C. Maths - 8 (1st Term Model).doc

BOUDDHA MERIDIAN

SCHOOL

FIRST TERMINAL MODEL QUESTION – 2016/17

Class: VIII Subject: C. Maths F.M.: 100

Time: 3 hours P.M.: 40

Group ‘A’ [5  (1 + 1) = 10]

1. a) Write the alternate angle of GHD from given figure.

b) Find the value of xo _{in the given}

figure.

2. a) Define complementary angles.

b) Write the degree of x2_y3 _{+ 2xyz + 8.}

3. a) How many subsets can be formed from the given set A = {a, b, c}.

b) Write the set notation of the given figure.

4. a) Rationalize the denominator of .

b) Express 0.0000003 in scientific notation.

5. a) Find the product of (2a + 3b)  (2a – 3b)

b) Factorized form of a2_b2 _{is ______________.}

Group ‘B’ [17  2 = 34] 6. a) Simplify: 46 − {28 − (15 + 3)} ÷ 2

b) Find AB, if A = {a ,e, i, o, u} and B = {a, b, c, d, e}.

c) Find the cube of .

7. a) If x = 2, y = 3 then find the value of x2 _{– 3xy + 2y}2_.

b) Find the product of (4a2 _{+ 2a + 1) and (2a – 1).}

c) If a + = 7, find the value of a2 _{+ .}

8. a) Simplify: 

b) Rationalize the denominator and simplify:

c) Resolve into factors: x2 _{+ 8x +15}

9. a) Simplify:

b) Evaluate:

c) Simplify and write the result in scientific notation:

(5 × 104_{) × (9 × 10}6₎

10. a) Convert 3067 into quinary numerals.

b) Convert 111011012 into decimal number system.

c) Add:1012 + 1102

11. a) Find the value of x and y from given figure.

b) Find thevalue of a and b from adjoining figure.

Group ‘C’ [14  4 = 56] 12.Expand: (a + b + c)2

13.If (x + y)2 _{= 6 and xy = 2, find the value of x}3 _{+ y}3_.

14.Find the total cost of 4 pens at Rs. 20 each, 5 pencils at Rs. 15 each

and 3 geometry boxes at Rs. 55 each, making the mathematical expression.

15.Simplify: 5x – 3[2a + 5{4x + 3(3a – 2x)}]

16.Simplify: 

17.If a = – 3, b = 2, c = 1, find the value of  (ab3_c2₎2_{ 2a}2_bc

18.Simplify: 2– 3+ –

19.If U = {natural numbers less than 11}, A = {First four prime numbers},

B = {First five odd numbers}, find A ( B and A ( B. Show the relation

of U, A and B in the Venn diagram.

20.Simplify: 9– 10– 11+ 2

21.Convert 33215 into binary numeration.

22.Factorise:

a) x3 _{+ 15x}2 _{+ 56x b) a}3 _{– 8}

23. Simplify: (x + y)2 _{– (x – y)}2

24.Find the value of p, q, x and y from adjoining figure:

25.From the given figure, find the value of x,

y and z:

***THE END***

Marking

Schemes

Group ‘A’ [5  (1 + 1) = 10]

1. a) Write the alternate angle of GHD from given figure. Ans: AGH...1

b) Find the value of x in the given figure.

x+1200₌₁₈₀

x = 600_...1

2. a) Define complementary angles.

Any two angles whose sum is equal to 1800_...1

b) Write the degree of x2_y3_{+ 2xyz +8.}

The degree of given polynomial is 5...1

3. a) How many subsets can be formed from the given set A={a, b, c}.

Ans: 8 ...1

b) Write the set notation of the given figure.

Ans: AUB...1 4. a) Rationalize the denominator of .

Ans: 2...1

b) Express 0.0000003 in scientific notation.

Ans: 3x10-7_...1

5. a) Find the product of (2a + 3b)  (2a – 3b)

Ans: 4a2_-9b2_...1

b) Factorized form of a2_b2 _{is (a+b) (a-b)...1}

Group ‘B’ [17  2 = 34]

6. a) Simplify: 46 − {28−(15+3)} ÷2 = 46 – {28-18}÷ 2...0.5 = 46 - 10÷2...0.5 = 46 – 5...0.5 =41...0.5

b) Find , if A={a ,e, i, o, u} and B={a, b, c, d, e}.

={ a, b, c, d, e , i, o, u}...2

= x3 _{+ 3x}2 _{+ 3x + ...1}

= x3 _{+ 6x+ ...1}

7. a) If x = 2, y = 3 then find the value of x2 _{– 3xy + 2y}2_.

