Stonelaw Mathematics Department

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1 Stonelaw Mathematics Department Blue Course Revision Sheets Block F BF BF BF BF4 BF5 Brackets, equations and inequalities Pythagoras Theorem and Significant Figures Scientific Notation, Indices and Surds Statistics, graphs, charts and probability Rotations and transformations

2 BF BF. BF. Brackets, Equations and Inequalities I have revised the use of algebraic shorthand. Substitution into epressions involving negative numbers.. Evaluate a b when a = and b = 7.. Evaluate 5y y when = and y = 4.. Evaluate t v u when t = 4, v = and u = 9. BF. I can multiply out brackets of the form: a b cy. Multiply out the brackets: aa tu t BF.4 I can multiply out brackets of the form : a by c dy Multiply out the brackets: a + a b y + y a + b

3 BF.5 I can multiply out brackets of the form : a b c d c. Multiply out the brackets: BF.6 I can multiply out brackets in more comple epressions and gather like terms. Simplify: BF.7 I can solve equations that contain brackets.. Solve:. 5 + = a = 9 BF.8 I can solve equations which contain fractions. Solve:. + = 8. a a+ = 4

4 BF.9 I can solve inequalities which may contain a change of direction of inequality sign. Solve: < 7 BF.0 I can use equations and inequalities to make mathematical models. The shape shown below is made from a small rectangle cut from a larger rectangle. If the shaded area is 87 square centimetres, find the value of The heights of 0 plants were measured as 5cm, cm, 4cm, cm, 5cm, cm, cm, cm, cm, 5cm. a Write down an epression in for the mean height of a plant. b If the mean height of the plants is greater than 9cm. Write down an inequality for the above information and solve it for. c Eplain your answer to b in the contet of this problem

5 BF Pythagoras and Significant Figures BF. I can use Pythagoras to find the length of a hypotenuse Calculate the length of the missing side in each triangle: a 8 5 b c

6 BF. I can use Pythagoras to find the length of a shorter side Calculate the length of the missing side in each triangle: a 0 8 b c 4 4.8

7 BF. I can use Pythagoras to solve problems. In the isosceles triangle shown, find the length of AB 5m A B 7 5cm 8cm. For the kite shown, find the length of the side marked. 6 5cm. Fairy lights are strung across a river in the shape of an isosceles triangle with a base length of 60 metres. A 6m B 60m C If the length of the string of fairy lights is 90 metres, calculate the width of the river to the nearest centimetre.

8 BF.4 I can use Pythagoras to find the distance between two coordinate points On squared paper plot these pairs of points and calculate the distance between them. a O 0, 0 and M 8, 6 b P, and Q 9, 8 c R, 6 and S 8, -6 BF.5 I can use the Converse of Pythagoras to prove or disprove that a triangle is right angled.. Use the Converse of Pythagoras to decide which of these triangles are right angled: a 9 5 b c 4.4

9 BF.6 I can apply the theorem of Pythagoras to construct mathematical models of real life situations.. A rope has to be fed through a pipe in the ground for the telephone wire to be connected from the house to the telephone pole. John has a 40 metre long rope to complete the job. House Pipe 0 m 5 m Is the rope long enough? You must justify your answer with appropriate working. Telephone Pole. A loop of rope is used to mark out a triangular plot, PQR. R P Q The loop of rope measures 4 metres. Pegs are positioned at P and Q such that PQ is 0 metres. The third peg is positioned at R such that QR is 8 metres. Prove that angle PRQ = 90. Do not use a scale drawing.

10 . The top of a crane is in the shape of a triangle, shown as PQR. PQ = 9m, PR = 5m, RQ = 6m. R 5m 6m Q M 9m P a Prove that angle PRQ is a right angle. b Hence calculate the area of PQR. c Calculate the length of altitude RM.

11 BF.7 I can round to a specified number of significant figures Round each of these numbers correct to sig fig. a 4948 b 65 4 c 789 d 7 77 Round each of these numbers correct to sig fig. a 44 b 6 08 c d 7 5 Complete the following calculations and give your answers correct to sig fig. a 7 9 b 7% of 5000 c Find the circumference of a circle with diameter 4.5cm 4 A plane departs Newtown and flies 65 miles north followed by 40 miles west, as shown, until it reaches Rivercity. Rivercity 40 miles 65 miles Newtown Calculate the direct distance from Newtown to Rivercity, giving your answer to significant figures.

