Q2. In a survey of 100 cars, 47 were white, 23 were blue and 30 were red. Express each of these numbers as a percentage of total.

Transcription

1 Question Bank for grade 6 PERCENTAGE Q1.Calculate the following. a. 50% of 300 b. 75% of 400 c. 40% of 600 d. 25% of 360 e. 80% of 250 f. 37.5% of 240 g of 880 h. 12.5% of 320 i. 75% of 40 j. 40% of 75 Q2. In a survey of 100 cars, 47 were white, 23 were blue and 30 were red. Express each of these numbers as a percentage of total. Q3. 7 of the surface of the earth is water. Express this as a percentage. 10 Q4. There are 200 birds in a flock. 120 of them are female. What percentage of the flock isa)femaleb)male Q5. Write these percentages as fractions of 100. a) 73% b) 28% c) 10% d) 25% Q6. Write these fractions as percentages. a) 27 b) 3 c) d)1 4 Q7. Convert the following percentages to decimals. a) 39% b) 47% c) 83% d) 7% e) 2% f) 20% Q8. Convert the following decimals to percentages. a) 0.31 b) 0.67 c) 0.09 d) 0.05 e) 0.2 f) 0.75

2 Question Bank for grade 6 Q9. In a survey of 100 cars, 45 were silver, 13 were blue and 30 were red. Express each of these numbers as a fraction, a decimal and a percentage of the total. Q10. 3 of the surface of the earth is land. Express this as a decimal and a percentage. 10 Q11. There are 500 students in a school. 220 of them are female. What percentage of the school is:a) Female b)male Q12. Write each of these percentages as afraction in its simplest form. a) 23% b) 68% c) 70% d) 75% Q13. Write these fractions as percentages. a) 49 b) c)17 50 d)3 4 Q14. Convert the following percentages to decimals. a) 69% b) 87% c) 83% d) 3% e) 102% f) 220% Q15. Convert each of these decimals to percentages. a) 0.61 b) 0.17 c) 0.89 d) 0.08 e) 1.25 f) 2.75 Q16. Workout the following. a. 10% of 60 b. 25% of 160q. 87.5% of 80 c. 12.5% of 80 d. 37.5% of 80r. 10% of 110 e. 46% of 50 f. 50% of 46t. 45% of 90 g. 70% of 125 h. 7% of 125 i. 12% of 180 j. 36% of 180 k. 90% of 90 l. 7% of 375

3 Question Bank for grade 6 m. 9% of 90 n. 60% of 180 o. 60% of 150 p. 9% of 9 Q17. 15% of students in a school of 720 students are left- handed. What number of students are right handed? Q18. At Cambridge college, 65% of the math students come from England. If there are 240 math students, how many are not from England? Q19. A survey showed that 75% of vehicles passing a school were cars. If 4200 vehicles passed the school in one day, how many were cars? Q20. In a village of 3500 people, 12% are left-handed, and 15% of left handed people have blonde hair. How many people in the village are blonde and left-handed? Q21. Write the first quantity as a percentage of the second. a. 36 out of 72 b. 18 out of 90 c. 6 out of 60 d. 36 out of 60 e. 7 out of 70 f. 21 out of 70 g. 45 out of 900 h. 135 out of 900 i. 11 out of 44 j. 11 out of 440 k. 5 out of 20 m. 54 out of 60 o. 49 out of 70 q. 180 of 900 s. 77 out of 440 Q22. A school football team plays 25 games in a season. They win 17, draw 2and lose the rest. Express the numbers won, drawn and lost as percentages of the total number of games played. Q23. An airline has a fleet of 80 planes. Of these, 10 are being serviced at any one time. What percentage of the fleet is available for flights? Q24. A car manufacturer produces sports cars a year. They are only available in white, black and red are white, are black and the rest are red. a) What percentage of the cars are black? b) What percentage is white? c) What percentage is red?

