2 a. What is the total cost of a fidget. 1. Calculate the following: spinner costing 4.68 and a cricket ball. a costing 8.59?
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1 Revision Pack REMOVE November 2017 This is the Upper summer pack to help you revise. NO CALCULATORS to be used unless π is needed or the question says to. 1. Calculate the following: a Name: 2 a. What is the total cost of a fidget spinner costing 4.68 and a cricket ball costing 8.59? Answer: b Answer: b. How much change would I receive from a 20 note? Answer:. c. 253 x 19 Answer: c. How much would 7 fidget spinners cost? Answer: d Answer: d. A multi-pack of 6 cricket balls is on e Answer:.. offer at How much does that mean 1 cricket ball costs in this pack? Answer:.. Answer:
2 3. Given that 42 x 24 = 1008, answer the following: 4 2 x 0 24 = 6a. Rewrite the following sum with each number correct to one significant figure: x 24 = x 25 = = 1 42 x 1 24 = b. Use this to estimate an answer to the calculation: Rewrite the following to the number of significant figures shown (1sf) = (2sf) = (3sf) = (1sf) = (2sf) = 5. Rewrite the following to the number of decimal places shown: (1dp) = (2dp) = (3dp) = (2dp) = (2 dp) = Answer:. c. Now USE THIS ANSWER to ESTIMATE the answer to: Answer:. d. Using a calculator, write down the value of this calculation in (c). Write down ALL the digits seen on your calculator: e. Give your answer in (c) to 3sf
3 7a. List the factors of Complete these equivalent fractions:. 1 7 = = = 32 b. List the prime numbers between 30 and 40.. c. Express 180 as a product of its prime factors, using indices. 9. Simplify these fractions: Calculate the following: f g = d. What is the smallest number we need to multiply 180 by in order to obtain a square number? h i e. What is the biggest odd number which is a factor of 180?.. j. 5 8 x 4 25 f. A certain number = 3 4 x 7 2 k x 6 7 What is the square root of this number? l m
4 12. Complete this table: (fractions in 11a. Jessie the dog eats 2 of a large bag 3 of dog food. Her puppy, Betsy eats 1 5 of the bag. What fraction of the bag have they both eaten in total? their simplest form, cancelled down) fraction decimal percentage b. What fraction of the bag remains? % 12 5% 13. ORDER the following numbers in order of size, starting with the smallest: 17 20, 80%, c. The large bag weighs 6kg. How much did Jessie s food weigh in kg? 11 25, 41%, 0.46 d. What is the ratio of Jessie s food to 0.909, 99%, 9 10 Betsy s food?
5 14. Simplify these expressions: 4h + 5h = 5m + 6n 7m = 7g 2 + 7g + 7g 2 = 6k 3j 4k + 7j = 16. If r = 3, s = 4 and w = -2, find the value of: rw 3s + 4r Multiply out the brackets and simplify: 5(r + h) = 7(3 s) = 3(f + 4) 2f 2w r s w 2r 2 5z + 2(3z 2) s 2 w 2 2(f + 3r) + 3(2f r) (s + w) 3 5(h 3) + 3(5 h) r+w r w 4(2m 3b) 2(m 3b) 17. Solve these equations: 3 + y = 7 5(7 + 4f) 3(3f + 5) 4y = 24 3y 5 = Fully factorise the following: a. 4a + 8 = b. 14b 35 = c. 15 c² + 10 = d d = y 4 = 8 5y = 3 e. 2mn + mp =
6 4y 3 = 2y My father gave my brother 125 and he gave me 75. In what ratio did he share his money? 6(y + 3) = Calculate the value of: : 21. I planted tulips daffodils and freesias in the ratio 3:5:4. Altogether I planted 60 bulbs. How many of each did I plant? x 5 = 3 x (4 3) 2 = = = Tulips:.. Daffodils:. Freesias: x = = 22. In a different bed, when I planted tulips, daffodils and freesias in the ratio 3:5:4, I planted 12 more daffodils than tulips. How many freesias did I plant in this bed? 30 5 x 6 = 19. In our library, fiction: non-fiction books are stocked in the ratio of 7:2. If there are 1400 fiction books, how many nonfiction books are there?.
7 23. Calculate 27. After buying a CD for 6.00 I sold it for What was my percentage loss? 10% of 60 = 30% of 60 = 40% of 8 = 5% of 7 = 3% of 50 = 75% of 120 = On a journey of 180 miles, Emma travels 108 miles before stopping for a cup of coffee. What percentage of the journey does she still have to travel? 24. When I bought a shirt priced 24, I was given a 20% discount. How much did I pay for the shirt? What is 2 as a percentage of 2.50? 29a) Mr X earned 2000 last month. He paid 22% tax on this amount. How much tax did he have to pay? I bought a book for 8.40 and later sold it on EBay, making a profit of 25%. How much did I sell it for?.. b) The following month his earnings increased by 5 1 %. How much had his salary 2 increased by?....