12 BF Scientific Notation, Indices and Surds BF. I can convert large and small numbers to and from scientific notation.. Write the following numbers in Scientific Notation: a 8,000 b 70,000 c 5,600 d 7,000 e 6,700,000 f 8,50,000 g 8,600,000 h 6,700 i 4,000,000 j,80 k 6,40 l 700 m 94 n,000,000 o 7, p 67 q 8,5 r 70 s 7,00,000 t 5,56,000 u 76,000,000 v 4,000,000 w 464, Write the following numbers in Scientific Notation: a 4 million b million c 6 5 million d 9½ million e 8 46 million f 5¼ million g million h ¾ million i 648 million. Write the following numbers out in full: a 0 4 b 5 0 c d e f g h i j k l m 0 n o p q 0 0 r

13 4. Write the following numbers in Scientific Notation: a b c d e f 0.04 g h i j k l m n o p Write the following numbers out in full: a 0 b c 5 0 d e 8 0 f g 0 h i j k l m n o 87 0 p q 0 0 r Write the following numbers in Scientific Notation: a 70,000 b 5,60,000 c d e,,000 f g 7,0,000 h Write the following numbers out in full: a 7 0 b c 5 0 d e f g h i 4 0

14 BF. I can solve problems involving multiplication and division of numbers epressed in scientific notation with and without a calculator.. Using your scientific calculator calculate the following, leaving your answer in scientific notation: a 0 0 b c d e f g h i 0 0 j k l m n o p q r s t u v w y z During the year 009, twenty thousand CHOCPOPS were eaten every minute. How many CHOCPOPS were eaten in total during 009. Give your answer in scientific notation.. The annual profit of a company was pounds for the year 0. What profit did the company make per second. Give your answer correct to three significant figures.

15 4. The moon has an approimate mass of kilograms. The planet Earth has a mass of 8 times that of the moon. Calculate the mass of the Earth. Give your answer in scientific notation. 5. Large distances in space are measured in light years. The Canis Major Dwarf galay is the closest galay to the planet Earth, a distance of approimately 5,000 light years away. A light year is approimately kilometres. Calculate the distance of the galay to Earth in kilometres. Give your answer in scientific notation. 6. A newspaper report stated Concorde has now flown miles. This is equivalent to 00 journeys from the earth to the moon. Calculate the distance from the earth to the moon. Give your answer in scientific notation correct to two significant figures. 7. The total number of visitors to an ehibition was The ehibition was open each day from 5 June to 9 September inclusive. Calculate the average number of visitors per day to the ehibition.

16 BF. I can use the rules of indices m a n b = mn a+b, m a n b = n a b b ab a m k k 0 n a and a applying them to my n a b and previous learning.. Using the rule a b = a+b simplify the following: a 4 b 5 c 7 d e f a 6 a g 4 4 h f 4 f 5 i z 6 z j 6 4 k a a 9 l 7 7 m n 8 8 o c 6 c 6 p z 9 z q a 4 a 6 r 0 0. Using the rule a b = a b simplify the following: a 6 4 b y 4 y c z 9 z 4 d a 8 a e c 8 c 4 f 7 g h i j 4 k 7 4 l 5 5 m 0 4 n o c c p z 9 z q k 0 k 9 r a 7 a 7

17 . Using the rule k a b = k b ab simplify the following: a 5 b 4 5 c d d e 7 f y 8 g z 8 h c 5 5 i a j ab 4 k ab l y 5 m y 4 n m 5 n o m p m q mn r m n 4 4. Using all of the above rules simplify the following: a 0 6 b y 00 y 00 c k 7 k d a 0 a 5 e 9 6 f a g 0 0 h 4z 6 i y BF.4 I know that m m n n a a and can apply this knowledge in problems.. Write the following as surds r q p o n m l k j i h g f e d c b a

18 . Simplify each of the following 4 l k j i h g f e d c b a BF.6 I can simplify, add, subtract, multiply and divide surds.. a 5 5 b c 5 d 6 e 6 f y g 8 h i 5 5 j 7 k 4 l 5 m 6 n 8 o 5 5 p 48. a - b + c 55 - e + 6 f 8 + g 6-8 i j k + 6. a + - b d + - e g h j + k +

