KS4: Algebra and Vectors
|
|
- Reynold Peters
- 6 years ago
- Views:
Transcription
1 Page1 KS4: Algebra and Vectors
2 Page2 Learning Objectives: During this theme, students will develop their understanding of Key Stage 4 algebra and vectors requiring algebraic manipulation. It will build on from knowledge gained from KS3 algebra, in order to develop students fluency in the topic. KS4 National Curriculum Algebra In addition to consolidating subject content from key stage 3, pupils should be taught to: simplify and manipulate algebraic expressions (including those involving surds {and algebraic fractions}) by: - factorising quadratic expressions of the form x 2 + bx + c, including the difference of two squares; {factorising quadratic expressions of the form ax 2 + bx + c} - simplifying expressions involving sums, products and powers, including the laws of indices know the difference between an equation and an identity; argue mathematically to show algebraic expressions are equivalent, and use algebra to support and construct arguments {and proofs} where appropriate, interpret simple expressions as functions with inputs and outputs; {interpret the reverse process as the inverse function ; interpret the succession of two functions as a composite function } use the form to identify parallel {and perpendicular} lines; find the equation of the line through two given points, or through one point with a given gradient identify and interpret roots, intercepts and turning points of quadratic functions graphically; deduce roots algebraically {and turning points by completing the square} recognise, sketch and interpret graphs of linear functions, quadratic functions, simple cubic functions, the reciprocal function with x 0, {the exponential function y = k x for positive values of k, and the trigonometric functions (with arguments in degrees) y = sin x, y = cos x and y = tan x for angles of any size} {sketch translations and reflections of the graph of a given function} plot and interpret graphs (including reciprocal graphs {and exponential graphs}) and graphs of non-standard functions in real contexts, to find approximate solutions to problems such as simple kinematic problems involving distance, speed and acceleration {calculate or estimate gradients of graphs and areas under graphs (including quadratic and other non-linear graphs), and interpret results in cases such as distance-time graphs, velocity-time graphs and graphs in financial contexts} {recognise and use the equation of a circle with centre at the origin; find the equation of a tangent to a circle at a given point} solve quadratic equations {including those that require rearrangement} algebraically by factorising, {by completing the square and by using the quadratic formula}; find approximate solutions using a graph solve two simultaneous equations in two variables (linear/linear {or linear/quadratic}) algebraically; find approximate solutions using a graph {find approximate solutions to equations numerically using iteration} translate simple situations or procedures into algebraic expressions or formulae; derive an equation (or two simultaneous equations), solve the equation(s) and interpret the solution
3 Page3 solve linear inequalities in one {or two} variable{s}, {and quadratic inequalities in one variable}; represent the solution set on a number line, {using set notation and on a graph} recognise and use sequences of triangular, square and cube numbers, simple arithmetic progressions, Fibonacci type sequences, quadratic sequences, and simple geometric progressions (r n where n is an integer, and r is a positive rational number {or a surd}) {and other sequences} deduce expressions to calculate the n th term of linear {and quadratic} sequences Geometry and measures In addition to consolidating subject content from key stage 3, pupils should be taught to: describe translations as 2D vectors apply addition and subtraction of vectors, multiplication of vectors by a scalar, and diagrammatic and column representations of vectors; {use vectors to construct geometric arguments and proofs}.
4 Page4 Introductory week: (KS4 Algebra Pre-requisites) Task 1: Simplify the following: 1) 5a x 4b = 2) 6c x 2d = 3) 2e x 8f = 4) 6m x 3m = 5) 4g x 3h = 6) 7i x 2k = 7) 5p x 5q = 8) 10n x 7n = Extension: 1) 3c x 4g x 2k = 2) 2y x 2h x 6p = 3) 5d x w x 6w =
5 Page5 Task 2: Algebraic Simplification
6 Page6 Task 3: Algebraic Simplification
7 Page7 Task 4: Expanding and Simplifying Brackets
8 Page8 Task 5: Expanding and Simplifying Brackets
9 Page9 Task 6: Worded Questions 1. Mr Smith owns minibuses and coaches. Each minibus has 12 seats. (a) Write an expression, in terms of m, for the number of seats in m minibuses. Each coach has 48 seats (b) Write an expression, in terms of m and c, for the number of seats in m minibuses and c coaches. 2. Lisa packs pencils in boxes. She packs 12 pencils in each box. Lisa packs x boxes of pencils. (a) Write an expression, in terms of x, for the number of pencils Lisa packs. Lisa also packs pens in boxes.... She packs 10 pens into each box. Lisa packs y boxes of pens. (b) Write down an expression, in terms of x and y, for the total number of pens and pencils Lisa packs. 3. Jennifer made x cakes. She put 4 sweets on top of each cake. (a) Write down an expression, in terms of x, for the number of sweets she used.
