PAF Chapter Comprehensive Paper Answer Key December 2015 Mathematics Class 7

The City School PAF Chapter Comprehensive Paper Answer Key December 2015 Mathematics Class 7 The City School / PAF Chapter/ Comprehensive Worksheet/ December 2015/ Mathematics / Class 7 /Ans Key Page 1 of 11

Section A Answer all questions. Q.1 Encircle the correct option. Choose only one option for each statement. [ /10] a) Round off 12.239 to the nearest hundredth. (i) 12 (ii) 12.2 (iii) 12.24 (iv) 12.23 b) Expression for thrice the difference of 13 and n: (i) 3 x 13 + n (ii) 13 + 3 x n (iii) 3 (13 n) (iv) - 12 c) Which of the following is NOT an equation? (i) 5 1 5 (ii) 4 + m (iii) 4 3 1 (iv) x 3 12 d) Express 7.4618 correct to 3 significant figures: (i) 7.352 (ii) 7.50 (iii) 7.47 (iv) 7.46 e) Area of a square of side 1.6 cm is: (i) 2.56 (ii) 25.6 (iii) 6.4 (iv) 6.36 f) If the perimeter of a rectangle is 28cm and its area is 48 then its dimensions are: (i) 24cm by 2cm (ii) 12cm by 4cm (iii) 16cm by 3cm (iv) 8cm by 6cm The City School / PAF Chapter/ Comprehensive Worksheet/ December 2015/ Mathematics / Class 7 /Ans Key Page 2 of 11

g) The next term of the sequence 0, 2, 2, 4,.. is: (i) 4 (ii) 6 (iii) 8 (iv) 10 h) -15xy + 7xy 3xy 2xy is equal to: (i) -27xy (ii) -13xy (iii) 17xy (iv) 10xy i) If x -5, and y 2, then the value of -3x + is: (i) -11 (ii) 17 (iii) -19 (iv) 19 j) Formula for perimeter of rectangle is: (i) Sum of all sides (ii) 2 ( l + b ) (iii) 2 ( l x b ) (iv) l x b Q.2 Fill in the blanks with correct answers. [ /10] a) A ribbon is 5m long and 3cm broad. The breadth in mm is 30 mm. b) The next two terms of the sequence 1,,,, are: and. c) On solving the equation 0.3d 1.8, the value of d will be 6. d) The value of x in the equation x + 9 37 is 28. e) The estimated value of 3.4 x 7.6 will be 24. f) If the perimeter of a square is 16cm, its area will be 16. g) A boy is x years old now. 5 years ago he was (x 5) years old. h) The diameter of a circle is 21 cm. its radius will be 10.5 cm. i) Two-fifth of 70 is 28. j) [ 9 (-3) ] 12. The City School / PAF Chapter/ Comprehensive Worksheet/ December 2015/ Mathematics / Class 7 /Ans Key Page 3 of 11

Q3. (a) Express: [ /06] (i) 5 as a decimal. : [ 5.75 ] (ii) 0.45 as fraction in its lowest term. : [ ] (iii) 7.398 to 2 decimal places. : [ 7.40 ] (b) Complete the sequence 7, 9, 13, 21, 37, 69, 133 [ /02] (c) Estimate correct to 1 significant figure: : [ 50 ] [ /02] Q4. (a) A square hall has an area of 324. Find the length of its sides. [ /03] Area 324 l 2x3x3 l l 18 Therefore, its sides are 18 m long. (b) Each side of the following pattern is 1 unit. Complete the given table. [ /04]. Pattern number 1 2 3 4 5 6.. 10 n Perimeter 4 8 12 16 20 24 40 4n (c) The area of a triangle is 56. Its height is 7cm. find its base. [ /03] Area x base x height 56 x b x 7 b b 16 cm The City School / PAF Chapter/ Comprehensive Worksheet/ December 2015/ Mathematics / Class 7 /Ans Key Page 4 of 11

Q5. (a) Insert parenthesis to make the following statements true: [ /02] (i) 88 64 35 23 12 (88 64) (35 23) 12 (ii) 100 25 15 x 2 + 3 50 100 (25 15) x (2 + 3) 50 (b) A bakery sells 8 chocolate cookies for Rs.12 and 5 vanilla cookies for Rs.8. Which type of cookies are cheaper to buy? [ /03] Price of 1 chocolate cookie Rs.1.5 Price of 1 vanilla cookie Rs.1.6 Therefore, chocolate cookies are cheaper. (c) Evaluate 5 3 x [ /03] x x x x x 1 (d) Solve the equation: 3 ( x 6 ) 8x - 13 [ /02] 3x 18 8x 13 3x 8x -13 + 18-5x +5 x x -1 The City School / PAF Chapter/ Comprehensive Worksheet/ December 2015/ Mathematics / Class 7 /Ans Key Page 5 of 11

