C. Maths - 9 (1st Term Model).doc

BOUDDHA MERIDIAN SCHOOL

FIRST TERMINAL MODEL QUESTION – 2016/17

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

Time: 3 hours P.M.: 40

Group ‘A’ [9  (2 + 2) = 36]

1. a) A company gives 10% bonus equally to its 40 workers from the net profit of last year. If the net profit of the last year was Rs. 4,50,000, find the bonus received by each worker.

b) At 5 % commission, an agent received Rs. 32500 by selling a second hand car, at what price did he sell the car?

2 a) A shopkeeper purchased an electric fan for Rs. 1560 and sold it at 5 % profit. Find his actual profit and selling price of the fan.

b) A retailer sold a camera for Rs. 28,500 and had a loss of 5%. Find the cost price of the camera.

3. a) A mobile set is sold for Rs. 6,630 after a discount of 15%. Find the marked price of the mobile set.

b) The price of an article is Rs. 1200 and a customer pays Rs. 1380 with VAT. Find the rate of VAT.

4. Factorize:

a) a2 _{+ c}2 _{– 2ca – 9b}2

b) 5x2 _{– 16xy – 21y}2

5. Factorize:

a) x4 _{+ x}2 ₊₁

b) x3_{y – 64y}4

6. a) Simplify:

b) Simplify: –

7. a) Factorize: 3x6 _{– 79x}3 _{– 54}

b) If p, 2p and 30 are the angles of a triangle, find the unknown sizes of the angles of the triangle.

8. a) Find the value of a and b from the given figure:

b) Identify and name the greatest and the smallest angles of the following triangle:

9. a) Find the value of x, y and z from the given ∆ABC where AB = AC

b) In the figure alongside, PQ = PR, PS  QR, write down the relation between QS and SR, and

QPS and RPS.

Group ‘B’ [16  4 = 64]

10.A fruit seller bought 50 kg of fruits. He sold 30 kg of fruits for the cost price of 35 kg of fruits and he sold the remaining quantity for the cost price of 16 kg of fruits. Calculate his profit or loss percent in the total transaction.

12.The marked price of a table fan is Rs. 1,400 and 10% discount is allowed on it. Find its cost with 15% VAT.

13.After getting 10 % discount a customer paid Rs. 2034 with 13 % VAT to buy a bag from a retailer. Find the marked price of the bag.

14.An insurance company offered 1 % commission for the first 10 lakh and 1.5% for the rest sum of money collected from new clients by agents. If an agent is able to collect a sum of Rs. 12,64,000 from his new clients, find his total commission.

15.The yearly income of a man is Rs. 1,50,000. The tax free allowances is Rs. 1,00,000. If the tax for the first Rs. 20,000 is 12% and for the remaining is 15%, find how much tax he should pay in a year.

16.Find the H.C.F. of:

(a – b)2_{, a}3 _{– b}3_{, a}2 _{+ ab – 2b}2

17.Find the L.C.M. of:

24x4 _{+ 3x, 2x}2 _{– x – 1, 4x}2 _{– 1}

18.Simplify: + +

19.Simplify: + +

20.Prove that the sum of angles of a triangle is equal to two right angles.

21.In the given figure, find the sizes of x, y and

z.

22.Prove that the bisector of vertical angle of an isosceles triangle is perpendicular bisector of the base.

23.In the given figure, PQ // SR and PS // QR. Prove that PQR PRS. Also show that PQ = RS and PS = QR.

24.In the given figure, PQ = PR, QS = TR and SPT = 30. Prove that

PST is an isosceles triangle and calculate the size of PST.

25.Construct a rectangle PQRS in which diagonals PR = QS= 6 cm and they bisect each other making an angle of 60̊.

Marking Schemes

Group ‘A’ [9  (2 + 2) = 36] 1. a) Total bonus distributed = 10% of Rs. 450000

= Rs. 45000  [1]

Bonus received by each worker =

= Rs. 1125  [1] b) Let S.P. of car be Rs. x.

 5% of Rs. x = Rs. 32500  [1]

x = 6,50,000  [1]

2. a) Profit = 5% of Rs. 1560

= Rs. 78  [1]

S.P. = C.P. + Profit

= Rs. 1638  [1]

b) C.P. =  [1]

=

= Rs. 30000  [1]

3. a) Let M.P. be Rs. x.