10 Page10.. Paul made 3 more cakes than Jennifer. (b) Write down an expression, in terms of x, for the number of cakes Paul made... Paul also put 4 sweets on each of his cakes. (c) Write down an expression, in terms of x, for the number of sweets Paul used Martin cleaned his swimming pool. He hired a cleaning machine to do this job. The cost of hiring the cleaning machine was for the first day, then for each extra day. Martin s total cost of hiring the machine was For how many days did Martin hire the machine?... days 5. Andrew, Brenda and Callum each collect football stickers. Andrew has x stickers. Brenda has three times as many stickers as Andrew. (a) Write down an expression for the number of stickers that Brenda has.. (1) Callum has 9 stickers less than Andrew. (b) Write down an expression for the number of stickers that Callum has..
11 Page11 Section A: Simplify and manipulate algebraic expressions (Rearranging difficult formulae) Starter: Task 1:
12 Page12 Task 2: Make the letter in brackets the subject of the formula 1. Make the subject 2. Make the subject 3. Make b the subject 4. V 2 = u 2 + av 2 Make v the subject 5. Make r the subject 6. Make y the subject 7. Make a the subject 8. Make r the subject 9. Make r the subject 10. Make x the subject Task 3: Rearrange for the subject of the formula
13 Page Task 4:
14 Page14 Task 5: 1. Rearrange a(q c) = d to make q the subject. 2. (a) Make n the subject of the formula m = 5n 21 (b) Make p the subject of the formula 4(p 2q) = 3p P = πr + 2r + 2a Make r the subject of the formula 4. Make a the subject of the formula 2(3a c) = 5c Make m the subject of the formula 2(2p + m) = 3 5m
15 Page15 6. Make x the subject of 5(x 3) = y(4 3x) 7. When you are h feet above sea level, you can see d miles to the horizon, where Make h the subject of the formula 8. Rearrange the formula to make t the subject 9. Make b the subject of the formula 10. Rearrange the formula to make a the subject 11. Make x the subject of the formula 12. Rearrange to make u the subject of the formula. Give your answer in its simplest form.
16 Page16 Task 6: Forming equations
17 Page17 Section B: Solve quadratics by Factorisation; solving quadratics using the Formula Task 1: Solve via factorisation method 1. (i) Factorise x 2 4x 45 (ii) Solve the equation x 2 4x 45 = 0 2. (i) Factorise x 2 7x + 12 (ii) Solve the equation x 2 7x + 12 = 0 3. (a) Factorise x 2 3x 18 (b) Solve x 2 3x 18 = 0 x = or x = 4. (a) Factorise x 2 + 6x + 8 (b) Solve x 2 + 6x + 8 = 0 x = or x = 5. (a) Factorise x 2 x 56 (b) Solve x 2 x 56= 0 x = or x = 6. (i) Factorise x 2 + 9x + 20 (ii) Solve the equation x 2 + 9x + 20 = 0 7. (i) Factorise x 2 12x + 35 (ii) Solve the equation x 2 12x + 35 = 0 8. (i) Factorise x 2 x 72 (ii) Solve the equation x 2 x 72 = 0 9. (a) Factorise x 2 15x + 56 (b) Solve x 2 15x + 56 = 0 x = or x = 10. (a) Factorise x 2 + 9x + 18 (b) Solve x 2 + 9x + 18 = 0 x = or x =
18 Page (a) Show that x 2 x 56 = 0 (b) (i) Solve the equation x 2 x 56 = 0 (ii) Hence find the length of the shortest side of the trapezium Task 2: Solve the following using the Quadratic equation formula a) 2x + x - 8 = 0 b) 3x + 5x + 1 = 0 c) x - x 10 = 0 d) 5x + 2x - 1 = 0 e) 7x + 12x + 2 = 0 f) 3x + 11x + 9 = 0 g) 4x + 9x + 3 = 0 h) 6x + 22x + 19 = 0 i) x + 3x 6 = 0 j) 3x - 7x + 1 = 0 k) 2x + 11x + 4 = 0 l) 4x + 5x - 3 = 0 m) 4x - 9x + 4 = 0 n) 7x + 3x - 2 = 0