Section - B Q6. (a) There is a crate containing 8 bottles of juice. The crate weighs 0.5 kg. if the total weight of the crate and bottles is 3.7kg, what is the weight of each bottle? [ /03] Crate + 8 bottles 3.7 kg Crate - 0.5 kg 8 bottles 3.2 kg 1 bottle 3.2 8 0.4 kg (b) Jim s mom bought 5 lemons at $0.25 each, kg of mutton at $8.36 per kg, and 2.5 litres of milk at $0.85 per litre. If she gave $50 bill to the shopkeeper, how much change will she receive? [ /04] Lemons: 5 x 0.25 $1.25 Mutton: x 8.36 $4.18 Milk: 2.5 x (2 x 0.85) $4.25 Total $9.68 50 9.68 40.32 Therefore, she will receive $40.32 as change. (c) Solve the equation: - 4 + 4 [ /03] - 4 + 4 8 8x 8 x 21 x x 21 The City School / PAF Chapter/ Comprehensive Worksheet/ December 2015/ Mathematics / Class 7 /Ans Key Page 6 of 11

Q7. (a) Estimate the values and give your answer correct to two significant figures: [ /03] 5.0 (b) Evaluate: (i) [ 42 x 12 + 125 25 (385 217)] x 6 [ /04] [ 42 x 12 + 125 25 168] x 6 [ 42 x 12 + 5 168] x 6 [ 504 + 5 168] x 6 [ 509 168] x 6 341 x 6 2046 (ii) 2 x + 28-7 [ /03] 10 The City School / PAF Chapter/ Comprehensive Worksheet/ December 2015/ Mathematics / Class 7 /Ans Key Page 7 of 11

Q8. (a) The product of two numbers is. If one of them is, find their sum. Let the other number be x. Hence, according to the given situation: [ /04] x x 9 x 5 x Therefore, sum of the numbers: + 1 (b) A school-garden measuring 10m by 12m has a path 1m wide around it. Find the area of the path. [ /04] 12m 1m 10m 1m Garden: Area l x b 12 x 10 120 Garden + path: Area l x b (12+1+1) x (10+1+1) 14 x 12 168 Path: Area 168 120 48 The City School / PAF Chapter/ Comprehensive Worksheet/ December 2015/ Mathematics / Class 7 /Ans Key Page 8 of 11

(c) If S (u + v) t, find the value of v when u 4, t 16 and s 48. [ /02] 48 (4 + v) x 16 48 (4 + v) x 8 48 32 + 8v 48 32 8v 16 8v v Q9. (a) Express: [ /04] (i) 2.65 in. (ii) 975? 0.0975 The City School / PAF Chapter/ Comprehensive Worksheet/ December 2015/ Mathematics / Class 7 /Ans Key Page 9 of 11

(b) Find area of the given figure: [ /04] Area of rectangle l x b 28 x 14 392 c Area of bigger semi-circle x 22 x 14 308 c Area of smaller semi-circle x 11 x 7 77 c Total area 392 + 308 + 77 777 c Q10. (a) The wheel of a machine has a radius of 21 cm. (i) How much distance will the wheel cover in 1 rotation? (ii) How much distance will the wheel cover in 5 rotations? [ Take π ] [ /03] (i) 1 rotation Circumference of the circle Circumference 2 π r 2 x x 21 2 x 22 x 3 132 cm (ii) 132 x 5 660 cm The City School / PAF Chapter/ Comprehensive Worksheet/ December 2015/ Mathematics / Class 7 /Ans Key Page 10 of 11

(b) Solve: + + [ /03] 1 (c) A trapezium of area 105 has parallel sides of length 5cm and 9 cm. how far apart are the parallel lines? [ /04] Area of Trapezium x height x sum of length of parallel lines 105 x h x (5 + 9) 105 x h x 14 105 7h h 15 Therefore, the parallel lines are 15 cm apart The City School / PAF Chapter/ Comprehensive Worksheet/ December 2015/ Mathematics / Class 7 /Ans Key Page 11 of 11