The City School PAF Chapter Prep Section MATHEMATICS Class 6 Worksheets for Intervention Classes

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1 The City School PAF Chapter Prep Section MATHEMATICS Class 6 Worksheets for Intervention Classes

2 FACTORS, COMMON FACTORS, MULTIPLES, FACTOR TREE, INDEX NOTATIONS AND PRIME NUMBERS Q1. List all factors of the following numbers and circle the prime factors. (a) 6 (b) 9 (c) 7 (d) 15 (e) 24 (f) 36 (g) 35 (h) 25 (i) 42 (j) 100 (k) 66 (l) 75 (m) 28 (n) 48 (o) 120 Q2. Find the common factors of the following numbers. (a) 6, 12 (b) 35, 42 (c) 9, 15 (d) 10, 20, 30 (e) 24, 30, 36 Q3. Find the common factors of the following numbers. (a) 8, 12 (b) 10, 25 (c) 12, 18, 24 (d) 15, 21, 27 (e) 36, 63, 108 Q4. Find the prime factors of the following numbers. Express each number as a product of prime numbers, using indices (index notations) when needed. (a) 12 (b) 64 (c) 72 (d) 80 (e) 144 Q5. (a) List all the factors of 30. (b) List the prime factors of 30. (c) Write 30 as a product of its prime factors (Multiply out to check your answer.) (d) Write down the first three multiples of 30. Q6. 1, 4, 30, 45, 5, 15, 9, 1500, 3, 10 From this list choose: (a) The multiples of 15, (b) The factors of 15. The City School /PAF Chapter/Mathematics Intervention worksheet/year 6/2017 Page 2

3 Q7. Use a factor tree to find the prime factors of 240. Write your answer: (a) (b) as a list of prime factors, as a product of prime factors. Q8. Write down all the prime numbers between 20 and 40. Q9. Which of the following numbers are prime numbers'? , 53, 81, 87, 93, 101 Q10. Write down a list of numbers between 80 and 90. Including 80 and 90. From your list find: (a) two prime numbers, (b) three multiples of 5, (c) a factor of 348. Q11. List all the factors of 8. Then list all the factors of 12. Q12. List all the factors of: (i) 15 (ii) 35 (iii) 20 Q13. List the first six multiples of 12 and of 8. Q14. Write each of these using index notations, a) b) c) 5 x 5 x 5 x 5 d) e) Q15. Write each of these numbers in full and find its value. a) 3 4 b) 2 5 c) 5 4 d) 10 6 e) 4 3 The City School /PAF Chapter/Mathematics Intervention worksheet/year 6/2017 Page 3

4 LCM AND HCF, TEST OF DIVISIBILITY Q1. Find the highest common factor of 8 and 12. Q2. Find the highest common factor of 21 and 42. Q3. Write down the highest common factor of 15, 35 and 20. Q4. Write down the lowest common multiple of 12 and 8. Q5. Find the lowest common multiple of 3, 5 and 12. Q6. Find Lowest Common Multiple of each set of numbers (a) 2, 5 (b) 3, 4 (c) 3, 5 (d) 4, 6 (e) 10, 15 Q7. Find Lowest Common Multiple & Highest Common Multiple of each set of numbers (a) 6, 12 (b) 9, 6 (c) 14, 21 (d) 22, 33 (e) 8, 5, 10 Q8. Find Lowest Common Multiple of each set of numbers (a) 6, 14 (b) 4, 15 (c) 2, 7, 10 (d) 3, 9, 10 (e) 3, 7, 11 Q9. Test for divisibility by 2, 3, 5 and 9. Explain your reasoning Q10. Test for divisibility by 2, 3, 5, 6 and 9. Explain your reasoning. The City School /PAF Chapter/Mathematics Intervention worksheet/year 6/2017 Page 4

5 SQUARE, SQUARE ROOT, CUBE AND CUBE ROOT Q1. Calculate how many squares of side length 1 cm there are in squares with the following side lengths. a) 13 cm d) 11 cm b) 15 cm e) 12 cm c) 18 cm f) 100 cm Q2. Work out the square roots of the following numbers. Give positive roots. Q3. Evaluate the following: Q4. Workout the positive square roots of the following decimals. a) 0.25 b) 0.49 c) 0.64 d) 0.81 e) 1.44 f) 1.69 Q5. How many 1cm 1cm 1cm cubes would make up cubes with the following side lengths? a) 4 cm b) 6 cm c) 10 cm d) 9cm Q6. Workout the cube roots of the following numbers. a) 8 b) 125 c) 27 d) 1000 Q7. Workout the following, (a) 25 (b) 9 (c) 121 (d) 169 Q8. Write down: (a) The square of 6 (b) The square root of 9 (c) 2 (d) 25 (e) 100 (f) 10 Q9. Evaluate the following without using calculator. (a) (e) (b) (f) (c) (d) The City School /PAF Chapter/Mathematics Intervention worksheet/year 6/2017 Page 5