19 Page19 o) 5x - 10x + 1 = 0 Extensions: 1) Mavis is solving a quadratic equation using the quadratic formula. She correctly substitutes in values for a, b and c to get: What is the equation Mavis is trying to solve? 2) Junior uses the quadratic formula to solve: Sienna uses factorisation to solve: They both find something unusual in their solutions. Explain what this is Task 3: Use the quadratic formula to solve the equations below. Leave your answers to 3sf where necessary. 1) 2) 3) 4) 5) 6) 7) 8) 9) 10) 11) 12) Extension: For each of the equations below substitute the values and solve them. Note down how many solutions they have. Which bit of the formula affects the number of solutions the equation has? Can you make a generalised statement about this? a) b) c) d) e) f) Task 4: 1. x 2 +4x+3=0 2. x 2 +6x-16=0
20 Page20 Task 5: 3. x 2-10x+21=0 4. x 2 +6x+2=0 5. 3x 2-6x- 30= 0 1. Solve x 2 2x 1 = 0 Give your solutions correct to 2 decimal places. 2. Solve x 2 + 3x 5 = 0 Give your solutions correct to 4 significant figures. 3. Solve 3x 2 + 7x 13 = 0 Give your solutions correct to 2 decimal places. 4. Solve the equation 2x 2 + 6x 95 = 0 Give your solutions correct to 3 significant figures. 5. The diagram below shows a hexagon. All the corners are right angles. All measurements are given in centimetres. The area of the shape is 25 cm 2. (a) Show that 6x x 39 = 0
21 Page21 Task 6: Using Quadratic formula 1. Solve 3x 2 + 7x 13 = 0 Give your solutions correct to 2 decimal places x =... or x = Solve the equation 2x 2 + 6x 95 = 0 Give your solutions correct to 3 significant figures. x =... or x = Solve x 2 + 3x - 5 = 0 Give your solutions correct to 4 significant figures. 4. Solve this quadratic equation. x 2 5x 8 = 0 Give your answers correct to 3 significant figures. 5. (a) Solve x 2 2x 1 = 0 Give your solutions correct to 2 decimal places. (b) Write down the solutions, correct to 2 decimal places, of 3x 2 6x 3 = 0 6. (a) Solve x 2 + x + 11 = 14 Give your solutions correct to 3 significant figures. y = x 2 + x + 11 The value of y is a prime number when x = 0, 1, 2 and 3. The following statement is not true. y = x 2 + x + 11 is always a prime number when x is an integer (b) Show that the statement is not true
22 Page22 (a) Show that 2x 2 + 6x 95 = 0 (b) Solve the equation 2x 2 + 6x 95 = 0 Give your solutions correct to 3 significant figures. 8. (a) Show that 6x x 39 = 0 (b) (i) Solve the equation 6x x 39 = 0 (ii) Hence work out the length of the longest side of the shape.
23 Page23 (a) Show that 9x 2 17x 85 = 0 (b) (i) Solve 9x 2 17x 85 = 0 Give your solutions correct to 3 significant figures. (ii) Hence, work out the length of the shortest side of the 6-sided shape.
24 Page24 Section C: The difference of 2 squares; solving quadratics by Completing the Square Task 1: Solve by completing the square
25 Page25 Task 2:
26 Page26 Task 3: Write an equivalent expression in the form (x ± a) 2 - b (a) x 2 + 4x + 3 (b) x 2 + 8x -13 (c) x 2 + 6x + 5 (d) x 2-4x + 5 (e) x 2-8x + 9 Task 4: Solve the following equations using completing the square leaving your answer in the form of a square root. (a) x 2 + 6x -1= 0 (b) x 2 + 4x + 3= 0 (c) x 2 + 8x +13 = 0 (d) x 2 + 2x - 3= 0 (e) x 2-4x - 6= 0 (f) x 2-10x -10 = 0 Task 5: Complete the square on the following (Note some answers involve fractions!!) (a) x 2 + 3x - 2 (b) x 2-7x +12 (c) x 2-3x - 5 (d) 2x 2-16x + 24 (e) 3x 2 + 6x -15 (f) 2x 2 + 6x + 5
27 Page27 Section D: Simultaneous equations using a Quadratics Starter: Simple Simultaneous equations 1. Solve the simultaneous equations 3x + 2y = 4 4x + 5y = Solve the equations 3x + 5y = 19 4x 2y = Solve the simultaneous equations 3x + 4y = 200 2x + 3y = Solve the simultaneous equations 5x + 2y = 11 4x 3y = Solve the simultaneous equations 4x 3y = 11 10x + 2y = 1 6. Solve the simultaneous equations 3x + 7y = 26 4x + 5y = Solve the simultaneous equations 6x 2y = 33 4x + 3y = 9 Task 1:
28 Page28 Task 2: 1. 2.
29 Page Extension:
30 Page30 Task 3: Exam style questions 1. By eliminating y, find the solutions to the simultaneous equations x 2 + y 2 = 25 y = x 7 x =... y =... or x =... y =... (Total 6 marks) 2. Bill said that the line y = 6 cuts the curve x 2 + y 2 = 25 at two points. (a) By eliminating y show that Bill is incorrect. (2) (b) By eliminating y, find the solutions to the simultaneous equations x 2 + y 2 = 25 y = 2x 2 x =... y =... or x =... y =... (6) 3. Solve the simultaneous equations x 2 + y 2 = 29 y x = 3 (Total 7 marks)
31 Page31 Section E: Algebraic Fractions Task 1: Simplifying Algebraic fractions
32 Page32
33 Page33 Task 2:
34 Page34 Task 3:
35 Page35
36 Page36 Task 4: Multiply/Divide Algebraic fractions
37 Page37
38 Page38 Section F: Vectors Pre-requisites: manipulating algebraic fractions, Pythagoras theorem, and ratio knowledge (to work out vector magnitude and manipulate data provided) Task 1: Column Vectors d) Task 2:
39 Page39 Task 3:
40 Page40
41 Page41 Task 4:
42 Page42 Section G: Supplementary Questions (Mock Exam Paper style) 1. (a) Solve the equation x 1 3x 1 = (4) (b) Solve the equation 3 5 = 1 x 1 3x (4)
43 Page43 2. Solve the equation 3x 1 2 2x 1 = (4) 3. Algebraic fractions... (Total 3 marks) (Total 3 marks) (Total 3 marks) 6.
44 Page44... (Total 3 marks) (Total 3 marks)... (Total 3 marks) (Total 3 marks) (Total 3 marks) (Total 3 marks)
45 Page (a) The triangle has angles x, 2x and 84 as shown. Find the value of x. 84 Not drawn accurately x 2 x Answer... degrees (3) 12. Here are four expressions. n n2 3 n n (a) If n = 3, which expression has the greatest value? Show your working. (b) Answer... If n = 0.3, which expression has the greatest value? Show your working. (2)......
46 Page Answer... (2) (Total 4 marks) 13. This shape is made up of rectangles. x Not to scale 4y 3x y (a) Write down an expression, in terms of x and y, for the perimeter of the shape Answer... (2) (b) If x = 2 cm and y = 5 cm, find the area of the shape Answer... cm 2 (2) (Total 4 marks)
47 Page x x z 2x y (a) (i) Write down and simplify an expression, in terms of x, for the area of the triangle x... (2) (ii) Write down an expression, in terms of x, y and z, for the total area of the triangle and the two rectangles (1) (b) (i) Factorise your answer to part (a)(ii) (ii)... Calculate the total area of the triangle and two rectangles, if x = 5 cm and x + y + z = 28 cm (2) (1)
2 year GCSE Scheme of Work
2 year GCSE Scheme of Work Year 10 Pupils follow the 2 year Pearsons/Edexcel Scheme of Work FOUNDATION ROUTE HIGHER ROUTE YEAR 4 YEAR 5 YEAR 4 YEAR 5 GCSE (9-1) Foundation GCSE (9-1) Foundation GCSE (9-1)
More informationBrockington College Mathematics Personal Learning Checklist
Brockington College Mathematics Personal Learning Checklist To help you use this personal learning checklist, the target levels for each topic have given to help you decide what to focus on for your tier
More informationFOUNDATION MATHS REVISION CHECKLIST (Grades 5 1)
FOUNDATION MATHS REVISION CHECKLIST 2017+ (s 5 1) Geometry and Measures Arc lengths and sectors 5 Derive triangle results 5 Enlargements and negative SF 5 Loci 5 Pythagoras 5 Similarity and Congruence
More informationMathematics. GCSE subject content and assessment objectives
Mathematics GCSE subject content and assessment objectives Contents Introduction 3 Subject aims and learning outcomes 3 Subject content 4 Scope of study 4 Number 4 Algebra 6 Ratio, proportion and rates
More informationHIGHER MATHS REVISION CHECKLIST (Grades 9 4)