19 BF.7 I can rationalise a surd denominator. Rationalise the surd denominator u t s r q p o n m l k j i h g f e d c b a

20 BF4 Stats, Graphs, Charts and Probability BF4. I have revised my knowledge of: average mean, median and mode and spread range including using Etended Frequency Tables and Cumulative Frequency Tables.. Calculate the mean for each of the following data sets: a,, 4, 7, 7, 9 b,,, 6, 6, 8 c 0, 0, 0 4, 0 5, 0 7, 0 7, 0 9 d, 7, 9, 6,, 8, 7,,,. Calculate the median for each of the following data sets: a 5, 8, 4,,, 6,, 9, 7 b,, 4, 6, 7, 9, 5 c, 7, 8, 6, 4, 7,, 0 d, 4, 0 8, 7,, 6, 0 9,. Calculate the mode for each of the following data sets: a,,, 54,,,, 0, b 7,,, 4,, 6 0, 8 c, 0,, 4,, 0, 4 d 4, 4,,, 4, 4 5, 4, 4 4. Calculate the mean, median, mode and range for each of the following data sets: a 07, 06, 9, 4, 06, 98 b 5 6,, 4, 4, 5 0, 4, 7 c 0,,, 4, 55, 6, 7, 0 d 5, 5,, 4, 7, 6, 7, 7

21 5. Copy and complete each of the following tables, add a third column and calculate the mean, median and mode. a b 6. Copy and complete each of the following tables, add a cumulative frequency column and calculate the median. a b

22 BF4. I can construct and interpret: a pie chart and a scatter graph.. In a local government election, four candidates stood for election in the Murraywood ward. There were 70 votes cast and the candidates received the number of votes shown below: T. Green 4 J. Black 86 R. White 0 K. Brown 90 Construct a pie chart which displays these results calculate the angle of each sector, clearly showing all working.. Some pupils in S sat a Literacy test and a Numeracy test. The results are shown below in the table. Pupil A B C D E F G H Numeracy Literacy a Display these results on a scattergraph. b Describe the correlation between the Literacy and Numeracy marks.. The pie chart shows the share of the votes received by candidates in the Gleniston constituency at the general election in 005. A total of people voted in the Gleniston constituency. How many people voted for the Liberal candidate?

23 BF4. I have investigated the eistence of discrete and continuous data. Which of the following are eamples of discrete data, and which are eamples of continuous data. a The number of red cars on a road. b The weight of a blue whale. c The height of a two year old child. d The number of people in S who like salt and vinegar crisps. BF4.4 I can find: the five figure summary and interquartile range for a sample and illustrate this information with a bo plot. Give the five figure summary and the interquartile range for each of the following sets of data. a, 7, 5, 6, 9, 4, 5, 60 b 6, 7,,, 5, 6, 8, 4, 5, 5, 6, 69, 7 c 5, 9,, 5, 7,, 7

24 BF4.5 I can find the Standard deviation of a sample and use it as an alternative measure of spread using both methods.. Use the formula in the following eamples. a Calculate the mean and standard deviation of i 4, 5, 8, 0,, 8 ii 4, 45, 4, 45, 46, 47, 50 b The costs of a can of diet coke in 6 different shops are 67p, 69p, 60p, 54p, 58p, 54p Calculate the mean and standard deviation of these costs. c The prices of a bag of sugar in 6 different shops are 86p, 88p, 84p, 79p, 8p, 86p Calculate the mean and standard deviation of these prices.

25 . Use the formula s = n in the following eamples. n a Scientists are studying the differences between crocodiles and alligators. The lengths of 6 crocodiles are recorded in feet. The results are shown below. 8, 0, 7, 0, 0 8, 8 Calculate the mean and standard deviation of these lengths. b Calculate the mean and standard deviation of 0 numbers where Σ = 80 and Σ = 56 c The cost of a printer in 6 different British shops is 66, 55, 70, 5, 6, 55 Calculate the mean and standard deviation of these costs.

26 BF4.6 I can compare two sets of data using average and spread and investigate the most appropriate measure of average in a given contet...

27 BF4.7 I can predict the number of desired outcomes given the probability of an outcome occurring....

28 4. 5.

29 BF5 Rotations and Transformations BF5. I can describe the order of rotational symmetry of a shape.. Write down the order of rotational symmetry for each shape a b c d. For each diagram write down the smallest angle of rotation about the centre of the shape so that it fits its outline. BF5. I can create a shape by rotating a template around a point.. Copy the diagram and complete the shape so that it has quarter turn symmetry about the dot.

30 BF5. I can translate points and shapes using displacement translation vectors.. Plot the points A-, 4, B, 5 and C4, - on a Cartesian coordinate diagram and join them to form triangle ABC. i On the same diagram show A B C, the image of ABC under the translation. ii Also on the same diagram show A B C the image of ABC under the translation.. P, Q and R have the coordinates, 4, -, and -, -4 respectively. State the translation which maps PQR onto P Q R where P, 5, Q -4, and R -5, -.

Paper 3 Unseen Topics

Paper 3 Unseen Topics This is a collection of questions based on the topics that are so far UNSEEN or are usually more prominent Make sure you revise all topics as it is very likely topics from Paper 1