Stonelaw Mathematics Department

Transcription

1 Stonelaw Mathematics Department Blue Course Block A Revision Sheets Block A BA0 Whole Numbers. BA1 & BA5 Angles, Triangles, Quadrilaterals and Symmetry. BA2 & BA3 Algebra BA4 Negative Numbers. BA0 Mixed Examples Whole Numbers BA0.1 I can read and write large numbers.

2 Using the number cards (each card can only be used once) write out: 1) The biggest possible 5 digit number. 2) The smallest possible 6 digit number. 3) The largest possible 7 digit number. 4) The numbers in a) to c) in words. 5) All possible numbers between and BA0.2 I can read scales to the nearest graduation. What numbers are located at positions a) to i) on theses number lines? BA0.3 I understand the meaning of the terms Natural Number, Whole Number, Sum, Difference, Product and Quotient.

3 2 ½ ⅔ 7 Using the number cards write out: 1) All of the numbers on the cards which are Whole Numbers. 2) All of the numbers on the cards which are Natural Numbers. 3) Which three cards give a sum of 37. 4) Which two cards have a difference of 26. 5) Find the 2 cards with a product of 14. 6) Find 2 cards with a quotient of 14. BA0.4 I can add and subtract mentally. Write down the answers to the following without using a calculator or working, you must try and do them in your head: a) b) c) d) e) f) 52 3 g) 61 9 h) i) j) k) l)

4 BA0.5 I can use addition and subtraction in problems without a calculator. Do not use a calculator but show all working. 1. The map shows the location of 5 cities along with the motorways connecting them. Tarby 135km 235km 273km 241km Brum Newton 182km Darly 141km 228km Carswell 371km a) How far is it from Tarby to Carswell:- i) Via Newton? ii) Via Brum? iii) Via Darly? b) A lorry driver leaves Brum and makes journeys to Tarby, Newton, Carswell and Darly, before returning to Brum. How far did he drive altogether? 2. In 2008, Waste Management was responsible for 23 million tonnes of greenhouse gases. This compares to 219 million tonnes of greenhouse gases from Energy Supply and 132 million tonnes of greenhouse gases from Transport. a) How many million tonnes of greenhouse gases is this altogether? b) Energy Supply produces more greenhouse gases than Transport. How many million tonnes more? 3. The Environmental Services Association reports that in 2008 its members were responsible for producing tonnes of greenhouse gases but saved tonnes of greenhouse gases through their material and energy recovery activities the difference being released into the atmosphere. How many tonnes of greenhouse gases did the Environmental Services Association members release into the atmosphere?

5 BA0.6 I can multiply and divide by a single digit without a calculator and can find the square of any whole number up to 10. You must not use a calculator for these questions. 1. Calculate a) 95 2 b) 41 6 c) 32 6 d) 4 21 e) 7 24 f) g) 5 23 h) Evaluate a) b) c) d) e) f) g) h) i) j) k) l) Find the remainder each time a) b) c) d) e) f) g) h) i) j) k) l) Write down which of the following numbers are Square Numbers: 1, 3, 4, 5, 6, 9, 12, 16, 18, 23, 25, 34, 36, 40, 52, 64, 78, 81, 100.

6 BA0.7 I can multiply and divide by multiples of 10, 100 or You must not use a calculator for these questions. 1. Calculate a) b) c) d) Evaluate a) b) c) d) e) f) g) h) i) 32 6 j) k) l) Calculate a) b) c) d) e) f) g) h) i) j) k) l)

7 BA0.8 I can multiply or divide more difficult numbers in a problem with a calculator. You can use a calculator for these questions. 1. The government spent 357 million on animal health in If this level of spending is maintained for 15 years how much would the total spend be? 2. The government audit office claims to have made savings and other efficiency gains worth 890 million in On average how much is this per month? 3. The government raised 837 million in Landfill Tax receipts. How much does this work out per person if the population of the UK is 62 million. 4. Recycling glass saves 315kg of carbon dioxide being released into the atmosphere per tonne of glass recycled. If tonnes of glass are recycled in Scotland each year, how much carbon dioxide does this save being released into the atmosphere?