4 Question Bank for grade 6 Q25. Copy and complete these sets of equivalent fractions and percentages. 1) 8 = 1 2) 5 = ) 7 11 = % 4) = % ) 13 = % 6)17 = 1 9) 7 = = % ) 8 = 10 = %8) = 35 = %10) = = % Q26. Which of the following are equivalent (in proportion)? Give reasons for your answers. 1) ) %2) %7) %4) %8) %6) %9) ) ) % Q27. Copy and complete this table % 0.9 9% % Fraction Ratio Percentage 1 1 to 2 50% to 25% 4 3 to to 12.5% 8 3 to to % to 10% or 1 5 to 5 20% to

5 Question Bank for grade or 2 to or 3 to or to Q28. Complete the following table. 70% Fraction Decimal Percentage % Q29. Calculate the following, showing your method. a. 75% of 64 b. 30% of 1550 c. 9% of 3400 d. 55.5% of 680 e. 3% of 73 Q30. Calculate the first number as a percentage of the second: a. 35, 140 b. 72, 600 c. 23, 50 d. 40, 125 e. 17, 250

6 RATIO Q1. Copy these set equivalent ratios and fill in the blanks. a)4: 5 = 8: = :50 = 12: b) 7: 2 = 14: = :10 = 49: c) 8: 5 = : 50 = 32: = 4: Q2.A school has 20 teachers and 480 students. What is the teacher : student ratio? Q3. A college has 250 staff and 3500 students. What is the staff : students ratio? Q4.A town in America has 2400 families and 4200 cars. What is the family : car ratio? Q5.In a batch of 10 dozen eggs, 25 are cracked. What is the ratio of cracked eggs to un-cracked eggs? Q6. A ship has 300 crew to 750 passengers What is the ratio of passengers to crew? Q7. The teacher : student ratio in a school is 1:21 There are 24 teachers. How many students are there? Q8. An alloy contains copper and tin in the ratio 3:1 40g of tin is used to make the alloy. How much copper is used? Q9. Which of the following pairs of ratios are in proportion? Give reasons for your answers. a) 1 to 5 and 4 to 20 f) 2 to 6 and 3 to 9 b) 5 to 25 and 15 to 75 g) 18 to 12 and 40 to 60 c) 7 to 21 and 21 to 42 h) 9 to 18 and 18 to 9 d) 5 to 10 and 12 to 24 i) 6 to 30 and 5 to 20 e) 1 to 3 and 3 to 1 j) 5 to 25 and 20 to 100 Q10. Copy these pairs of equivalent fractions and fill in the missing numbers. a) 3 2 and 6 f) 8 9 and 24 b) 7 8 and 16 g)4 5 and 50

7 c) 3 4 and 9 h) and 3 d) 8 and 12 i) and e) 4 and 40 j) 1 and Q11. Simplify these ratios. a) 27:36 f) 45:75 b) 28:70 g) 20 minutes:1 hour c) 3kg:750g h) 8m:75cm d) 7 litres to 750ml i) $2 to 20 cents e) 3 hours to 1 day j) 8 weeks to 1 year Q12. a) divide 250 in the ratio 3:2 i) divide 144 in the ratio 1:2 b) divide 10 kg in the ratio 3:2 j) divide 1 hour in the ratio 5:7 c) divide 8m, in the ratio 3:2 k) divide 45 km in the ratio 7:8 d) divide 4 hours in the ratio 3:2 l) divide 2 kg in the ratio 3:7 e) divide 3 litres in the ratio 3:2 m) divide 1 m in the ratio 2:3:5 f) divide 70 litres in the ratio 1:2:4n) divide 1 hour in the ratio 5:6:9 g) divide 2 km in the ratio 3:8:9o) divide 9 kg in the ratio 3:14:19 h) divide $75 in the ratio 3:5:7 Q13. Simplify the following ratios: a. 3: 48 b. 50:75:125 c. 45:360 d. 15 litres : 3 litres e ml : 2.8 litres f. 2.5 cm : 5 m g. 3 7 : 1 2 h : Q14. A school has 25 teachers and 750 students. Write the teacher : student ratio in its simplest form. Q15. A builder mixes up a mortar by mixing 3 shovels full of cement with 12 shovels full of sand. Write the cement: sand ratio in its simplest form.

