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1 Contents Mathematics (National 5) Expressions and Formulae... Mathematics (National 5) Relationships...3 Mathematics (National 5) Applications...4 Arcs & Sectors...5 Brackets...6 Completing the Square...7 Equations and Inequalities...8 Factorisation Factorisation...10 Formulae...11 Fractions Fractions...13 Line of Best Fit...14 Money & Finance Money & Finance...16 Properties of Shapes...17 Pythagoras Theorem...18 Quadratic Check-up...19 Scale Factor and Area...0 Scale Factor and Volume...1 Similar Triangles... Simultaneous Equations...3 Standard Deviation & Boxplots...4 The Straight Line The Straight Line...6 Surds & Indices...7 Trigonometry...8 Trig Equations...9 Trig Area of triangle and exact values...30 Trig graphs...31 Vectors...34 Volume...36 Solutions...37 An attempt has been made to match these homework sheets to the relevant outcomes of the new Scottish National 4 and National 5 units, but it is stressed that this is the author s interpretation only.

2 Mathematics (National 5) Expressions and Formulae Topic Homework Sheet Working with surds Surds & Indices Pythagoras' Theorem Simplifying expressions using the laws of indices Surds & Indices E&F 1. Working with algebraic expressions involving expansion of brackets Brackets E&F 1. E&F 1. E&F 1.3 E&F 1.3 Factorising an algebraic expression Completing the square in a quadratic expression with unitary x coefficient Reducing an algebraic fraction to its simplest form Applying one of the four operations to algebraic fractions Factorisation 1 Factorisation Quadratic Check-up Completing the square Quadratic Check-up Fractions 1 Fractions Fractions 1 Fractions Formulae E&F 1.4 E&F 1.4 E&F 1.4 E&F 1.4 E&F.1 E&F. Determining the gradient of a straight line, given two points Calculating the length of arc or the area of a sector of a circle Calculating the volume of a standard solid (Rounding to a given number of significant figures) Interpreting a situation where mathematics can be used and identifying a strategy Explaining a solution and/or relating it to context The Straight Line Arcs & Sectors Properties of shapes Volume Formulae Volume Fractions Fractions Mathematics (National 4) Expressions and Formulae Using the distributive law in an expression with a numerical common Brackets factor to produce a sum of terms Simplifying an expression which has Brackets more than one variable Formulae Evaluating an expression or a formulae which has more than one variable Brackets Calculating the gradient of a straight line from horizontal and vertical distances The Straight Line 1 Page National 5 Mathematics Revision Homework A Forrest 013

3 Mathematics (National 5) Relationships Topic Homework Sheet Rel 1.1 Rel 1.1 Determining the equation of a straight line, given the gradient Working with linear equations and inequations The Straight Line 1 The Straight Line Equations and Inequalities Rel 1.1 Working with simultaneous equations Simultaneous Equations Rel 1.1 Changing the subject of a formula Formulae Recognise and determine the equation of Rel 1. a quadratic function from its graph Completing the square Rel 1. Sketching a quadratic function Completing the square Rel 1. Identifying features of a quadratic function Quadratic Check-up Rel 1.3 Working with quadratic equations Quadratic Check-up Rel 1.4 Applying the Pythagoras theorem Pythagoras' Theorem Rel 1.4 Rel 1.4 Rel 1.5 Rel 1.5 Rel.1 Rel. Applying the properties of shapes to determine an angle involving at least two steps Using similarity Working with the graphs of trigonometric functions Working with trigonometric relationships in degrees Interpreting a situation where mathematics can be used and identifying a strategy Explaining a solution and relating it to context Properties of shapes Scale Factor and Area Scale Factor and Volume Similar Triangles Trig Equations Trig Equations Trig Area of triangle and exact values Trig graphs Properties of shapes Properties of shapes Rel 1.1 Mathematics (National 4) Relationships Drawing and recognising a graph of a linear equation. The Straight Line 1 Rel 1.1 Solving linear equations. Equations and Inequalities Rel 1.1 Changing the subject of a formula. Formulae Rel 1. Using Pythagoras theorem Pythagoras' Theorem Rel 1.4 Drawing and applying a best-fitting straight line Line of Best Fit National 5 Mathematics Revision Homework A Forrest 013 Page 3

4 Mathematics (National 5) Applications Topic Homework Sheet Calculating the area of a triangle using Trigonometry Apps 1.1 trigonometry Trig Area of triangle and exact values Using the sine and cosine rules to find a Apps 1.1 Trigonometry side or angle Apps 1.1 Using bearings with trigonometry Trigonometry Apps 1. Working with D vectors Vectors Apps 1. Working with 3D coordinates Vectors Apps 1. Using vector components Vectors Apps 1.3 Working with percentages Money & Finance - Worksheet 1 Apps 1.3 Working with fractions Fractions 1 Formulae Apps 1.4 Comparing data sets using statistics Standard Deviation & Boxplots Forming a linear model from a given set Apps 1.4 Line of Best Fit of data Interpreting a situation where Apps.1 mathematics can be used and identifying Money & Finance - Worksheet a strategy Explaining a solution and/or relating it to Money & Finance - Worksheet Apps. context Vectors Page 4 National 5 Mathematics Revision Homework A Forrest 013