 Discount = 15% of Rs. x

= Rs. 0.15x  [1]

S.P. = M.P. – Discount or, 6630 = x – 0.15x

 x = 7800  [1]

b) Vat amount = Rs. (1380 – 1200) = Rs. 180

 Rate of VAT =  100%

=  100%  [1]

= 15%  [1]

4. a) a2 _{+ c}2 _{– 2ca – 9b}2

= (a – c)2 _{– (3b)}2 _{ [1]}

= (a – c + 3b) (a – c + 3b)  [1]

b) 5x2 _{– 16xy – 21y}2

= 5x2 _{– 21xy + 5xy – 21y}2 _{ [1]}

= x (5x – 21y) + y (5x – 21y)

= (5x – 21y) (x + y)  [1]

5. a) x4 _{+ x}2 ₊₁

= (x2₎2 _{+ 1}2 _{+ x}2

= (x2 _{+ 1)}2 _{– 2x}2 _{+ x}2 _{ [1]}

= (x2 _{+ 1)}2 _{– x}2

= (x2 _{+ 1 + x) (x}2 _{+ 1 – x)}

= (x2 _{+ x + 1) (x}2 _{– x + 1)  [1]}

b) xy (x3 _{– 64y}3₎

= xy {(x)3 _{– (4y)}3_{}  [1]}

= xy (x – 4y) (x2 _{+ 4xy + 16y}2_{)  [1]}

6. a)

=

=  [1]

=

=  [1]

b) –

=  [1]

= = = =

=  [1]

= 3x6 _{– 81x}3 _{+ 2x}3 _{– 54}

= 3x3 _(x3 _{– 27) + 2 (x}3 _{– 27)}

= (x3 _{– 27) (3x}3 _{+ 2)  [1]}

= (x3 _{– 3}3_{) (3x}3 _{+ 2)}

= (x – 3) (x2 _{+ 3x + 9) (3x}3 _{+ 2)  [1]}

b) p + 2p + 30 = 180

or, 3p = 180 – 30

or, 3p = 150

or, p =

 p = 50  [1]

And

2p = 2  50

= 100  [1]

8. a) a + 60 + 75 = 180

 a = 45  [1]

b + 60 = 180

 b = 120  [1]

b) Greatest angle = ABC  [1]

Smallest angle = ACB  [1]

9. a) x + 110 = 180

x = 70

y = x = 70  [1]

x + y + z = 180

 z = 40  [1]

b) The required relations are:

QS = SR  [1]

QPS = RPS  [1]

Group ‘B’ [16  4 = 64] 10.Let, C.P. of 1 kg fruits = Rs. x

Then C.P. of 50 kg fruits = Rs. 50x C.P. of 35 kg fruits = Rs. 35x

C.P. of 16 kg fruits = Rs. 16x  [1]

Now, by question

S.P. of 50 kg fruits = Rs. (35x + 16x)

= Rs. 51x  [1]

Since, S.P. > C.P., there is a profit.

 Profit = S.P. – C.P. = Rs. 51x – Rs. 50x

= Rs. x  [1]

 Profit percent =  100% =  100%

= 2%  [1]

11.For finding C.P. = Rs. 8360  [2]

For finding profit = Rs. 360  [1]

For finding profit percent = 4.5%  [1]

12.For finding discount amount = Rs. 140  [1]

S.P. = Rs. 1260  [1]

VAT amount = Rs. 189  [1]

S.P. with VAT = Rs. 1449  [1]

13.Let, M.P. = Rs. x Discount = Rs.

S.P. = Rs.  [1]

S.P. with VAT = Rs. + Rs.

Rs. 2034 =  [1]

 x = Rs. 2000

 M.P. = Rs. 2000  [1]

14.Writing given information correctly  [1]

Commission for first 10 lakh = Rs. 10000  [1]

Commission for rest sum of money = Rs. 3960  [1]

Total commission = Rs. 13960  [1]

15.Taxable income = Rs. 1,50,000 – Rs. 1,00,000

= Rs. 50,000  [1]

Income tax for first Rs. 20,000 = Rs. 2400  [1]

Income tax for rest = Rs. 4500  [1]

Total income tax = Rs. 6900  [1]

16.1st _{expression = (a – b) (a – b)  [1]}

2nd _{expression = (a – b) (a}2 _{+ ab + b}2_{)  [1]}

3rd _{expression = (a – b) (a + 2b)  [1]}

 H.C.F. = (a – b)  [1] 17.1st _{expression = 3x (2x + 1) (4x}2 _{– 2x + 1)  [1]}

2nd _{expression = (x – 1) (2x + 1)  [1]}

3rd _{expression = (2x + 1) (2x – 1)  [1]}

 L.C.M. = 3x (2x + 1) (x – 1) (2x – 1) (4x2 _{– 2x + 1)  [1]}

18. + +

= + + [1]

= + +

= [1]

= [1]

= 1 [1]

19. + +

= – –  [1]

=  [1]

=  [1]

=  [1]

20.For correct Figure, Given,

To prove and construction  [1] AXB = ABC

YAC = ACB  [1] XAB + BAC + YAC = 180  [1] ABC + BAC + ACB = 180

= 2 right angles  [1]

21.x = 75  [1]

BAC = 75  [1]

y = 75  [1]

z = 30  [1]

22.For correct Figure, Given, and

To prove  [1]

ABD ACD  [1]

ADB = ADC

AD  BC  [1]

BD = DC

AD is the perpendicular bisector of BC  [1]

23.PQR PRS  [2]

PS = QR  [1]

24.PQS PTR  [2]

PST is an isosceles triangle.  [1]

PST = 75  [1]

25.

Drawing PR = 6 cm and POS = 60  [1]

Taking 'S' and 'Q' points correctly  [1]

Joining consecutive points properly  [1]

Correct conclusion  [1]