8 BA4 Negative Numbers 1 BA4.1 I have revised how to extend the number line below zero and know the meaning of the term Integer. 1. Use a ruler to neatly copy and complete these number lines filling in all the gaps. a) b) c) d) 2. Copy the list of numbers below and circle all the integers Copy the list of numbers below and circle the numbers which are not integers

9 BA4.2 I can use negative numbers in the context of temperature 1. Write down the temperature shown on each thermometer. The temperatures are all in degrees Celsius. a) b) c) d) e) 2. a) It was -6 C in the morning. By lunchtime the temperature had risen to 8 C. How many degrees had the temperature risen? b) The temperature in Glasgow on Monday was 5 C, but by Friday it had fallen to -3 C. How many degrees had the temperature fallen? 3. a) The temperature in East Kilbride was -15 C. The weather report said that the temperature would rise by 7 degrees. What would be the new temperature after this rise? b) A liquid is stored at -14 C.If the temperature of the liquid is reduced by 9 degrees it would reach its freezing point. What is the freezing point of this liquid?

10 BA4.3 I can read and plot points in four quadrants. 1. Write down the coordinates of each points A to L 5 2. a) Draw a blank coordinate diagram similar to the one above. Plot each of the sets of points below on your coordinate diagram and join the points in order and finally close each shape to produce a quadrilateral. Quadrilateral A (0, 1) (2, 5) (0, 4) (-2, 5) Quadrilateral B (2, 0) (3, 3) (4, 0) (3, -3) Quadrilateral C (2, -2) (1, -4) (-4, -4) (-2, -2) Quadrilateral D (-3, 3) (-1, 1) (-3, -3) (-5, 1) b) Write down the name of each of the quadrilaterals produced in part a).

11 BA1 & BA5 Angles, Triangles, Quadrilaterals and Symmetry BA1.1 I can use and understand the terms Acute Angle, Right Angle, Obtuse Angle, Straight Angle and Reflex Angle Classify each angle using the words Reflex, Straight, Obtuse, Right or Acute. (1) (2) (3) (4) (5) BA1.2 I can use letters to name vertices, lines, angles and shapes. For each of the angles above: (a) Name the vertex (use one letter). (b) Name the arms (use two letters each arm). (c) Name the angle (use three letters).

12 BA1.3 I can use Corresponding, Supplementary, Vertically Opposite, Corresponding and Alternate Angles, sums of angles in a triangle or quadrilateral to deduce the size of missing angles. Use angle facts to calculate the missing angle. (1) (2) 120 o b 65 o a (3) (4) 35 o c d 90 o (5) (6) e o 130 o 155 o f (7) (8) 248 o g 38 o h i (9) (10) j 95 o k l 148 o m p n (11) (12) 105 o q r 44 o 28 o 35 o

13 (13) (14) s t 137 w v u 109 (15) y x BA5.1 I can illustrate the lines of symmetry for a range of 2D shapes and apply my understanding to create complete symmetrical pictures and patterns. 1. Trace each diagram and show all lines of symmetry.

14 2. Copy each of the shapes and complete them so that the dotted lines are lines of symmetry. (a) (b) (c)

15 BA1.4 Working as part of a team I can carry out a practical investigation into the properties of a variety of quadrilaterals. Use the clues to identify each quadrilateral. Illustrate each quadrilateral with a sketch. (1) All of my sides are equal and I have opposite angles which are equal. However none of my angles are right angles. (2) I have opposite sides which are equal and parallel and opposite angles which are equal. However none of my angles are right angles. (3) I have one pair of parallel lines however none of my sides are equal and none of my angles are equal.

16 BA2 and BA3 Substitutions, Equations and Brackets BA2.1 I can use algebraic shorthand and gather like terms. 1. Write the following using algebraic shorthand to simplify Support Video a) 2 x b) 4 y c) 3 p + 2 q d) a b + a c 2. Simplify by gathering Like Terms a) 3x + 4y + x + 2y b) 2a + 6b + 4a + 5 Support Video c) 5p + 4q 3p p d) 3c + 7d 2c + d BA2.2 I can use the correct order of operations (BODMAS). Support Video Evaluate the following 1) ) ) ) 3 (5 + 1) 5) 30 (4 + 2) 6) (3 + 2) (6 4) 5 BA2.3 I can evaluate expressions using substitution. Support Video 1. Evaluate the following a) 2a + b when a = 3 and b = 1. b) 10 2x when x = 4. c) m (n + 4) when m = 2 and n = 5. d) c 3 + 4d when c = 15 and d = Given that A = 3b + 2, find A when b = Given that y = 5 (x + 4) find y when x = 3.

