PAF Chapter Comprehensive Worksheet May 2016 Mathematics Class 7 (Answering Key)

Transcription

1 The City School PAF Chapter Comprehensive Worksheet May 2016 Mathematics Class 7 (Answering Key) The City School / PAF Chapter/ Comprehensive Worksheet/ May 2016/ Mathematics / Class 7 / Ans Key Page 1 of 10

2 Q1. Fill in the blanks. [ /10] (i) Simplified form of 27:36 is 3 : 4. (ii) Mode of the data: 0, 1, 2, 5, 2 is 2. (iii) 2.25 hrs = 135 minutes. (iv) The gradient of the equation y = 9x 6 is 9. (v) If 7a = 28, then a = 4. (vi) Total surface area of a cube with side 10 cm is 600. (vii) Simplify 7z + 5z z = 11z. (viii) The sum of two opposite interior angles is equal to exterior angles. (ix) For an isosceles triangle, the base angles are equal. (x) The simplest form of is = 3 Q2. Multiple Choice Questions Select the correct answer from the options provided. There is only one correct option for each statement. [ /10] (i) Solution of = is: (a) (b) (c) (d) 18 (ii) (iii) The order of symmetry of the given diagram is: (a) 1 (b) 3 (c) 4 (d) 5 Algebraic equation for the sum (S) of three numbers x, y and z, divided by another number a is: (a) S = (b) S = (c) S = (d) S = (iv) What is the coefficient of x in the expression + x? (a) 2 (b) 1 (c) (d) x (v) How many grams are there in 10kg? (a) 1 (b) 10 (c) 10,000 (d) 1,000 (vi) The sum of adjacent angles on a straight line is. (a) 90 (b) 180 (c) 360 (d) none of the three (vii) A triangle with all sides equal is called triangle. (a) Equilateral (b) Isosceles (c) Scalene (d) Right-angled The City School / PAF Chapter/ Comprehensive Worksheet/ May 2016/ Mathematics / Class 7 / Ans Key Page 2 of 10

3 (viii) A cube with side 1 m has a volume of. (a) 10 (b) 100 (c) 1 (d) 1000 (ix) Mean of 5, 0, 10 ad 1 is: (a) 3 (b) 4 (c) 0 (d) 1 (x) How many triangles are formed in a pentagon? (a) 2 (b) 3 (c) 5 (d) 6 Q3a. (i) If =, find x : y [ /2] = = 8 Therefore x : y = 8 : 1 (ii) If 8 : x = 26 : 65, find x [ /2] = Cross multiplying 8 x 65 = x x 26 x = x = 20 Q3b. The salaries of five staff members are given as follows: $2500, $500, $1500, $2000 and $750. Find their mean salary. [ /3] = = $1450 The City School / PAF Chapter/ Comprehensive Worksheet/ May 2016/ Mathematics / Class 7 / Ans Key Page 3 of 10

4 Q3c. A player scored the following number of runs in different matches: 27, 16, 27, 36, 58, 89, 27. Find the mode and median of the data. [ /3] Mode = 27 For median, arranging the data in order: 16, 27, 27, 27, 36, 58, 87 Median = 27 Q4a. A book contains 120 pages. Each page has 35 lines. How many pages would the book have contained if every page had 24 lines? [ /3] Pages Lines x 24 This is inverse relationship. Therefore: 24x = 120 x 35 x = x = 175 Q4b. 10 identical pipes can fill a tank in 15 minutes. Calculate the time required to fill the same tank with 6 pipes. [ /3] Pipes Minutes x This is inverse relationship. Therefore: 6x = 10 x 15 x = x = 25 minutes, that is, The City School / PAF Chapter/ Comprehensive Worksheet/ May 2016/ Mathematics / Class 7 / Ans Key Page 4 of 10

5 Q4c. Solve the equation = [ /4] Cross multiplying 5k = 2k + 2 5k 2k = 2 3k = 2 k = Q5a. Find the unknowns: [ /3] x + 56 = 125 x = x = 69 y = y = 111 Q5b. Find the unknowns: [ /3] a = 35 (alternate angles) b = (alternate angles) b = 73 The City School / PAF Chapter/ Comprehensive Worksheet/ May 2016/ Mathematics / Class 7 / Ans Key Page 5 of 10

