The City School PAF Chapter Prep Section Mathematics Class 6 Worksheets for Intervention Classes
Topic: Percentage Q1. Convert it into fractions and its lowest term: a) 25% b) 75% c) 37% Q2. Convert the following decimals to fraction: a) 0.5 b) 1.75 c) 1.39 Q3. Convert the following fractions to percentages: a) b) c) d) 3 100 1 4 2 25 1 9 2 Q4. Complete the following table. Fraction Decimal Percentage 11% 0.855 Q5. Fill in the blank: a) 10% of 240 = b) 5% of 240 = c) 50% of 240 = The City School /PAF Chapter / Prep Section / Worksheet for Intervention Class /Mathematics /Class 6 Page 2 of 18
RATIO AND RATE Q1. Express the following ratio in their simplest form: a) 45cents:1dollar b) 54:30 c) 3:48 d) 7 1 : 3 2 e) 10 km: 5cm f) 15 litres: 3 litres Q2. Find the value of x: a) 3:12=2:x b) x:25=3:5 Q3. Complete the following to form equivalent ratios: a) 2:6=1: 6 b) : 18 c) 3: =9:15 20 d) : 6 Q4. In a box, the ratio of red marbles to green is 5:6, while the green marbles to yellow are 3:10. Find the ratio of red marbles to green marbles to yellow marbles in its simplest form. Q5. A club has an enrolment of 630 French people, 120 German people and 60 local people. Find the ratio of German people to French people to local people. Q6. A man earns $2400 and spends $900 per month. Find the ratio of a) his income to his expenditure and b) his savings to his income. Q7. 15 Kg of fish cost Rs.3750. a) Find the rate of fish (1Kg) b) What will be the cost of 8 Kg of fish. Q8. A boy earns $500 in a five-day a week. What is his pay per day? Q9. A bike uses 20 liters of petrol to travel 170 km. How far can it travels if it has only 16 liters of petrol? Q10. A wire 44 cm long has a mass of 748 g. What is the mass of 26 cm of this wire? The City School /PAF Chapter / Prep Section / Worksheet for Intervention Class /Mathematics /Class 6 Page 3 of 18
TOPIC: ALGEBRA Q1. Write an algebraic expression for of following; a) Add 4x to 28. b) Subtract 10x from the half of y. c) Multiply 2 by 4k. d) Divide 16x by 24y. Q2. Evaluate the following 2x+5y when a) x=3 and y=5; (b) x=2 and y= -1; (c) x=-2 and y=3. Q3. Evaluate the following when a=3, b=4, and c=6: a) a(2c-b) (b) ab[(3b-c)-a] (c) (a+b)(c b)+ab (d) a b a c c c b Q4. Simplify the following expression: a) 3x + 8x 2x (b) 4x + 2y +7x y (c) 3a 2b + c a + 5b d) 10n x 12 (e) -4 x (-2k) (f) (-26v) (-2) g) (h) Q5. Find the sum of following: a) 2a+3b-4c, 3a-2b, -4a+5c and a-2b+c. b) p+4q-2r, 4p-6q+5r, 3p-2q+4r. c) 2x-9y+10, 10y+5x-6 and -12x+3y. d) 4a 2-7y 3 +18, 2y 3-6a 2-9 and 8a 2-5y 3 +15. Q6. Find the subtract of following: a) 3a+4b-2c from 2a+5b-d b) 8a-6b+10c-4d from 5a-2b-4c-12d c) 2a-3b+6 from 15a +17b-18 d) 8y 2 +8x 2 from 4x 2-6y 2 Q7. Choose the best answers. 1. An algebraic expression of twelve subtracted from thrice the number x is a) 3(x 12) b) 3x 12 c) 12 3x d) 12(x 3) 12. Expanded form of (-2x)(-3y) a) 6xy b) 6xy c) 6xy d) 5xy The City School /PAF Chapter / Prep Section / Worksheet for Intervention Class /Mathematics /Class 6 Page 4 of 18
Q8. a) Write an algebraic expression for the following i) Divide the sum of x and y by z ii) Product of r and sum of s and t b) Find the value of x³ + 2xy² + y², when x = 2 and y = -1. Q9. If a=5, b=-2 and c = 2; find the value of: a) -b +c 3 b) 2-6 c) 8 +15 d) 2 +6b 2-9c e) 18a-2b+9c Q10. Let a number be n. Write down an algebraic expression in terms of n for the following statements: a. Subtract 2 from n b. Multiply the result obtained in (a) by 3 c. Divide the sum of n and 3 by 4 d. Add the product of 5 and n to the square of n Q10. Simplify each expression. a) 2 (k + 4) + 7(2k 2) 2 b) 12 + 4n + 5 2n 10 c) 3a 4 + 5a + 7 + 2(a + 1) d) 3 + 2s 4 + 3s e) 7p 6 + 8p 2 2p f) 15 3(y + 5 7 g) c + 6 + 4c 3 + 4 h) 10m + 2 + 7m 3 + 5m i) 8 2(11b) + 4 (5b) + b j) 8(r + 9) + 5 k) 20 + 5(7t 2) l) 4(3z + 5 + 7z) 12 m) 3a²b² x 12ab n) 1 x³ y² 1 2 o) 2ab x (-3abc) p) -49m² 7m q) 6xy x ( -4xy ) The City School /PAF Chapter / Prep Section / Worksheet for Intervention Class /Mathematics /Class 6 Page 5 of 18