6 INTEGERS Solve the following Q1. (a) (+6) + (-3) (b) (+4) + (-4) (c) (+9) + (-6) Q2. (a) (-7) + (+5) (b) (-6) + (+5) (c) (-1) + (-7) Q3. (a) (-2) + (-4) (b) (-4) + (-1) (c) (-7) + (-1) Q4. (a) (-4) + (+4) + (-1) (b) (-3) + (-5) + (+6) (c) (+3) + (-6) + (-3) Q5. Write each of these sets of integers in order, lowest first. (a) (+6) (-3) (+9) (-5) (-1) (b) (+9) (-8) (-2) (+6) (-3) (c) (+5) (-5) (+2) (+4) (-9) (d) (+7) (-8) (+5) (+4) (-6) (-3) (e) (+12) (+43) (-21) (+65) (-43) (-26) Work out the answers to the following calculations. Q6. (a) (+5) - (+4) (b) (+6) - (+3) (c) (+6) - (+4) (d) (+5) - (+2) (e) (+7) - (+1) (f) (+8) - (+5) Q7. (a) (+3) - (+4) (b) (+5) - (+6) (c) (+2) - (+5) (d) (+1) - (+6) (e) (+2) - (+3) (f) (+8) - (+9) Q8. (a) (-3) - (+3) (b) (-4) - (+4) (c) (-2) - (+12) (d) (-3) - (+4) (e) (-1) - (+5) (f) (-6) - (+6) Q9. (a) (-9) - (-5) (b) (-3) - (-2) (c) (-4) - (-1) (d) (-8) - (-7) (e) (-4) - (-4) (f) (-9) - (-7) Q10. (a) (-3) - (-4) (b) (-2) - (-5) (c) (-2) - (-6) (d) (-4) - (-5) (e) (-3) - (-7) (f) (-2) - (-4) The City School /PAF Chapter/Mathematics Intervention worksheet/year 6/2017 Page 6

7 Q11. Find the new temperature for each of the following. (a) The temperature is -5 C and rises by 15 C (b) The temperature is -8 C and rises by 12 C (c) The temperature is -20 C and rises by 10 C (d) The temperature is -3 C and rises by 8 C (e) The temperature is 3 C and rises by 15 C (f) The temperature is 3 C and falls by 15 C (g) The temperature is 8 C and falls by 12 C (h) The temperature is -4 C and falls by 5 C (i) The temperature is -9 C and falls by 11 C (j) The temperature is 5 C below zero and falls by 16 C Q12. Work out the answers to the following calculations a) (+5) + (-3) b) (+7) + (-4) c) (+10) + (-6) d) (-8) + (-7) + (-4) e) (-7) + (-1) f) (-7) + (-5) g) (-5) + (+4) + (-1) h) (+9) - (+4) i) (+13) - (+4) j) (-6) - (+3) k) (-9) - (-15) l) (-8) + (-5) + (+6) m) (+5) - (+3) n) (+4) - (+6) o) (-4) - (+14) q) (-3) - (-12) r) (+12) (+5) s) (+7) + (-6) + (-3) t) (+11) (+4) u) (-5) + (+7) v) (+6) (+2) w) (-8) + (-7) x) (-22) (+12) y) (-3) (-12) z) (-4) (-11) Q13. Work out the following. a) (+8) (-6) b) (+6) (-5) c) (+4) (-7) Q14. Work out the following. a) (-5) (+4) b) (-7) (+9) c) (-7) (+7) The City School /PAF Chapter/Mathematics Intervention worksheet/year 6/2017 Page 7

8 Q15. Copy and complete this multiplication grid. x Q16. Work out the following. a) (+4) x (+2) b) (-3) x (+1) c) (+3) x-(-4) d) (-2) x (-5 ) e) (-5) x (-1) f) (-3) x (-3) Q17. Calculate the following. a) (+18) + (+6) b) (-18) + (-6) c) (18) + (+6) d) (-18) + (-6) e) (-24) + (-6) f) (-25) + (+5) Q18. Copy and complete the following, writing in the missing numbers to make the calculations correct. a) x (+5) = (+25) b) x (-3) = (-21) c) x (-5) = (-20) d) (+6) x = (-42) e) (-7) x = (-28) f) (-8) x = (+32) Q19. The table gives pairs of numbers x and y which add together to make 8. x + y = 8. Copy and complete this table. x y Q20. If p + q = 3, copy and complete this table. p q The City School /PAF Chapter/Mathematics Intervention worksheet/year 6/2017 Page 8

