The City School PAF Chapter Workbook for Intervention Classes Mathematics Class 7
Rules/Tests of Divisibility Is divisible by Why? 654 2? Yes / No 423 2? Yes / No 352 3? Yes / No 1,956 3? Yes / No 2,076 4? Yes / No 1,345 4? Yes / No 8,700 4? Yes / No 1316 4? Yes / No 2052 4? Yes / No 2,345 5? Yes / No 560 5? Yes / No 3,672 5? Yes / No 1,950 6? Yes / No 396 6? Yes / No 1786 6? Yes / No 1488 6? Yes / No 570 7? Yes / No 1,666 7? Yes / No 1015 7? Yes / No The City School /PAF Chapter / Prep + Senior I Section / Worksheet for Intervention Class /Mathematics /Class 7 Page 2 of 31
570 7? Yes / No 4,954 8? Yes / No 1,720 8? Yes / No 6,000 8? Yes / No 2224 8? Yes / No 174 8? Yes / No 7,434 9? Yes / No 6,254 9? Yes / No 102 9? Yes / No 3771 9? Yes / No 675 10? Yes / No 780 10? Yes / No 3576 11? Yes / No 253 11? Yes / No 7161 11? Yes / No 238 11? Yes / No 1140 12? Yes / No 440 12? Yes / No The City School /PAF Chapter / Prep + Senior I Section / Worksheet for Intervention Class /Mathematics /Class 7 Page 3 of 31
Integers Q1. Fill the following blanks with appropriate operation symbol and mention the law applied: (a) -34 (-12) = -12 (-34) = -46 Law: (b) -64 (-13) = -13 (-64) = -77 Law: (c) -44 (-3) = -3 (-44) = 152 Law: (d) -33 (-19) = -19 (-33) = -52 Law: (e) -54 2 = 2 (-54) = -108 Law: Q2. Fill the following blanks with an integer and mention the law applied: (a) (-7) (-3 - ) = [(-7) (-3) (-7) 8] = Law: The City School /PAF Chapter / Prep + Senior I Section / Worksheet for Intervention Class /Mathematics /Class 7 Page 4 of 31
(b) (-5) (-3 - ) = [(-5) (-3) (-5) 7] = Law: (c) (-8) (-2 - ) = [(-8) (-2) (-8) 4] = Law: Q3. Evaluate: (a) 4 4 4 + 4 4 (b) 7 7 7 + 7 7 (c) 10 10 10 + 10 10 The City School /PAF Chapter / Prep + Senior I Section / Worksheet for Intervention Class /Mathematics /Class 7 Page 5 of 31
(d) [(-3) + (-4)] 7 (e) (-56) [7 + (-14)] (f) 2 5 + ( 20) ( 10) (g) 123 [19 + 19 ] 38 (h) ( 9) (-4) (-12) The City School /PAF Chapter / Prep + Senior I Section / Worksheet for Intervention Class /Mathematics /Class 7 Page 6 of 31
Rational Numbers Q1. Arrange the following in descending order: (a) 2 3, 3 5, 0 (b) 14 25, 26 59, 11 20, 53 100 (c) 19 27, 2 3, 13 18, 7 9 (d) 17, 5, 2, 11 24 8 3 16 The City School /PAF Chapter / Prep + Senior I Section / Worksheet for Intervention Class /Mathematics /Class 7 Page 7 of 31
Q2. Arrange the following in ascending order: (a) 7 10, 13 20, 2 3 (b) 13 20, 11 15, 3 4 (c) 13, 5, 37 15 6 45 (d) 5, 7, 11 12 18 27 The City School /PAF Chapter / Prep + Senior I Section / Worksheet for Intervention Class /Mathematics /Class 7 Page 8 of 31
Q3. Evaluate the following and express the answer in its lowest terms. (a) 2 3 (-3 3 20 ) + ( - 2 5 ) (b) ( - 1 2 + 1 3 ) + [ 1 4 + (- 1 3 ) ] + (- 1 20 ) (c) (-2 2 5 ) 5 6 (-13) (d) 1 7 15 (-17 2 7 ) 3 3 14 The City School /PAF Chapter / Prep + Senior I Section / Worksheet for Intervention Class /Mathematics /Class 7 Page 9 of 31
(e) [(-9 1 4 ) (-7 3 5 )] 2 3 4 (f) 3 3 5 (-6) (-4 4 5 ) (g) (-12 1 2 ) + 1 2 3 (-4) - 5 7 (-2 4 5 ) The City School /PAF Chapter / Prep + Senior I Section / Worksheet for Intervention Class /Mathematics /Class 7 Page 10 of 31
Q4. Ali, Babar and Kamran buy a business. Ali pays 3 What fraction of the cost price does Kamran pay? 10 of the cost price and Babar pays 3 10 of it. Q5. A man left 3 of his money to his wife and 1 of the remainder to his brother. If his brother gets Rs. 7 2 120, how much does his wife receive? The City School /PAF Chapter / Prep + Senior I Section / Worksheet for Intervention Class /Mathematics /Class 7 Page 11 of 31