TOPIC: AREA & PERIMETER Q1 Choose the best answer: a) If the area of a rectangle is 96cm 2 and its length is 8cm, its breadth will be i. 12 cm ii. 20 cm iii. 13 cm b) If the perimeter of a square is 36cm, its length must be iv. 14 cm i. 6cm ii. 4cm iii. 9cm iv. 10cm c) The perimeter of a rectangle is 22cm and its width is 4cm, its length must be i. 12cm ii. 2cm iii. 18cm iv. 7cm d) If the base of a triangle is 6cm and its height is 10cm, its area will be i. 60c ii. 36c iii. 30c iv. 16c e) If the area of a square is 144, the length of each side will be i. 10cm ii. 8cm iii. 2cm f.) The formula for finding out the area of a square is iv. 12cm i. L x B x H ii. 2(L x B) iii. iv. 4L Q2 For the shapes that have sides of whole number lengths. State whether these statements are true or false: a) If two sides of a rectangle are double the length of the other two sides, the perimeter could be 12 cm. b) The perimeters of all rectangles are even. c) All squares have a perimeter that will divide exactly by 4. d) A rectangle where one side is 1cm can have a perimeter of 19cm. e) If two sides of a rectangle are even and the other two sides are odd, then the perimeter will always be even. f) If all sides of a rectangle are even, then its area must be odd. g) If all sides of a rectangle are odd, then its area must be odd. The City School /PAF Chapter / Prep Section / Worksheet for Intervention Class /Mathematics /Class 6 Page 6 of 18
3. Find the area and perimeter of the following shapes: a) b) c) d) The City School /PAF Chapter / Prep Section / Worksheet for Intervention Class /Mathematics /Class 6 Page 7 of 18
4) Find the side of square whose perimeter is 96cm. 5) Find the area of a square whose perimeter is 24cm. 6) Find the perimeter and area of the given triangle ABC. 7cm 5cm 3cm 9cm 7) A square shaped park has an area of 225 ft 2, what is the perimeter of the park? 8) Ronald wants to paint his drawing room wall which measures 8 feet by 9 feet. The cost of the paint is $14 per square foot. How much will it cost Ronald to paint the wall? The City School /PAF Chapter / Prep Section / Worksheet for Intervention Class /Mathematics /Class 6 Page 8 of 18
9) Find the area of the given triangles: a) b) 9cm c) 6cm 4cm 6cm Q11. Find the area and perimeter of the following figures: a) b) The City School /PAF Chapter / Prep Section / Worksheet for Intervention Class /Mathematics /Class 6 Page 9 of 18
c) d) e) f) The City School /PAF Chapter / Prep Section / Worksheet for Intervention Class /Mathematics /Class 6 Page 10 of 18
TOPIC: VOLUME & SURFACE AREA Q1. Fill in the blanks a) A cube has sides. b) 5 liter is equal to cm 3. c) Find the length of the cube whose volume is 27cm 3. Q2 The volume of the cube is 27cm3, find the surface area. Q3. Find the surface area of a cube with side 4cm. Q4. Complete the following table Length Width Height Volume Surface Area 4cm 3cm 5cm 5cm 3cm 120 3cm 4cm 60 Q5. The volume of a cube is 729 cm³. The total surface area in cm² is? The City School /PAF Chapter / Prep Section / Worksheet for Intervention Class /Mathematics /Class 6 Page 11 of 18
Q6. Find the surface area of the following cuboids. 3 cm 7 cm 4 cm Q8. Find the volume of a cuboids of length 20 cm, breadth 15 cm and height 10 cm. Q9. A wall has to be built with length 8 m, thickness 3 m and height 5 m. Find the volume of the wall in cubic cm. Q10. If the volume of a room is 512 m 3 and the area of the floor is 132 m 2, find the height of the room. Q11. Length, breadth and height of a tank are 6 m, 5 m and 3 m respectively. Find the capacity of the tank in litres. The City School /PAF Chapter / Prep Section / Worksheet for Intervention Class /Mathematics /Class 6 Page 12 of 18