9 FRACTIONS Q1. Calculate the following, simplifying and writing your answers as mixed numbers if necessary: Q2. Simplify Q3. How many sweets would be in a bag of 28 sweets after 1 4 of them had been eaten? Q4. One third of a class of 45 students has gone away on a field trip. How many students have gone on the trip? Q5. Calculate the following, simplifying your answers and changing to mixed numbers as necessary. Q6. Place these fractions in order of size, starting with the smallest: Q7. Work out the following. Simplify your answers where possible. Q8. Work out the following. Simplify your answers where possible. Q9. Write down whether each of the following statements is true or false The City School /PAF Chapter/Mathematics Intervention worksheet/year 6/2017 Page 9

10 Q10. In a tennis match player A managed to get 13 of her first serves in. 25 Player B managed to gets 2 of her first serves in. Which player got a higher proportion of her first serves in? 5 Q11. Two schools hold their school plays on the same evening. At one school, 7 of the 20 audience are children. At the other, of the audience are children. Which school has the highest proportion of children in the audience? Q12. A tropical fruit juice states on the label that it is made up of the following fractions of fruit: 1 orange 1 mango 3 passion fruit 7 pineapple 15 grape Write down the fruits in ascending order of their proportion in the juice. DECIMALS Q1. (a) Convert each of the following fractions to decimals. (i) (iv) (ii) (iii) (v) (vii) The City School /PAF Chapter/Mathematics Intervention worksheet/year 6/2017 Page 10

11 (b) Put the fractions in part (a) in order of size, largest first. Q2. Convert each of the following decimals to fractions in its simplest form. (a) 0.3 (b) 0.12 (c) (d) 0.37 (e) Q3. Write each of the following sets of decimals in order of size, smallest first. a) 0.7, 0.5 b) 0.27, c) 0.625, 0.8, 0.73 d) 0.33, 0.303, e) 0.101, 0.01, 0.10 f) 0.32, 0.43, Q4. Rewrite each sum vertically and then carry out each operation: (a) (b) (c) (d) (e) (f) (g) (h) (i) (j) (k) (l) (m) (n) The City School /PAF Chapter/Mathematics Intervention worksheet/year 6/2017 Page 11

12 (o) (p) (q) (r) (s) Q5. Write the answers to the following: (a) (b) (c) (d) (e) (f) (g) (h) (i) (j) 2.97 x 19 (k) 1.76 x 46 (l) x 126 (m) x 370 Q6. Write the answers to the following: (a) (b) (c) (d) The City School /PAF Chapter/Mathematics Intervention worksheet/year 6/2017 Page 12

13 Q7. Calculate the following giving your answer as a decimal (non-recurring/terminating or recurring decimal) (a) 5 4 (b) 26 8 (c) (d) Q8. Find the cost of 6.5 meter of cloth at $ per meter Q9. Akram purchased 17.5kg of sugar. He wants to put it in bags. If one bag contains 3.5kg of sugar, find the number of bags required for this purpose Q10. The product of two decimal numbers is If one of them is 2.16, find the other Q11. The price of a book is $.6.25 and that of a pen is $ 12.75, then find a. What is the total of a book and a pen b. How much more does the pen cost than the book c. What is the cost of 12 books? d. What is the cost of 20 pens? ROUNDING OFF Q1. Round the following numbers (i) to the nearest thousand, (ii) to the nearest hundred and (iii) to the nearest ten. (a) (b) (c) (d)58437 Q people attended a football match in Madrid. (a) This was reported in the programme as attendance. (b) The club estimate was in the crowd. (c) A closer estimate in a newspaper was All of those estimates are acceptable. However, they are to different degrees of accuracy. Write down the degree of accuracy for each one. The City School /PAF Chapter/Mathematics Intervention worksheet/year 6/2017 Page 13

14 Q3. Round the following numbers to the nearest thousand. (a) (b) 9288 (c) (d) Q4. Round the following numbers to the nearest hundred. (a) 483 (b) 1692 (c) 93 (d) Q5. Round the following numbers to the nearest ten. (a) 63 (b) 846 (c) 5839 (d) 8 Q6. Round the following numbers (i) to the nearest whole number and (ii) to one decimal place. (a) 6.37 (b) 4.13 (c) 0.85 (d) (e) (f) Q7. Round the following numbers (i) to the nearest whole number and (ii) to two decimal place. (a) (b) (c) (d) (e) (f) Q8. Round the following numbers (i) to the nearest whole number and (ii) to three decimal place. (a) (b) (c) (d) (e) Q9. Round each of these numbers to the degree of accuracy shown in brackets. a) 4865 (nearest ten) b) 7843 (nearest hundred) c) (nearest thousand) d) (nearest hundred) e) 684 (nearest ten) f) 7346 (nearest hundred) g) (nearest thousand) i) (nearest thousand) j) (nearest thousand) The City School /PAF Chapter/Mathematics Intervention worksheet/year 6/2017 Page 14

15 Q10. A survey showed that cars went through a village on one Saturday. a) Round this number (i) to the nearest ten (ii) to the nearest hundred and (iii) to the nearest thousand. b) Which number might be used by a local newspaper campaigning for safe crossing to be built in the village? Q11. A village hall holds 567 people. a) Round this number to the nearest hundred. b) What would you say is its safe capacity to the nearest hundred? Q12. The rock band muse played in front of people in China. Round this number to the nearest thousand. Q13. From London to Boston is 4827 km. Round this distance to the nearest 100 km. Q14. A company made a profit $ Round this amount to the nearest $ Q15. Round each of the followings (i) to the nearest whole number, (ii) to one decimal place and (iii) to two decimal places. (a) (b) (c) (d) (e) (f) (g) (h) (i) (j) The City School /PAF Chapter/Mathematics Intervention worksheet/year 6/2017 Page 15

16 Q16. The table shows the capacities of some of the largest sports stadiums in the world. round the number for the capacity of each stadium to the nearest thousand. Stadium Sport Capacity Rungrado May Day Stadium Pyongyang, North Korea Association Football Salt Lake Stadium Kolkata India Association Football Michigan Stadium Ann, Arbor, USA Association Football Estadio Azteca Mexico city, Mexico Association Football Melbourne Cricket Ground Melbourne, Australia Cricket, Association Football Azadi Stadium- Tehran, Iran Association Football Camp Nou Barcelona, Spain Association Football FNB Stadium - Johannesburg, South Africa Association Football Gelora Bung Karno Stadium Jakarta, Indonesia Association Football Bukit Jalil National Stadium Kuala lumpur, Malaysia Association Football Estadio do Maracana Rio de Janeiro, Brazil Association Football Q17) A bridge can safely carry a weight of tonnes. Round this weight sensibly to a whole number of tonnes. Q18) A pilot needs to know the height of a mountain the aircraft is to fly over. The mountain is 6.35km high. Round this height appropriately: a) to a whole number of kilometers b) to one decimal place. Q19) An aqualung will work safely to a depth of 67.3 meters. What rounded figure would you use as the safe working depth? Q20) A stadium has seats. What would you say was its maximum capacity: a) to a whole thousand b) to a whole hundred? The City School /PAF Chapter/Mathematics Intervention worksheet/year 6/2017 Page 16

17 Q21) A bridge is to be built over a river 2315 m wide. Write down a sensible estimate of its length, to a whole 100 m Q22) Round to the stated accuracy to the nearest ten to the nearest ten to the nearest hundred to the nearest hundred to the nearest ten to the nearest hundred to the nearest thousand to 1 decimal place to 2 decimal places to 3 decimal places to 1 decimal place to 2 decimal places: The City School /PAF Chapter/Mathematics Intervention worksheet/year 6/2017 Page 17

18 NUMBER SEQUENCE Q1. 4,5,6,7 for the given sequence shown. Find the 50 th term Q2. 7, 8,9,10 for the given sequence shown. Find the 50 th term Q3. -6, -3, 0, 3, 6, 9,..., Find: (a) the next two terms Q4. 16, 25, 36, 49 Find: (a) the next two terms Q5. 3, 6, 11, 18, 27, 38, Find: (a) the next two terms Q6. Shape Number Number of sides Number of diagonals (a) (b) Copy the diagram above and fill in the blank spaces How many sides would there be in the 50 th shape? The City School /PAF Chapter/Mathematics Intervention worksheet/year 6/2017 Page 18

19 Q7) These diagrams show the first three patterns in a sequence of growing tile patterns. a) Draw the next two diagrams in the sequence. b) Copy and complete this table Number of white tiles Number of red tiles c) Describe the pattern linking the number of white files and the number of red tiles. d) Use your rule in part c) to predict the number of red tiles in a pattern with 100 white files. Q8). a) Draw the next two diagrams in the sequence. b) Copy and complete this table. Number of white tiles Number of green tiles c) Describe the pattern linking the number of white tiles and the number of green tiles. d) Use your rule in part c) to predict the number of green tiles in a pattern with 100 white tiles. The City School /PAF Chapter/Mathematics Intervention worksheet/year 6/2017 Page 19

20 Q9) a) Draw the next two diagrams in the sequence. b) Copy and complete this table Number of white tiles Number of orange tiles Q10) a) Draw the next two diagrams in the sequence. b) Copy and complete this table Number of white tiles Number of blue tiles Q11) The City School /PAF Chapter/Mathematics Intervention worksheet/year 6/2017 Page 20

21 a) Draw the next two diagrams in the sequence. b) Copy and complete this table Number of white tiles Number of yellow tiles SYMMETRY State the number of lines of symmetry (if any) for each of the shapes shown below Regular pentagon The City School /PAF Chapter/Mathematics Intervention worksheet/year 6/2017 Page 21