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. 87.5 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.

Q3.710 of the surface of the earth is water. Express this as a percentage.

Q4. There are 200 birds in a flock. 120 of them are female. What percentage of the flock is a) Female b) Male

Q5. Write these percentages as fractions of 100.a) 73% b) 28% c) 10% d) 25%

Q6. Write these fractions as percentages.

a) 27100 b)

310 c)

750 d)

14

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

Question Bank for grade 6

d) 0.05 e) 0.2 f) 0.75

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.

Q10.310 of the surface of the earth is land. Express this as a decimal and a percentage.

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 a fraction in its simplest form. a) 23% b) 68% c) 70% d) 75%

Q13. Write these fractions as percentages.

a) 49100 b)

910 c)

1750 d)

34

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. Work out the following.

a. 10% of 60 b. 25% of 160 q. 87.5% of 80

c. 12.5% of 80 d. 37.5% of 80 r. 10% of 110

Question Bank for grade 6

e. 46% of 50 f. 50% of 46 t. 45% of 90 g. 70% of 125 h. 7% of 125i. 12% of 180 j. 36% of 180k. 90% of 90 l. 7% of 375m. 9% of 90 n. 60% of 180o. 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 90c. 6 out of 60 d. 36 out of 60e. 7 out of 70 f. 21 out of 70g. 45 out of 900 h. 135 out of 900i. 11 out of 44 j. 11 out of 440k. 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 2 and 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 175000 sports cars a year. They are only available in white, black and red. 52500 are white, 78750 are black and the rest are red.

Question Bank for grade 6

a) What percentage of the cars are black?b) What percentage is white?c) What percentage is red?

Q25. Copy and complete these sets of equivalent fractions and percentages.

1) 824

= 1❑ 2) 59= ❑18

3)710

=% 4) 11100

=¿¿

5)1350

=¿% 6) 1751

= 1❑ 9)

750

= ❑100

=¿%

7)825

=❑50

=¿% 8) 10125

= ❑1000

=¿% 10¿351000

= ❑200

=¿%

Q26. Which of the following are equivalent (in proportion)? Give reasons for your answers.

1) 1100.110% 2)

150.550% 7)

230.660%

3) 180.12512.5% 4)

130.33% 8)

9100

0.99%

5) 450.88% 6)

380.37537.5% 9)

1200.055%

10) 22.0200%

Q27. Copy and complete this table.

Fraction Ratio Percentage12

1 to 2 50%

14

1 to ___ 25%

34

____ to 4

Question Bank for grade 6

18

1 to ____ 12.5%

38

____ to 8

58

5 to ____

78

87.5%

110

1 to ____ 10%

210

∨15

____ to 5 20%

310

3 to ____

410

∨25

____ to 5

610

∨35

____ to 5

710

70%

810

∨45

910

9 to 10

Q28. Complete the following table.

Fraction Decimal Percentage

12

0.25

110

0.3

0.2

12.5%

Q29. Calculate the following, showing your method.

Question Bank for grade 6

a. 75% of 64b. 30% of 1550c. 9% of 3400d. 55.5% of 680e. 3% of 73

Q30. Calculate the first number as a percentage of the second:

a. 35, 140b. 72, 600c. 23, 50d. 40, 125e. 17, 250

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 passengersWhat is the ratio of passengers to crew?

Q7. The teacher : student ratio in a school is 1:21There are 24 teachers. How many students are there?

Q8. An alloy contains copper and tin in the ratio 3:140g 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) 32∧6

❑ f)

89∧24

❑

b)78∧❑

16 g)

45∧❑

50

c)34∧9

❑ h)

1824

∧3

❑

d)812

∧12

❑ i)

1636

∧24

❑

e) 410

∧40

❑ j)

19∧9

❑

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 1:2:4 n) divide 1 hour in the ratio 5:6:9 g) divide 2 km in the ratio 3:8:9 o) 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 : 48b. 50 : 75 : 125

c. 45 : 360d. 15 litres : 3 litrese. 14000 ml : 2.8 litresf. 2.5 cm : 5 m

g.37 : 12

h. 234 : 1

25

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.

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?

ALGEBRA

Q1. Simplify the following expressions using the correct order of operations.

1) 2a+3a−4 a 2) 2b−5b+7b−b 3) 3c+2b+2c−4 b 4) 5d−4 f+3e-2d+f−2e 5) 4 g+2 (3 g−4 h )+2h 6) 3 (2 j−k )−4 ( j−2k ) 7) 4m+5 (2n+3 p )−4 (n−m−p ) 8) 8q+6 (4 q−3 r+5 t )+2(r−7 t) 9) 5u−8v+9 (2u−3v )−4 (2v−5u) 10) 7 (4w+x+2 y )−5(w−x+3 y )

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.

1. 2. 3.

4. 5. e+1 6.

6

7.

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+5 a b) 4 b−2b+7b c) 3c+8−5c+7+8c d) 4 d−5+8−2d e) 3e+8e+7−e f) 6 f−7 f−3+4 f−8 g) 4 g+6−8g−9 h) 3h−7−9h+11 i) 6 i−3 i−14+9 i−4 j) 3 j−4+8 j−11− j

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.