Topic: Graphs and Statistics Q1. Choose the correct answer. 1. A vertical bar graph with no space in between the bars. i) histogram ii) bar graph iii) line graph 2. The coordinates of origin are i) (0,1) ii) (1,0) iii) (0,0) 3. Average of 14,18,16,12 i) 20 ii) 15 iii) 18 4. The average of first five odd numbers is i) 5 ii) 3 iii) 10 5. Averages are also called i) Mean ii) Median iii) Mode 6. The ordered pair of second quadrant is i) (+, - ) ii) (+, +) iii) (-, +) Q2. Fill in the blanks. a) A plane consisting of four quadrants are called. b) The diagram which uses pictures to represent statistics is called. c) The collection of facts and figures is called. d) The pairs of numbers (2,4), (4,6), (3,3), (5,3) are examples of. e) The x-axis is called. f) The point O is known as point. g) The co-ordinates ( 1, 4) lies in the quadrant. h) The vertical axis is also known as the. i) The point where x-axis and y-axis meet to form a right angle is known as. j) A pictogram uses to represent statistics. k) The science of collection, organization and interpretation of data is. The City School /PAF Chapter / Prep Section / Worksheet for Intervention Class /Mathematics /Class 6 Page 13 of 18
Q3. Write the coordinates of the points in the diagram below. Q4. Find the average temperature of a week from the given data. Friday Saturday Sunday Monday Tuesday Wednesday Thursday 26.5 C 28.4 C 27.9 C 27.5 C 25.5 C 27.2 C 26.0 C The City School /PAF Chapter / Prep Section / Worksheet for Intervention Class /Mathematics /Class 6 Page 14 of 18
Q5. The bar chart shows the value of a company over a number of years. a) What was the value of sales in? i. 2002 ii. 2004 iii. 2006 b) In which year was the value of sales $1 000,000? c) Between which years was there the greatest increase in the value of sales? What was the increase in the value of sales? d) In 2005 the sales target was $1300000. By how much did the company exceed its target? Express this as a percentage of the sales target. e) In 2006 the sales target was $ 1 650 000. By how much did the company fall short of its target? Express this as a percentage of the value of sales in 2006. f) Find the total value of sales over the 6 years. Q6. A study was made on the absenteeism in a School. As part of the findings, the table below shows the number of students present in a class of 42 for a week: Day Monday Tuesday Wednesday Thursday Friday Students Present 42 36 40 36 38 a) Draw a chart to show the above information. b) On which day were no students absent? c) What fraction of students were absent on Friday? d) Was any student absent for the whole week? The City School /PAF Chapter / Prep Section / Worksheet for Intervention Class /Mathematics /Class 6 Page 15 of 18
Q8. Plot the vertices of ABC on the graph, where A = ( 2, 1) B = (6, 5) C = (6, 2). Calculate the area of ABC. The City School /PAF Chapter / Prep Section / Worksheet for Intervention Class /Mathematics /Class 6 Page 16 of 18
TOPIC: TIME The City School /PAF Chapter / Prep Section / Worksheet for Intervention Class /Mathematics /Class 6 Page 17 of 18
TOPIC: MEASUREMENT Q1.Convert the following a) 32.45cm= mm b) 2.08mm= cm c) 3.5l= ml d) 425ml= l e) 1kg= g f) 3750g= kg g) Height of mount Everest is measured in h) Length of hairs can be measured in i) Weight of mutton and chicken can be measured in j) Capacity of a can of water is measured in Q2.Steven goes to the grocery store and is looking for a winter squash. It has a mass of 1.8 kilogram. How many grams is the winter squash? Q3. A box contains 4 bags of sugar. The total mass of 4 bags is 6kg. What is the mass of 1 bag in grams? Q4.Carol has a 1.2 meter long piece of wood. She wants to cut into 3 equal pieces. How long should each piece be in millimeters? Q5.Chase measured a line for his art project. It is 200 millimeters long. How many meters is the line? The City School /PAF Chapter / Prep Section / Worksheet for Intervention Class /Mathematics /Class 6 Page 18 of 18