8 RATE Q1. A heater uses 3 units of electricity in 40minutes. How many units does it use in 2 hours? Q2. A machine prints 1500 newspaper in 45 minutes. How many does it print in 12 hours? Q3. A bricklayer lays 12 bricks in an average 8-hour day. How many bricks does he lay in 40- hour week? Q4. A combine harvester produces 9 tonnes of grain in 6 hours. How many tonnes does it produce in 54 hours? Q5.A machine puts tar on a road at the rate of 4 metres in 5 minutes. a) How long does it take to cover 1 km of road? b) How many metres of road does it cover in 8 hours?

9 ALGEBRA Q1. Simplify the following expressions using the correct order of operations. 1)2a + 3a 4a2)2b 5b + 7b b 3)3c + 2b + 2c 4b4)5d 4f + 3e 2d + f 2e 5)4g + 2 3g )3 2j k 4 j 2k 7)4m + 5 2n + 3p 4 n m p 8)8q + 6 4q 3r + 5t + 2(r 7t) 9)5u 8v + 9 2u 3v 4(2v 5u)10)7 4w + x + 2y 5(w x + 3y) Q2. i) Write the following expression for the distance around the edges of each of these shapes. ii) Simplify your expression where possible. a) b) c) d)e) f) Q3. Write the expressions for the area of these shapes

10 4. 5. e Q4. Write an expression for the total number of counters in each of these cases. a. 3 full boxes of red counters and 2 full boxes of blue counters. b. 1 full box of red counters, 3 full boxes of green counters and 5 full boxes of yellow counters. c. 4 full boxes of blue counters and 7 extra blue counters. d. I box of yellow counters from which 5 counters have been removed. e. 1 box of blue counters from which 25 counters have been removed and then the remaining number has been doubled. Q5.Simplify the following expressions a)2a + 3a + 5a b)4b 2b + 7b c)3c + 8 5c c d)4d d e)3e + 8e + 7 e f)6f 7f 3 + 4f 8 g)4g + 6 8g 9 h) i)6i 3i i 4 j)3j 4 + 8j 11 j

11 Q6. i) Write the simplified expression for the perimeter. ii) Derive a formula for the perimeter in the form P = a) b) c) d) e) Q7. Complete the following table by using algebraic shorthand to simplify, and the rules of arithmetic (BODMAS) to calculate. Simplify a. x + x + x b. 5y 4y c. z z z d. x + x + x y e. x + x + y + y f. y y g. x x + y y h. 5x + 3x 2y Q8. Simplify a. 5x + 7x x b. 3x + 10x c. 2x + 5x 4y d. 6x 3x + 2y y e. 2a + 5a 3a + 6b f. 3x g. 4z + 2w + 2z + w 2z h. 7c c + 6d 3 6d i a 3 a j. 4x + y 3x y k. 8x² + 4y² 7x² 2y² l. x² + xy + 4x² + 2xy m. 3x² + 2xy xy 4y² n. 5x²y² 3x²y x²y² + x²y o. 3x² 5x3 + 2x²y x²y p. 2x² + y² xy + x² q. 6x 2 + 2x 3x 2 + x