6 Q5c. Find the gradient of a straight line passing through the points (4, 3) and (5, 7). [ /4] Gradient of the given line = = 4 Q6a. A bus travels from Town A to Town B. It leaves Town A at 9:30 am on Monday. The journey takes 26 hours and 20 minutes. When will the bus arrive at Town B? [ /4] Arrival time = Departure time + Journey time Hours Minutes Arrival time = 11:50 am the next day Q6b. The sum of four consecutive odd numbers is 64. Find the largest number. [ /3] Let the first number be x. Therefore: x + (x + 2) + (x + 4) + (x + 6) = 64 x + x x x + 6 = 64 4x + 12 = 64 4x = x = = 13 Largest number is 19. The City School / PAF Chapter/ Comprehensive Worksheet/ May 2016/ Mathematics / Class 7 / Ans Key Page 6 of 10

7 Q6c. The sum of three numbers is 109. The second number is four times the first, and the third is eight less than the second. Find the three numbers. [ /3] Let the first number be x. Therefore, the second number is 4x, and the third number is (4x - 8). Hence: x + 4x + 4x - 8 = 109 9x = x = = 13 4x = 4 x 13 = 52 4x 8 = 52 8 = 44 The numbers are 13, 52 and 44. Q7.The table shows marks obtained by students in a test: Marks Number of students x F fx f = 40 fx = 185 (i) the total number of students who took the test [ /1] 40 (ii) the mean marks [ /3] = = 4.62 The City School / PAF Chapter/ Comprehensive Worksheet/ May 2016/ Mathematics / Class 7 / Ans Key Page 7 of 10

8 (iii) the percentage of students who passed the test, if passing marks are 5 [ /3] x 100 = 57.5% (iv) the percentage of students who passed the test. [ /1] 100% % = 42.5% (v) the modal marks [ /2] 2 Q8a. Find: (i) the exterior angle of a 12-sided polygon. [ /2] = 30 (ii) the sum of interior angles of a decagon. [ /2] (10-2) x 180 = 1440 Q8b. 300 students of grade seven were asked to choose their favourite drink from Coca Cola, Sprite and Mountain Dew. The result is represented by the following pie-chart: Calculate: (i) the value of x [ /3] x + 3x = 360 4x = x = x = 60 The City School / PAF Chapter/ Comprehensive Worksheet/ May 2016/ Mathematics / Class 7 / Ans Key Page 8 of 10

9 (ii) the number of students whose favourite drink is Sprite. [ /3] x 120 or x 300 = 100 students Q9. For the linear function y = 2x + 5: (a) Complete the grid: [ /2] x y (b) Draw its graph. [scale: /1] [axes: /1] [plotting of points: /4] Scale: 5 small squares = 1 unit on both axes (c) From the graph, find the value of: (i) x, when y = -1 [ /1] x = -3 (ii) y, when x = -1 [ /1] y = 3 The City School / PAF Chapter/ Comprehensive Worksheet/ May 2016/ Mathematics / Class 7 / Ans Key Page 9 of 10

10 Q10a. Find the mean, median and mode of the following ungrouped data: [ + + /2+2+1] 7, 9, 8, 7, 6, 8, 3, 1 Mean = = = Median: = Arranging the data in order: 1, 3, 6, 7, 7, 8, 8, 9 Number of units of data: n = 8 Median = th unit = = 4.5, that is, mean of 4 th and 5 th unit = 7 Mode: 7 and 8 Q10b. The price of a watch is Rs.160 and it is sold for Rs.140. Find the percentage loss. [ /3] x 100 = 12.5% Q10c. A Ferris wheel can accommodate 54 people in 27 minutes. What is the rate: (i) per minute [ /1] = 2 people (ii) per hour [ /1] 2 x 60 = 120 people The City School / PAF Chapter/ Comprehensive Worksheet/ May 2016/ Mathematics / Class 7 / Ans Key Page 10 of 10