17 BA3.1 Support Video I understand Inverse Operations and know how to use them in backward number machines. Find the input to each of the following number machines a X b X c d BA3.2 Support Video I can solve equations by using Inverse Operations and by keeping the equation balanced. Solve the following equations 1. 5x + 3 = 2x a 3 = 2a b + 2 = 7b p + 9 = 5p r = 3r s = s + 5

18 BA3.3 Support Video I can construct and evaluate simple formulae from diagrams, problems or statements. 1. For each statement below use the information given to construct a formula in symbols. a) Profit can be calculated by subtracting costs from sales. b) The total number of pupils in a class can be found by adding the number of boys and the number of girls. c) The area of a rectangle can be found by multiplying the length by the breadth. 2. Use the information in the diagram below to write a formula for calculating the perimeter of the shape.

19 BA3.4 I can solve problems by constructing and solving simple equations. Support Video For each question, use the information to construct an equation, then solve your equation and give the answer to the question. 1. I think of a number, multiply it by 5, I then add 42. The answer is 57. What is my number? 2. Zoe goes shopping with a friend and buys five bangles and one pair of earrings. She knows the earrings cost 3 and she pays 13. How much does one bangle cost? 3. Look at the diagram below Find the value of x. 4. The two shapes below have the same perimeter. Find the value of x.

20 BA3.5 I can use the Distributive Law to multiply out brackets. Support Video 1. Expand the brackets : a. 2 (4a 3) b. 6 (4y 3) c. 3 (2x 5) d. 4 (5c 6) e. 7 (2a 1) f. 2 (8x 3) g. 5 (6 7y) h. 3 (8t 5) i. 3 (9x 4) j. 8 (7 5y) k. 7 (2b 9) l. 2 (12x 7) 2. Expand and simplify: a. 2a + 3(a + 5) b. 3x + 2(x + 3) c. 4b + 8(b + 2) d. 5h + 4(2h + 1) e. 11x + 5(3x + 4) f. 10c + 3(2c + 1) g. 2(4t + 3) + 10t h. 3(5p + 4) + 7p i. 7(1 + 3c) + 10 j. 3(3a 1) + 2a k. 2(5x + 3) 3x l. 8(b + 2) 9

21 Mixed Examples In the following examples you have to interpret, select, implement and communicate. Do not use a calculator for questions Jim notices that the number in his address has some arithmetic properties. The difference of the first two digits gives the third digit. The product of the first two digits gives the last two digits. Which of these addresses could be Jim s? 6318 Station Road Main Street High Street. Illustrate your answer with calculations. 2. The two shapes below have the same perimeter. 5 cm 10 cm 3 cm 2x cm 9 cm 11 cm 3x cm Find the perimeter of the two shapes. Show all of your working clearly.

22 3. Hilda knows that her gloves will keep her fingers warm even if the outside temperature goes down to -23 C but won t keep her fingers warm if the outside temperature is any lower. The temperature on the mountain at night is 8 C and it is predicted that the temperature will drop by 30 C by the next morning. Hilda will be on the mountain in the morning. Will her gloves keep her fingers warm? Give reasons for your answer. 4. The council in Mankiton decide that they have to reduce the amount of rubbish being produce in their town by at least tonnes per year. To achieve this they start a campaign. At the start of the campaign the 2340 households in Mankiton produced on average 19 tonnes of waste per household in a year. By the end of the campaign there were 2520 households producing on average 14 tonnes of waste per household in a year. Was the campaign successful? Show all working clearly. 5. Use the clues to identify the shape. o It has 4 sides. o All angles are right. o Opposite sides are equal and parallel. o It has two lines of symmetry What shape is it? Illustrate your answer with a diagram