8 30. The accompanying graph shows Marie s distance from home (A) to work (F) at various times during her drive. 32a) An Olympic sprinter can run 12 metres in a second. How far could he run in one minute? Answer:. b) What would his speed be in km per hour? a) She left her briefcase at home and had to go back for it. Which letter on the graph shows the point that she turned around to fetch it? b) She had to wait at a train crossing for a train to pass. How long did she have to wait?.. c) What was her speed in miles per hour between E and F?. d) What was her average speed in miles per hour for the trip from C to F?.. e) On which two legs of the journey did Answer: A plane travels at 300 km/hour. How long would it take to cover 200km? she travel fastest? i. Between.. and. ii. Between.. and. 31.It is 330 miles from London to Edinburgh. My plane leaves at and arrives at What is the average speed of the plane? Answer: Traveling at 45km/hour, how long would it take me to cover a distance of 105 km? Answer:....hours...min
9 35. In a test a group of children scored the following results: 5, 7, 3, 8,2, 4, 3, 7, 3, 6 a) What was the modal score? Answer: b) What was the median mark? 39. The temperatures measured at midnight one week were -3, 0, 1, 7, -5, 3, 0. What was the range of temperatures? Answer: 40. In a test, the marks scored by the children are 1, 5, 6, 11, 3, 4, 5. What was the median score? Answer:.. c) What was the mean mark? Answer: 36. A fisherman caught 5 fish with masses of 200g, 300g, 220g, 190g and 90g. what was the mean mass of the fish? Answer: 41. In a maths test, the marks for the boys were 9, 3, 5, 7, 4, 8 and the marks for the girls were 10, 6, 7, 3. a) Find the mean mark for the boys. b) Find the mean mark for the girls.. Answer:. 37. The total mass of 7 cows is 3570kg. What is the mean mass of the cows?. c) Find the mean marks for the whole class The shoe sizes of a group of children are: 3, 2, 3, 4, 3, 2, 3, 4, 3, 3, 42. Three friends have a mass of 34kg, 41kg and 37kg. When a fourth person joins them, their mean mass is 40kg. What is the mass of the fourth person? 3, 3, 4, 5, 4, 3, 2, 3 What shoe size is the mode?... Answer:..
10 43. Complete the following sequence: a) 1, 5, 9,., 17,..,. b) List the square numbers you can see:... a) Draw pattern 4: c) Continue the sequence until you reach another square number. b) How many squares will there be in pattern 10? 44. Different sequences follow the rule: multiply by 3 then subtract 2 a) If a sequence begins with the number 2, what is the fourth number in the sequence? c) Which pattern has 27 squares? b) If the second number in the sequence is 28, what is the first number?. 46. This table shows the number of white and grey tiles in the patterns below:. 45. This table contains a sequence: Pattern white grey Pattern No. of squares a) Fill in the table. b) How many white tiles in pattern 10?.. c) Which number pattern has 49 grey tiles?..
11 47. A straight line has the equation: y = 2x 2 a) Complete the table of values for the line: y = 2x 2 x y b) Label the axes below and mark on the x-axis scale form -4 to 7 and the y- axis scales from -6 to 9 using 1 square as 1 unit c) Draw and label the line: y = 2x 2 on the cm grid below: d) Another straight line has the equation: y = x i) What is the value of y when x = 0? y = ii) What is the value of x when y = 0? x = e) Now draw and label the line: y = 3-1 x on the cm grid above. 2 f) State the coordinates of the point of intersection of the two lines you have drawn. (, ) g) Calculate the area of the triangle bounded by the x-axis, the line y = 2x 2 and the line y = x Area = cm 2
12 48. Using your π button on your calculator, and remembering to give all answers to 3 significant figures, answer the following questions: a) Work out the CIRCUMFERENCE of a circle with diameter 5cm cm b) Work out the CIRCUMFERENCE of a circle with radius 5cm cm c) Work out the AREA of a circle with radius 5m m 2 d) What out the AREA of a circle with diameter 5m e) m 2 f) A gardener has a semi-circular garden with a radius of 12 metres. What is the PERIMETER of this garden?..m
13 TRANSFORMATIONS 1. Draw a reflection of the triangle in the x-axis. 2.Translate the triangle 5 square left, 4 squares down. 3. Draw a reflection of the triangle in the line y = Draw a reflection of the triangle in the line x = Draw a rotation of 90 clockwise about the origin for the parallogram. 6. Draw a rotation of 180 about the point (-1, 1) for the trapezium. AXES SCALE: 1 SQUARE = 1 UNIT
14 ANGLES Calculate the lettered angles. DIAGRAMS NOT DRAWN TO SCALE
15 MORE ANGLES
16 PROBABILITY 1. Mr Kanzig has 4 different coloured pens (Black B, Red R, Orange O, Green G) and 3 different coloured pencils (Yellow Y, Red R, Green G). He wants to pick 1 pen and 1 pencil to use. Complete this table below to show the possible pairs of colours of pen and pencil that Mr Kanzig may choose: Pencil Pen B R O G Pencil Y YB YO YG R RB G GO GG If Mr Kanzig picks 1 pencil and 1 pen at random from his pencil case. a) What is the probability that he chooses an orange pen? b) What is the probability that he chooses a red pencil? c) At least one item that is red? Mr Kanzig lends his black pen to a pupil in his set to borrow. He then chooses 1 pen and 1 pencil from those remaining. d) How many possible pairs of colours can he have? e) What is the probability of Mr Kanzig choosing a pen and a pencil that are different colours?