Estimation and Approximation Q1. Estimate: (a) 9.034 0.2106 0.0289 24.778 (b) 2905 (0.512)3 0.004987 (c) 4.311 0.02916 3 981 0.0231 The City School /PAF Chapter / Prep + Senior I Section / Worksheet for Intervention Class /Mathematics /Class 7 Page 12 of 31
Q2. Round off to 881 cm the nearest 100 cm 108.356 kg the nearest 0.1 kg 4.45 cm the nearest cm 49153 g the nearest 10 kg 138.08 one decimal place 18.5095 one decimal place 26.8047 two decimal places 0.045 two decimal places 7.4495 three decimal places 0.03764 three decimal places Q3. Express Correct to the number of significant figures indicated. 5003.583 4 37.87 2 18.1356 4 0.03256 3 19.64851 2 The City School /PAF Chapter / Prep + Senior I Section / Worksheet for Intervention Class /Mathematics /Class 7 Page 13 of 31
Q4. Estimate the value of the following and give your answer correct to one significant figure: (a) 163.4 0.0818 (b) (398) 2 0.062 Q5. Estimate, correct to one significant figure, the value of the following: (a) 4.9 57 0.389 20.128 (b) 24.977 28.0349 19.897 The City School /PAF Chapter / Prep + Senior I Section / Worksheet for Intervention Class /Mathematics /Class 7 Page 14 of 31
Number Sequence / General Term Q1. Fill in the missing terms in the following sequences: (a) 21, 23, 26, 30,, (b) 4, 5, 9, 18, 34,,, (c) 2, 1, 3, 2, 4,, 5 (d) 25,, 26, 23, 27, 22 (e) 0, 6, 12, 18,, (f) 1, 3, 6, 10, 15,,, (g) 0, 1, 4, 10, 20, 35,, The City School /PAF Chapter / Prep + Senior I Section / Worksheet for Intervention Class /Mathematics /Class 7 Page 15 of 31
Q2. (a) Given the sequence 1, 1, 2, 3, 5, 8, 13,., write down the next five terms of the sequence. (b) Consider the pattern: 1 2 + 1 2 = 1 2 1 2 + 1 2 + 2 2 = 2 3 1 2 + 1 2 + 2 2 + 3 2 = 3 5 1 2 + 1 2 + 2 2 + 3 2 + 5 2 = 5 8 1 2 + 1 2 + 2 2 + 3 2 + 5 2 + 8 2 = 8 13 (i) Verify the result of the 5 th line. (ii) Using the result in (a), write down the next four lines in the pattern. (iii) Describe how the terms in the sequence in (a) are connected in the pattern. The City School /PAF Chapter / Prep + Senior I Section / Worksheet for Intervention Class /Mathematics /Class 7 Page 16 of 31
Q3. Consider the pattern: 1 3 1 = 0 = 6 0 2 3 2 = 6 = 6 1 3 3 3 = 24 = 6 4 4 3 4 = 60 = 6 10 5 3 5 = 120 = 6 20 6 3 6 = 210 = 6 35 m 3 m = n = k 84 (a) Write down the ninth and tenth lines in the pattern. (b) Find the value of m and n. The City School /PAF Chapter / Prep + Senior I Section / Worksheet for Intervention Class /Mathematics /Class 7 Page 17 of 31
Algebra - Linear Expressions and Equations Q1. Solve the following: (a) 6x 2x 1 = 2 (b) 3 x+1 = 8 x+2-5 x+3 (c) x 3-3(x+5) 4 = 3 7 (d) 5 2x 5-4 7x+1 = 0 The City School /PAF Chapter / Prep + Senior I Section / Worksheet for Intervention Class /Mathematics /Class 7 Page 18 of 31
(e) 84 x 4 = 1 + 75 x (f) 1 3 ( 1 5x 3 ) = 1 2 (2-1 x ) (g) x+1 x 2 = 1 7 (h) 1 (x 3) + 3 = x + 2(x 1) 3 (i) 1 x = 1 20-1 2x 3 The City School /PAF Chapter / Prep + Senior I Section / Worksheet for Intervention Class /Mathematics /Class 7 Page 19 of 31
Algebra Substitution in Formula Q1. If a = 3, b = 2 and c = -1, find the value of each of the following. (a) a 3 + b 3 + c 3 2abc (b) (2a + b c)(4b c) (c) (a b) 2 - (b c) 2 (d) a b - c a + b a (e) a+b c - ab c b (f) a2 b 2 - a3 c c 2 c 3b The City School /PAF Chapter / Prep + Senior I Section / Worksheet for Intervention Class /Mathematics /Class 7 Page 20 of 31