5 Nat 4 Brackets 1) Simplify the following : a) 5x 3x b) y 6y c) - z - z d) k - k e) 5(m n) 3( m + n) f) 3( a + b) = ( a 5b) ) Find the sum of : a) x + 3y and -6x + 1y b) p 3q r and 5p + 3q + r c) 4c 6d + 5e and c 3d 7e d) x - x - 4 and 3x x + 5 3) Simplify the following: a) 4x 4x x x b) k( k 1) k( k + ) c) x(x 3) x(x +) + (x + x) d) (x -x) +3(x + x) (x + x) 4) Simplify the following: a) (a + )(b + 5) b) (x 1)( y 4) c) (x + 3)(x x 3) d) (a + b) ( a b) e) (x + 3) (3x + ) f) 1 1 x x x x 5) Writing.01 as , show that.01 = 4.04 to two decimal places. 6) Prove that ( a + b)(a ab + b ) = a 3 + b 3. Page 6 National 5 Mathematics Revision Homework A Forrest 013

6 Factorisation 1 1) Remove the brackets a) ( x 4)( x 5) b) (x 5)( x 1) c) ( a 5)( a 5) d) ( x 4)(3x 15) ) Copy and complete 3) Factorise ) 7 1 ( 4)( ) a x x x x ) 6 5 ( )( ) b x x x x ) 8 15 ( 3)( ) c x x x x ) 1 0 ( )( ) d x x x a x x ) 3 b x x ) c b b ) 10 5 d x x ) 5 36 e c c ) 9 8 f r r ) 6 7 g x x ) 4 45 h z z ) 71 7 i) 4 11x x j) 5 10a a 4) Factorise a x x ) 5 3 b a a ) 6 7 c c c ) d x x ) 19 9 e c c ) f r r ) g x x ) 1 h z z ) i) 1 3x 18x j) 15 7p p 5) Factorise (Difference of two squares) a) b) c) x t x 36 4 y d) 16x 9y e) 4c 100 National 5 Mathematics Revision Homework A Forrest 013 Page 9

7 Line of Best Fit Test scores for an S4 maths and physics test are shown below: Pupil Maths Physics They are plotted on a scatter graph. Maths and Physics scores Physics Score Maths Score a) Is there a correlation between scoring well in maths and physics? Explain your answer. b) Draw a line of best fit on the scatter graph and use it to find an equation linking the physics and maths test results for this data set. c) Use your equation to predict the physics test score for a pupil who scored 55 in the maths test. Apps 1.3 Apps 1.4 Page 14 National 5 Mathematics Revision Homework A Forrest 013

8 Money & Finance 1 1) Glenfox Lodge was valued at 365,000 on 30 th April 001. If appreciation is 4% per annum, what is the value of Glenfox Lodge on 30 th April 011? ) A car was bought for 8000 in Each year, it depreciated in value by 0%. What was the car worth 4 years later? 3) Calculate the compound interest earned on: a) 500 for 3 years at 6% per annum. b) 875 for years at 4.5% per annum c) 550 for 7 months at 6.% 4) Greg Gregson earns 96 per week. He pays 6% superannuation. a) How much superannuation does he pay per week? b) How much superannuation does he pay per year? National Insurance is payable at % on the first 56 earned and 9% on the rest. c) How much National Insurance does he pay per week? d) How much National Insurance does he pay per year? He also pays tax and.80 union dues each week. e) What is his weekly net pay? 5) HMRC Income tax rates Basic rate ,400 at 0 per cent ,000 at 0 per cent. Higher rate Additional rate 37, ,000 at 40 per cent. Over 150,000 at 50 per cent. 35, ,000 at 40 per cent. Over 150,000 at 50 per cent. Charlie Charleson has a personal allowance of 7,475.Her salary is 44,350. a) Calculate her annual income tax for the tax years 010/11 and 011/1. b) How much more tax does she have to pay in 011/01? c) Express this increase as a percentage of her annual income tax for 010/11. d) Calculate her monthly income tax for 011/1. Nat 4 Rel 1.4 Apps 1.3 National 5 Mathematics Revision Homework A Forrest 013 Page 15

9 1) What is the volume of the enlargement? Scale Factor and Volume 15 cm 3 x cm 3 3 cm 9 cm ) What is the volume of the larger can? 150 x cm 3 cm 3 cm 4 cm 3) Orangi is a new drink sold in similar triangular cartons. What is the volume of the smaller carton? 640 cm 3 x cm 3 5cm 0 cm Rel 1.4 National 5 Mathematics Revision Homework A Forrest 013 Page 1

10 Trigonometry Apps 1.1 1) Calculate the missing values a) 7 cm x cm b) c) x cm x cm 1 cm 7 cm 70 8 cm ) Calculate the bearing of the robot from the jogger. 150 m 168 m 5 m Page 8 National 5 Mathematics Revision Homework A Forrest 013

National 5 Mathematics Revision Homework with Worked Solutions. Alexander Forrest

National 5 Mathematics Revision Homework with Worked Solutions Alexander Forrest Contents Mathematics (National 5) Expressions and Formulae... Mathematics (National 5) Relationships...3 Mathematics (National