17 2. The children in a class are equally likely to enter their classroom in any order. There are 10 boys and 6 girls in the class. a) What is the probability that a boy enters the room first? b) What is the probability that the youngest child enters the room first?.. c) 5 boys and 5 girls enter the room. What is the probability that the next child is a boy?.. Look at the following table carefully: Glasses No glasses BOYS 5 5 GIRLS 2 4 If all the names of these 16 pupils were put in a hat and one name was randomly picked out of the hat, what is the probability of choosing a: d) Boy with glasses?... e) Girl without glasses?.. (Remember to simplify your fraction) ANGLES IN POLYGONS Fill in the table below: Type of polygon Number of sides Size of one exterior angle Size of one interior angle Sum of the interior angles Regular Pentagon Regular Hexagon Regular Octagon Regular Decagon
18 VOLUME AND SURFACE AREA 1. a) Find the VOLUME of the cuboids above: (i) Volume = cm 3 (ii) Volume = cm 3 (iii) Volume = cm 3 b) Find the SURFACE AREA of the cuboids above: (i) Surface Area = cm 2 (ii) Surface Area = cm 2 (iii) Surface Area = cm 2 2. A room has dimensions 4m by 3m by 2m. How many cardboard boxes of dimension 50cm by 50cm by 50cm can be exactly stacked into the room? No. of boxes =
19 PIE CHARTS 1.
20 2.
21 CONVERSION GRAPHS
22 CONVERSIONS You may use your calculator for these 1. If 1 = 1.28: a) How many can you get for 100? b) How many can you get for 100?.. 2. If 1 km = miles: a) How many km in 10 miles? b) How many miles in 50 km? ALGEBRA PROBLEMS 1. In a quick game of cricket, William scored y runs and Max scored 2 more runs. a) Write Max s score in terms of y. Harry scored three times as many runs as William. b) Write Harry s score in terms of y. In total, William, Max and Harry scored 37 runs. c) Write down an equation and solve it to find y. y =..
23 2. A packet of 25 biscuits is to be shared between 5 boys and 5 girls. a) If the 5 boys each take y biscuits, write down an algebraic expression for how many biscuits are left for the girls? b) If the remaining biscuits are to be shared between the 5 girls, write down an algebraic expression for how many biscuits each girl will receive. SIMPLIFY you answer.. AREA AND PERIMETER Find the missing lengths a, b, p and q, and then find the PERIMETER and AREA of each shape. Perimeter = cm Perimeter = cm Area = cm 2 Area = cm 2
24 STATISTICS Below is a bar graph for the number of newspapers bought by a group of people: a) What was the modal number of newspapers bought? b) What was the median number of newspapers bought? c) What was the total number of newspapers bought? d) Calculate the mean number of newspapers bought. You may use your calculator. Give your answer to 3 decimal places.
25 BEARINGS Scale 1cm = 1km The diagram above shows the position of Anglesey boat at A and Blackpool boat at B with respect to the lighthouse point at P. What is the bearing of Anglesey boat from the lighthouse? The Calais boat is on a bearing of 105 from P and is 7km from the Blackpool boat. Mark the Calais boat above, labelling it C. The Dunkirk boat is on a bearing of 75 from the Blackpool boat and is 8km away from the Anglesey boat. Draw a NORTH line at B and then mark where the Dunkirk boat is, labelling it D. What is the distance in km between the C and D? km
26 ENLARGEMENTS 5. A shape X has an area of 25 cm². It is then enlarged by a scale factor of 2 to give shape Y. What is the area of Y? cm² NUMBER MACHINES Fill in the missing boxes to work out the values of a, b, c and d. a = b = c =. d =
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