Simplifya. x+x+xb. 5 y−4 yc. z× z× zd. x+x+x – ye. x+x+ y+ yf. y – yg. x× x+ y× yh. 5 x+3x –2 yQ8. Simplify

a. 5 x+7x – x b. 3 x+10x

c. 2 x+5 x – 4 yd. 6 x – 3 x+2 y – ye. 2a+5a – 3a+6bf. 3 x+10– 7g. 4 z+2w+2 z+w– 2 zh. 7c – c+6d –3 – 6di. 6+3 a– 3– aj. 4 x+ y−3 x− yk. 8 x ²+4 y ² – 7 x ²−2 y ²l. x ²+xy+4 x ²+2 xym. 3 x ²+2xy – xy – 4 y ²n. 5 x ² y ² –3 x ² y – x ² y ²+x ² yo. 3 x ² – 5x 3+2 x ² y−x ² yp. 2 x ²+ y ²−xy+x ²q. 6 x2+2 x – 3 x2+x

Q9. Translate each verbal phrase into an algebraic expression:a. 6 multiplied by m

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 partsk. sum of v and 3 l. d squared m. 5 fewer than gn. . x increased by 2 o. 8 divided by z p. The sum of b and 6 divided by 2q. 5 times the difference of q and 1r. 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)–2b. 12+4 n+5 –2n –10c. 3a – 4+5 a+7+2(a+1)d. 3+2 s – 4+3 se. 7 p– 6+8 p –2 – 2 pf. 15 –3( y+5– 7)

g. c+6+4c –3+4h. 10m+2+7m– 3+5m

i. – 86– 2 (11b )+4 (5b )+26

j. 8(r+9)+7 r

k. –20+5(7 t – 2)l. 4 (3 z+5+7 z) –12

m. 3 a ²b ² x 12ab4n. 2ab x (−3abc)

o. −49m ²÷7m

p. 15e²÷5e

6 xy x(−4 xy )Q11. Find the sum of:a. (2 x−9 y+10), (10 y+5 x−6)∧(−12 x+3 y)b. (4a ²−7 y ³+18) ,(2 y ³−6 a ²−9)∧(8a ²−5 y ³+15)

Q12. Subtract:a. (2a−3b+6)¿(15a+17b−18)

b. (8 y2+8 x2 )¿ (4 x2−6 y2 )

c. (9 x+3 y−21) from the sum of (5 y+x2)∧¿)

d. (6a ²+3b ²−2) from the sum of (a ²+7b ²−12)∧(9b ² – 7a ²+13)

Q13. If a=5, b=-2 and c = 2; find the value of:

a. a ²−b+c ³b. 2b ³−6c. 8c ²+15d. 2a ³+6b ²−9c

18a−2b

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°

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)

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 7.2 cm 4.8 cmb 20 cm 100cm2

c 15 cm 15cm2

d 11 cm 55cm2

Q3. Calculate the area of each of these shapes.

a)

b)

c)

Q4. Calculate the area of the coloured region of each of these shapes.

a)

b)

Q5. Calculate the area of the following:

(a) (b)

4cm

(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)

PERIMETER

Q1. Calculate the perimeters of the following shapes.

(a) (b)

(c) (d)

(e) (f)

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 cmb) L = 5 cm, W = 5cm, H = 6 cmc) L = 10 cm, W = 1 cm, H = 4 cmd) L = 40 cm, W = 0.2 m, H = 5 cme) L = 50 mm, W = 30 cm, H = 0.1 m

Q2. This cuboid has a volume of360cm3.

5 cm

x

12 cm

Calculate the length (in cm) of the edge marked x.

Q3. The volume of this cuboid is 180 cm3. 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 cm3 and marked p in this cuboid. Its volume is 320 cm3. the edges marked a equal in length. Calculate the value of a.

SURFACE AREA

Q1. Calculate the surface area of each of these cuboids.

a) b)

b)

c)

Q2. A cube has edge length 3 cm. Calculate its surface area.

Q3. A cube has sides of 5cm. Calculate a) the surface area of the cuboidb) the volume of the cuboid

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?

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.

STATISTICS

Q1. Find the mean, median, mode, and range of each set of data set of data

A. 1 1 2 3 3 4 4 4 4 5 5 B. 3.2 4.8 5.6 5.6 7.3 8.9 9.1 C. 1 2 3 4 4 3 2 4 2 3 6 4 0D. 17 23 36 112 18 23 40 23 E. 1 2 0 2 1 0 2 3 4 1 5 0 3 2 1

Q2. Two discus throwers keep a record of their best throws (in metres) in the last ten competitions.

Discus thrower A 32 34 32 33 35 35 32 36 36 35

Discus thrower B 32 30 38 38 33 34 36 38 34 32

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.

410 410 411 412 408 411 409 414 416 410 410 412 413 415 410 415 409 410 412 411Does the canning machine need to be adjusted ? Give reasons for your answer

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.

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.

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

Calculate: a) Calculate the frequency of the vehicles with four passengersb) The mean number of number of passengers carried in the vehicles was 2.75. Calculate the number of passengers represented by y in the tablec) Deduce the modal number of passengers carried.

Number of fish Frequency0 61 202 453 704 355 106 2

Number of DVDs Frequency1 202 653 1104 305 4

Number of passengers

Frequency

0 61 42 83 104 Xy 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 Frequency100 7110 10120 15130 2140 6150 3160 7

ii.

Data Value

25 26 27 28 29 30 31

Frequeny 51 70 69 32 15 43 15

iii.

Data Value Frequency12.4 312.5 512.6 212.7 112.8 012.9 513.0 013.1 2