12 Q9. Translate each verbal phrase into an algebraic expression: a. 6 multiplied by m j. 8(r + 9) + 7r b. 13 plus f c. Take away 4 from y d. 10 times w e. 7 more than g f. k minus 16 g. One-Fifth of s h. The total of r and 10 i. q reduced by the quotient of 2 and 3 j. b separated into 9 equal parts k. sum of v and 3 l. d squared m. 5 fewer than g n.. x increased by 2 o. 8 divided by z p. The sum of b and 6 divided by 2 q. 5 times the difference of q and 1 r. The quantity k plus 10 divided by 4 s. 5 divided by z cubed t. 48 times the difference of a and 79 Q10. Simplify each expression. a. 2 (k + 4) + 7(2k 2) 2 b n + 5 2n 10 c. 3a 4 + 5a (a + 1) d s 4 + 3s e. 7p 6 + 8p 2 2p f. 15 3(y + 5 7) g. c c h. 10m m 3 + 5m i b + 4 5b + 26 k (7t 2) l. 4(3z z) 12 m. 3a²b² x 12ab 4 n. 2ab x ( 3abc) o. 49m² 7m p. 15e² 5e q. 6xy x ( 4xy )

13 Q11. Find the sum of: a. (2x 9y + 10), (10y + 5x 6) and ( 12x + 3y) b. (4a² 7y³ + 18), (2y³ 6a² 9) and (8a² 5y³ + 15) Q12. Subtract: a. (2a 3b + 6) from (15a + 17b 18) b. 8y 2 + 8x 2 from 4x 2 6y 2 c. (9x + 3y 21) from the sum of (5y + x 2) and (9 x 7y + 3) d. (6a² + 3b² 2) from the sum of (a² + 7b² 12) and (9 b² 7a² + 13) Q13.If a=5, b=-2 and c = 2; find the value of: a. a² b + c³ b. 2b³ 6 c. 8c² + 15 d. 2a³ + 6b² 9c e. 18a 2b

14 ANGLES Q6. Name the angles and sides shown by small letters is the diagrams below. (a) (b) c) (d) Q7. For each of the angles below states whether it is acute, obtuse,, reflex or a right angle and draw the angles from c k (a) (b) (c) 25 (d) 225 (e) 125 (f) 325 (g) 100 (h) 90 (i) 89 (j) 189 (k) 174

15 Q8. Using the facts that angles on a straight line add up to 180 and angles around a point add up to 360 degree, find the value of x in each of the following diagrams. (a) (b) (c) (d) (e)

16 AREA Q1. Calculate the area of each of these triangles. a) b) c) Q2. Use the formula for the area of a triangle to work out the missing values in this value. Base length Perpendicular height Area a 7.2cm 4.8cm b 20cm 100cm 2 c 15cm 15cm 2 d 11cm 55cm 2 Q3. Calculate the area of each of these shapes. a) b)

17 c) 4cm Q4. Calculate the area of the coloured region of each of these shapes. a) b) Q5. Calculate the area of the following: (a) (b)

18 (c) (d) Q6. Calculate the volume of the following: (a) A cube of side 7 m (b) A cube of side 10 cm (c) (d ) A cuboid measuring 2 cm by 5cm by 20cm Q7. Calculate the area and perimeters of the following: (a) (b)

19 PERIMETER Q1. Calculate the perimeters of the following shapes. (a) (b) (c) (d) (e) (f)

20 VOLUME Q1. Calculate the volume of each of these cuboids, where L = length, W = width, and H = length. a) L = 4cm, W = 2 cm, H = 3 cm b) L = 5 cm, W = 5cm, H = 6 cm c) L = 10 cm, W = 1 cm, H = 4 cm d) L = 40 cm, W = 0.2 m, H = 5 cm e) L = 50 mm, W = 30 cm, H = 0.1 m Q2. This cuboid has a volume of 360 cm 3. 5 cm x 12 cm Calculate the length (in cm) of the edge marked x. Q3. The volume of this cuboid is 180 cm 3. Calculate the length (in cm) of the edge marked y. Q4. Calculate the length (in cm) of the edge Q5.This cuboid has volume 768 cm 3 and marked p in this cuboid. Its volume is 320 cm 3. the edges marked a equal in length. Calculate the value of a.

