - 4) – (8y – y² - 4)

Subtract:

(i) -5y² from y²

(ii) 6xy from -12xy

(iii) (a - b) from (a + b)

(iv) a(b - 5) from b(5 - a)

(v) –m² + 5mn from 4m² – 3mn + 8

(vi) –x² + 10x – 5 from 5x - 10

(vii) 5a² – 7ab + 5b² from 3ab – 2a² – 2b²

(viii) 4pq – 5q² – 3p² from 5p² + 3p² - pq
 

(a) What should be added to x² + xy + y² to obtain 2x² + 3xy?

(b) What should be subtracted from 2a + 8b + 10 to get -3a + 7b + 16?

What should be taken away from 3x² – 4y² + 5xy + 20 to obtain –x² – y² + 6xy + 20?

(a) From the sum of 3x – y + 11 and – y – 11, subtract 3x – y - 11

(b) From the sum of 4 + 3x and 5 – x + 2x², subtract the sum of 3x² – 5y and –x² + 2x + 5

If m = 2, find the value of:

(i) m – 2          

(ii) 3m – 5        

(iii) 9 – 5m        

(iv) 3m² – 2m - 7           

(v)  – 4

If p = -2, find the value of

(i) 4p + 7                         

(ii) -3p² + 4p + 7                    

(iii) -2p³ – 3p² + 4p + 7

Find the value of the following expressions, when x = -1:

(i) 2x - 7            

(ii) –x + 2              

(iii) x² + 2x + 1                

(iv) 2x² – x - 2  

If a = 2, b = -2, find the value of:

(i) a² + b²                    

(ii) a² + ab + b²                  

(iii) a² – b²      

When a = 0, b = -1, find the value of the given expressions:

(i) 2a + 2b           

(ii) 2a² + b² + 1         

(iii) 2a² b + 2ab² + ab        

(iv) a² + ab + 2      

Simplify the expressions and find the value if x is equal to 2:

(i) x + 7 + 4(x - 5)                

(ii) 3(x + 2) + 5x – 7                 

(iii) 6x + 5(x - 2)            

(iv) 4(2x - 1) + 3x + 11

Simplify these expressions and find their values if x = 3, a = -1, b = -2

(i) 3x – 5 – x + 9                   

(ii) 2 – 8x + 4x + 4           

(iii) 3a + 5 – 8a + 1       

(iv) 10 – 3b – 4 – 5b            

(v) 2a – 2b – 4 – 5 + a

(i) If z = 10, find the value of z³ – 3(z - 10).

(ii) If p = -10, find the value of p² – 2p – 100.   

What should be the value of a if the value of 2x² + x – a equals to 5 when x = 0?

Given, 2x² + x – a = 5

=> 2 * 0² + 0 – a = 5               [Put x = 0]

=> 0 + 0 – a = 5

=> -a = -5

=> a = -5                      [Multiply by (-) sign]                     

 

Observe the patterns of digits made from line segments of equal length.

You will find such segmented digits on the display of electronic watches or calculators.

            

If the number of digits formed is taken to be n, the number of segments required to form n digits is given by

the algebraic expression appearing on the right of each pattern. How many segments are required to form

5, 10, 100 digits of the kind .

Use the given algebraic expression to complete the table of number patterns: