MATHS WORKSHEET NAME GRADE 6 Date I. Evaluate the following: a) 2y+6 where y=5 (b) at+3a (d) (y +2)2 + (40 - xy) c) 3n-8 ifn=8 e) t2 -6 where t=5; (f) 15—y3 when t=8 a=7 when x=5; y 7 when y=2 (h) (3p-4)(p+2) where p=5 g) (n+3) (n -2) when n=7 II. Simplify the following: (c) 3y + 7z — 2y + 4y — 3z (b) 2a+6b-2b—a+5a a) 5p-4q+6p-2q+7 ci) y- 3p+5y +6p+9-2y (f) 2p+4q-3q—p+5 (e) 3e+5f—f Ill. Expand and simplify: a) 3(y+6) e) 3(3y-5)+2(7y+8) (b) 2(3p-2) (c) 4(3x+2y-2x—y) (f) 4(3w +7) + 3(8 — w ) Page 1 of 11 (d) 5(2p—p) (g) 5(3a+2b) +3(4b—a) IV. Solve the equation: a) p+8=15 (b) 4y-3=29 (c) 2b+8=20 e) 4a-8=24 (f) 3(2x+4) =48 (g) 5(3y-2) = 20 (d) 4y+2=54 (h) 2(5+4a)=66 V. Write the equation and solve: a) I think of a number, multiply it by 3 and add the result to 7. The total is 28. What is the number? b) I think of a number, double it and add 3. The result is 15. What is the number? c) The lengths of three sides of a triangle are n cm, n cm and 6 cm. The perimeter is 20 cm. Find n. d) A fishing rod is 27 feet long and consist of three parts. The first part is x feet long, the second part is 1 feet longer than the first and the third is 1 feet longer than the second part. Form an equation in x and solve it to find the length of each part. e) I bought a magazine for £5 and four erasers. I spent a total of £25. How much does each eraser cost? f) The sum of 3 consecutive number is 72. Find the numbers. g) How old am I, if 40 reduced by 2 times my age is 24.? h) The sum of three consecutive even number is 48. Find the numbers. i) Jack has some CDs. John has 9 more CDs than Jack. David has 7 times as many CDs as Jack. Altogether they have 45 CDs. How many does each person have? Page 2 of 11 Geometry and Measures I. Complete the following sentences: 1. When two rays meet at a point an formed. 2. A Right angle measures 3. A straight line angle measures 4. An angle less than 900 is called an 5. An angle more than 900, but less than 1800 is called an 6. A angle. measures more than 1800 . 7. The sum of angles around a point is 8. A closed shape with 3 angles and 3 sides is called 9. A triangle with 3 equal sides and 3 equal angles is called an 10. A triangle with 2 equal sides and 2 equal angles is called an 11. A triangle with one angle as a right angle is called 12. The sum of angles in a triangle is a 13. One angle of an equilateral triangle is 14. Angles on a straight line add up to 15. If one angle in a right angled triangle is 16. 350, the other two angles are and lines meet another line at a right angle. 17. Base angles of an Isosceles triangle are 18. What is the angle made by an hour hand in one hour? 19. A clock is started at 6 o'clock in the morning. Though how many degrees will the hour hand rotate when the clock shows 11 o'clock in the morning? 20. lines always remain the same distance apart from one another. Il. Use a protractor to measure the following angles. Page 3 of 11 III. Without using a protractor, write down the measures of the following angles. 3 a) N IV. Use a protractor to draw the following angles: 0 a) LABC = 45 (b) L PQR =100° (c) LXYZ = 135° (d) LEFG = 225° e) LXYZ = 65° (f) LABC = 315° (g) L PQR = 80° (h) LRST = 105° V. Calculate the missing angles: (Give reasons for your answer) a a) L. W c) Page 4 of 11 VI. Construct these triangles with the given measures. a) A ABC; where BC = 5.5 cm; LB = 65°; LC = 400 b) A PQR; where QR = 6 cm; RP = 4.5 cm; LR = 65° c) A EFG; where EG = 7 cm; FE = 6.3 cm; LF = 850; Measure EG. d) A XYZ; where XY = 6.5 cm; LY = 75°; LX = 45°; Measure LZ VII. Calculate the missing angles: a) ge 5 of 11 Not to sI. 110* Page 6 of 11 PROBABILITY 1. How many possible outcomes are there in the following experiments? a) Tossing a lOp coin. b) Taking a disc from a bag containing 1 red, 1 blue and 1 yellow disc? c) Choosing a card from a pile of ordinary playing cards. d) Choosing one number from the first 5 prime numbers. 2. In the following questions, assume that all possible outcomes are equally likely. a) One letter is chosen at random from letters of the word SALE. What is the probability that it is A? b) What is the probability of choosing the colour blue from the colours of the rainbow. c) What is the probability of choosing an integer that is exactly divisible by 5 from 6, 7, 10, 11, 12? d) In a raffle 200 tickets are sold. If you have bought one ticket, what is the probability that you have got 15t prize? 3. A box of replacement lights for Christmas set has S plain, 8 red, 3 blue and 4 green lights. If one is selected at random what is the probability that it will be a) red (b) green (c) yellow (d) plain 4. Two bags of sweets contain different numbers of strawberry and orange sweets. Bag 1 has 13 strawberry sweets and 11 orange sweets. Bag 2 has 15 strawberry sweets and 9 orange sweets. Emma does not like strawberry sweets. She can take a sweet at random from either bag. Which bag should she pick from? Why? 5. The probability that Maria will pass her next maths test is 0.68. What is the probability that Maria will not pass her next Maths test. Page 7 of 11 Fractions, decimals and percentages 1. An average banana weighs 120g, a super size banana is 10% is heavier. How much does a super-size banana weigh in grams? 2. Henry earns £500 per week. If he keeps being late for work and gets a 25% pay cut, what is his new salary each week? 3. Match each sentence with a percentage. Use a line. *76% Eight out of ten people trust their dentist. *78% . Fifteen out of twenty people don't use public transport. • Nineteen out of twenty five homes have window locks. • Thirty nine out of fifty people listen to music regularly. *75% *80% 4. a Which of those has the greatest percentage shaded? A B LtJtLIIL C 5. Testing times . .. a Mark got 80% in his geography test. Write this as a decimal. b You need to get at least Did he pass? 3 of the questions right to pass a driving test. Matthew got 72 right. c Ashleigh got 65% in her science test. Write this as a fraction. d Beth got 56 out of 100 in her ballet exam. Write this as a percentage _____, decimal fraction e Fenton got 90 out of 100 questions in his maths test right. What fraction did he get wrong? Page 8 of 11 and 6. A pet shop had 6 puppies. 5 of them were sold. a) What fraction is sold? b) What fraction is left? 7. Choose two fractions that are equivalent. 231 a) — -- 452 8. 12412 (b) -— - 20515 of a stall at a fair is used for sweets and 1 for cakes. The rest is used for biscuits. What fraction the stall is left for biscuits? 9. Which is greater, 70% of 45 or 45% of 70? 10. Arrange in order, small to big. 75% 0.9 11. How many in 2Y~ ? (a) 12. Write a percentage that is bigger than these fractions. 13. Write a decimal number between these. (a) 1/z 70% (b) (b) 5% % 14. 1500 people went to a play at the Sunset Theatre. 15% had seen the play before. How many had not seen the play before? 15. There are 80 pupils on a computer camp. 30% are under 14. How many are under 14? 16. Put<, a) 40% > or = (b) 0.7 (c) 33% 0.4 17, In a school there are 600 students and 50 teachers. 15% of the students are left-handed. 12% of the teachers are left-handed. How many left-handed students and teachers are there altogether? Page 9 of 11 NUMBERS 1. Circle the following: 39 47 5 13 83 91 11 a) Prime numbers 5 6 12 15 24 36 b) Triangular numbers. c) Square numbers 4 6 9 25 62 81 196 200 2. Work out the following: (b) 92 42_ a) 52 18= (d) 112 +62 (c) 132 -- 95 = 3. Complete the following: a) 12x3 e) 54— (b) =9 x5=45 (f) 30 x 40 = (c) 15X (g) = 1500 10 = 160 (d) 42 x 30= (h) 2800 + - 4. Answer the following: a) How many nines are there in 864? b) One pencil costs isp. Find the cost of 24 pencils. c) How many hundreds are there in 38109? d) I think of a number. I double it and add 5. The answer is 13. What is my number? e) Alex cut 12 pieces of wool, each 28 cm long, from a 400 cm length. What length of the wool was left? f) Total weight of 1 text book and 9 note books is 975 grams. The weight of the text book is 300 grams. If the note books are of the same weight, find the weight of each note book. g) Amy put 248 photographs into an online photo album. On each page she could fit in 10 photos. i) How many photos were on the last page? - (ii) How many pages were full? Page 10 of 11 = 28 h) Temperature during the day is 6°C. At night it falls by 7°C. What is the new temperature? i) Tom earns £20 per hour. How much will he earn in a 40 hour working week? j) If I halve my number, my answer is 16. What is my number? ) Jack bought 15 apples at 35p each. How much did he pay? A fruit seller had 1136 oranges. 16 of them were rotten. He packed the rest into boxes of 8. How many boxes of oranges were there? n) During the last half of 2010, Mr. Wilson's salary was £1985 each month. He saved £4025 during those six months and spent the rest. How much did he spend? n) Greg and Harry each buy a book. Greg pays with a £5 note and gets £1.05 change. Harry's book costs £7. How much more does Harry's book cost than Gerg's book? o) Ten friends won £36.50. It was shared evenly between them. How much did each get? p) I think of a number. I double it and add 5. The answer is 13. What is my number? q) I have two numbers. The sum of my numbers is 1000. The difference between my two numbers is 100. Find my numbers. r) Sue had 250 stickers first. Her mother gave her another 178 stickers. How many more stickers would Sue need in order to fill up her sisters album with 1000 stickers. Page 11 of 11