Q2. Find the value of x 3 + 2xy + y 3 when x = 2 and y = -1 Q3. Find the value of x+1 x 1 + 2x 1 when x = -2 2x+1 Q4. If x y = xy p q, find x when y = 2, p = 5 and q = 6. Q5. If 2x + y 3z y+3z = x 2y, find x when y = 4 and z = 1. The City School /PAF Chapter / Prep + Senior I Section / Worksheet for Intervention Class /Mathematics /Class 7 Page 21 of 31
Algebra Construction of Formula Q1. Write an algebraic expression for each of the following. (a) The sum of seven times x and three times y (b) Cube of x added to square of y (c) Four times the cube root of y subtracted from twice the square of x (d) The cost of y apples which are sold at 3 for a dollar. (e) The difference between nine times the product of x and 3h (f) The cube of the sum of x and y minus the square root of the sum of 5x and 3y The City School /PAF Chapter / Prep + Senior I Section / Worksheet for Intervention Class /Mathematics /Class 7 Page 22 of 31
Measurements (Length, Weight and Capacity) Q1. Do the following conversions: 670 mm cm 1,560 mm m 2,500 mm km 450 cm m 3,580.5 cm km 750,000 m km 4.8 km m 0.85 km cm 24 km mm 9,300 g kg 550 g tone 150 kg tone 5.04 tonne kg 1.1 tonne g 23 kg g 3,600,456 ml liter 72,000 liter ml The City School /PAF Chapter / Prep + Senior I Section / Worksheet for Intervention Class /Mathematics /Class 7 Page 23 of 31
Q2. A table weighs 5.5 kg and a chair weighs 4,500 g. Find the total mass of 6 pairs of such tables and chairs. Q3. My school is 18.5 km away from my home while the sea-side is 4,850 m away from the school. What is the distance between my home and the sea-side? Q4. The capacity of a tank is 65 liters while only 7,600 ml is filled in it. How much more water can the tank hold? Q5. A cake recipe requires 850 g flour and half kg sugar. What will be the combined weight of both ingredients in 3 such cakes? The City School /PAF Chapter / Prep + Senior I Section / Worksheet for Intervention Class /Mathematics /Class 7 Page 24 of 31
Perimeter and Area of Simple Geometric Figures Q1. Complete the following table for each circle. Take π = 3.14. Space for calculations is provided at the end of the table. Radius Diameter Circumference Area 4.2 cm 60 inches 132cm 78.5 cm 2 2826 m 2 244.92 mm 56 cm 14 inches The City School /PAF Chapter / Prep + Senior I Section / Worksheet for Intervention Class /Mathematics /Class 7 Page 25 of 31
Q2. Complete the following table for each trapezium. Space for calculations is provided at the end of the table. Height Parallel side 1 Parallel side 2 Area 14 cm 8 cm 12 cm 45 m 75 m 0.72 m 2 6 inches 7 inches 54 inches 2 The City School /PAF Chapter / Prep + Senior I Section / Worksheet for Intervention Class /Mathematics /Class 7 Page 26 of 31
Q3. Complete the following table for each parallelogram. Space for calculations is provided at the end of the table. Base Height Area 18 cm 4.2 cm 4.6 m 11.5 m 2 7 inches 8.4 inches 2 The City School /PAF Chapter / Prep + Senior I Section / Worksheet for Intervention Class /Mathematics /Class 7 Page 27 of 31
Q4. Find the area and perimeterof the following shaded parts: The City School /PAF Chapter / Prep + Senior I Section / Worksheet for Intervention Class /Mathematics /Class 7 Page 28 of 31
The City School /PAF Chapter / Prep + Senior I Section / Worksheet for Intervention Class /Mathematics /Class 7 Page 29 of 31
Q5. Find the area of the following shaded parts: The City School /PAF Chapter / Prep + Senior I Section / Worksheet for Intervention Class /Mathematics /Class 7 Page 30 of 31
Q6. Find the area of the following trapeziums: The City School /PAF Chapter / Prep + Senior I Section / Worksheet for Intervention Class /Mathematics /Class 7 Page 31 of 31