21 SURFACE AREA Q1. Calculate the surface area of each of these cuboids. a)b) b) c) Q2. Acube has edge length 3 cm.calculate its surface area. Q3.A cube has sides of 5cm. Calculate a) the surface area of the cuboid b) the volume of the cuboid

22 COORDINATES Q1. Draw a grid with centre (0,0), the origin, and mark the x and y axes with scales from -8 to 8. Marks these points on your grid. A = (5,2) B = (7,3) C = (-8,5) D = (-6,-8) E = (7,-3) F = (6,-6) G = (2,4) H = (2,4) I = (3,-7) J = (3,-9) Q2.Draw a separate grid with x and y axes from -6 to +6. Plot the points, join them up in order and name the shape you have drawn. a) A(3,2) B(-3,4) C(-2,-4) D(-2,2) b) D(1,3) E(4,-5) F(-2,-5) c) G(-6,4) H(0,-4) I(4,-2) J(-2,6) Q3.Plot the P= (-6,4), Q= (6,4), and R= (6,-2). Plot point S such that PQRS is a rectangle. a) Write down the coordinates of S. b) Draw diagonals PR and QS. What are the coordinates of their point of intersection? c) What is the area of PQRS? Q4.(on the same graph of question 3) On the same grid plot points M = (-8,4) and N = (4,4). a) Joint points MNRS. What shape have you drawn? b) What is the area of MNRS? c) Explain your answer to parts b). Q5.(on the same graph of question 3) On the same grid plot point J where point J has y coordinate +10 and JRS forms an isosceles triangle. a) Write down the coordinates of J. b) What is the x coordinate of all the points on the line of symmetry of triangles JRS?

23 Q6.(a) Draw a grid with both the axes running from -10 to + 10, as in the diagram above. (b) Plot and label the following points. (i) A (6,1) (ii) B (-5,-3) (iii) C (4,-6) (iv) D (-8,5) Q7. (a) Draw another grid as on question 1. (b) Plot and label the following points. (i) A (3,1) (ii) B, (6,2) (iii) C, (3,7) (iv) D (-6,2) (v) E (-3,2) (vi) F(-3,7) (c) Join A, B and C to form a triangle. (d) Join D, E and F to form another triangle. (e) In what way are the two triangles the same? (f) In what way are they different? Q8. Write down the coordinates of all points in the diagram below.

24 STATISTICS Q1. Find the mean, median, mode, and range of each set of data set of data A B C D E Q2.Two discus throwers keep a record of their best throws (in metres) in the last ten competitions. Discus thrower A Discus thrower B As a coach, you can only choose one of them for the next competition. Which would you choose? Justify your choice mathematically. Q3. The mean mass of the 15 players in a rugby team is 85.2kg. The mean mass of the team plus a substitute is 85.4kg. What is the mass of the substitute? Q4. After 8 matches a basketball player has a mean of 27 points. After ten matches his mean was 31 points. How many points in total did he score in his last two matches? Q5. A factory makes tins of tomatoes. On the average, a full can should weigh 410g. A sample of 20 cans is tested. The weights are shown below Does the canning machine need to be adjusted? Give reasons for your answer

25 Q6. This frequency table shows the numbers of fish caught by the competitors in fishing competition over a two hours period. Calculate: a) the mean number of fish caught per competitor. b) the modal number of fish caught. Number of fish Frequency Q7. A DVD rental store keeps a record of the number of DVDS each customer rent over a one-week period. The result is shown in the table below. Calculate: a) The mean number of DVDS rented per person. b)the modal number of DVDS rented. Number of DVDs Frequency Q8. The number of passenger in cars and minibuses driving past a school gate one morning were recorded. The results of the survey are shown in the table. The total number of vehicles surveyed was 40 Number of Frequency passengers 0 6

26 Calculate: a)calculate the frequency of the vehicles with four passengers b)the mean number of number of passengers carried in the vehicles was Calculate the number of passengers represented by y in the table c) Deduce the modal number of passengers carried X y 2 Q9. Copy each of these frequency tables, and use them to: a) Calculate the mean, b) Work out the median, c) Find the mode For each of the data set. i. Data Value Frequency ii. Data Value Frequeny

27 iii. Data Value Frequency