= 22 _{-3x2 x3+ 2x 3}2

=4 -18 +18...1 = 4...1

b) Find the product of (4a2 _{+ 2a + 1) and (2a – 1).}

(2a – 1) (4a2 _{+ 2a + 1) = (8a}3 _{– 1)...1}

c) If a + = 7, find the value of a2 _{+ .}

For squaring both sides...0.5 Applying formula correctly...0.5 For correct value of a2 _{+ As 47...1}

8. a) Simplify: 

= 9x5 -16x2...1 = 45 -32...0.5 =13...0.5

b)

= x ...0.5

= ...0.5

= ...0.5

= ...0.5

c) Resolve into factors: x2 _{+ 8x +15}

= x2 _{+ 5x+3x +15...1}

= x(x+5) + 3(x+5)...0.5 = (x+5) (x+3)...0.5

9. a) Simplify:

For making 225 the square of 15, 4 the square of 2, 324 the square if 18 and 9 the square of 3...1

For calculating the result as 5/9...1

b) Evaluate.

= ...0.5

=( z6_{) ...0.5}

= ...0.5

= z2_{. ...0.5}

c) Simplify and write the result in scientific notation:

(5 × 104_{) × (9 × 10}6₎

=5× 9 ×104_×106

=45×1010...1

= 4.5 × 1011...1

10. a) Convert 3067 into quinary numerals.

For correct division by 5 and writing the remainder...1

For writing the correct quinary number as 442325...1

b) Convert 111011012 into decimal number system.

For correct distribution of binary numeral with 2 and their correct powers...1

For correct calculation as237...1

c) Add:1012 + 1102

Forcorrect addition as 10112...1

For x= 720 _{with correct reason as corresponding...1}

Y= 1080 _{as linear pair...1}

b) Find the value of a and b from adjoining figure. a= 800 _{co-interior angles...1}

b= 800 _{altermate angle...1}

Group ‘C’ [14  4 = 56] 12. Expand: (a+b+c)2 = (a+b)2 _{+2 (a+b) c + c}2_...2

=a2_+2ab+b2_+2ac+2bc+c2_...2

13.If (x + y)2 _{= 6 and xy = 2, find the value of x}3_{+ y}3 x3_+y3 _{= (x+y)}3 _{– 3xy (x+y)...2}

= 63 _{– 3x2 x6} = 216 - 36...1

= 180...1

14. Find the total cost of 4 pens at Rs. 20 each, 5 pencils at Rs. 15 each and 3 geometry boxes ar Rs. 55 each, making the mathematical expression. =4x20+ 5x15+ 3x55...2

= 80+ 75+ 165...1

= 320...1

15.Simplify: 5x – 3[2a + 5{4x + 3(3a – 2x)}] = 5x – 3[2a + 5{4x + 9a- 6x}]...1

= 5x – 3[2a + 5{9a- 2x}]...1

= 5x – 3[2a + 45a-10x] = 5x – 3[47a-10x]...1

= 5x –141a +30x =35x–141a ...1

16.Simplify:  = 17.If a = – 3, b = 2, c = 1, find the value of  (ab3_c2₎2_{ 2a}2_bc For substituting the value and calculating their power correctly...1

Cancelling the appropriate terms...1

Calculating the remaining number including sign...1

Calculating the final value as 1152...1

18.Simplify: 2– 3+ – Finding the appropriate squared number and rationalizing the denominator...1+1 Collecting the like terms and calculating...1

Finding the final value as ...1

19.If U= {natural numbers less than 11}, A={First four prime numbers}, B={First five odd numbers}, find and . Show the relation of U , A and B in the Venn diagram. U= {1, 2, 3, ...,10},

A={2,3,5,7} & B={1,3,5,7,9} ...1

...1

For finding For correct Venn diagram ...1

20.Simplify: 9– 10– 11+ 2 For finding the prime factors of given numbers correctly...2

Calculating the final answer as

21.Convert 33215 into binary numeration.

For converting the given number into decimal number correctly as

461...2

For converting the decimal number into binary by dividing it with 2 and with correct remainder...2

22. Factorise: a) x3 _{+ 15x}2 _{+ 56x.} = x(x2 _{+ 15x + 56)} = x(x2 _{+ 7x + 8x + 56)...1}

=x{x(x+7) +8(x+7)} = x (x+7) (x+8)...1

b) a3 _{– 8} = a3 _-23_...1

= (a-2) (a2 _{+2a +4)...1}

23. Simplify. (x+y)2 _{- (x-y)}2 =x2 _+2xy+y2_-(x2_-2xy+y2_)...1

= x2 _+2xy+y2_{- x}2_+2xy-y2_...1

=2xy+2xy...1

= 4xy...1

24.Find the value of p, q, x and y from adjoining figure. a= 400 _{with the reason angles at a point of a straight line...1}

p= 750 _{with the reason alternate angles...1}

x= 1150 _{Co-interior angles...1}

y= 1050 _{with the reason co-interior angles...1}

25.From the given figure, find the value of x, y and z. (PQ is drawn parallel to AB and CD) x=200 _{vertically opposite angles...1}

y= 450 _VOA... = 200 _{Corresponding angles...} b= 450 _{Corresponding angles} z=a+b=650_...2