HIGHER MATHS REVISION CHECKLIST 2017+ (s 9 4) Geometry and Measures Circle theorems 8 Vector arguments and proof 8 Area of a triangle 7 Cosine Rule 7 Pythagoras and trig 2D and 3D 7 Sine Rule 7 Combined
More informationThe Grade Descriptors below are used to assess work and student progress in Mathematics from Year 7 to
Jersey College for Girls Assessment criteria for KS3 and KS4 Mathematics In Mathematics, students are required to become familiar, confident and competent with a range of content and procedures described
More information1. Peter cuts a square out of a rectangular piece of metal. accurately drawn. x + 2. x + 4. x + 2
1. Peter cuts a square out of a rectangular piece of metal. 2 x + 3 Diagram NOT accurately drawn x + 2 x + 4 x + 2 The length of the rectangle is 2x + 3. The width of the rectangle is x + 4. The length
More informationPLC Papers. Created For:
PLC Papers Created For: Algebra and proof 2 Grade 8 Objective: Use algebra to construct proofs Question 1 a) If n is a positive integer explain why the expression 2n + 1 is always an odd number. b) Use
More informationPLC Papers. Created For:
PLC Papers Created For: Algebraic argument 2 Grade 5 Objective: Argue mathematically that two algebraic expressions are equivalent, and use algebra to support and construct arguments Question 1. Show that
More informationYEAR 9 SCHEME OF WORK - EXTENSION
YEAR 9 SCHEME OF WORK - EXTENSION Autumn Term 1 Powers and roots Spring Term 1 Multiplicative reasoning Summer Term 1 Graphical solutions Quadratics Non-linear graphs Trigonometry Half Term: Assessment
More informationScope and Sequence: National Curriculum Mathematics from Haese Mathematics (7 10A)
Scope and Sequence: National Curriculum Mathematics from Haese Mathematics (7 10A) Updated 06/05/16 http://www.haesemathematics.com.au/ Note: Exercises in red text indicate material in the 10A textbook
More informationMathematics programmes of study: key stage 3. National curriculum in England
Mathematics programmes of study: key stage 3 National curriculum in England September 2013 Mathematics key stage 3 Purpose of study Mathematics is a creative and highly inter-connected discipline that
More informationANNUAL NATIONAL ASSESSMENT 2014 ASSESSMENT GUIDELINES MATHEMATICS GRADE 9
INTRODUCTION The 2014 cycle of Annual National Assessment (ANA 2014) will be administered in all public and designated 1 independent schools from 16 to 19 September 2014. During this period all learners
More informationMathematics KSHSSA Key Stage 3 Grade Descriptors
Developing Fluency, reasoning Mathematically and Problem Solving consolidate their numerical and mathematical capability from develop their mathematical knowledge, in part through key stage 2 and extend
More informationMethod marks are awarded for a correct method which could lead to a correct answer.
Pre Paper 3F Question Bank Answers November 2017 GCSE Mathematics (AQA style) Foundation Tier This set of answers is not a conventional marking scheme; while it gives a basic allocation of marks, its main
More informationPLC Papers. Created For:
PLC Papers Created For: Algebra and proof 2 Grade 8 Objective: Use algebra to construct proofs Question 1 a) If n is a positive integer explain why the expression 2n + 1 is always an odd number. b) Use
More informationUnit 3: Number, Algebra, Geometry 2
Unit 3: Number, Algebra, Geometry 2 Number Use standard form, expressed in standard notation and on a calculator display Calculate with standard form Convert between ordinary and standard form representations
More informationMathematics skills framework
Mathematics skills framework The framework for MYP mathematics outlines four branches of mathematical study. Schools can use the framework for mathematics as a tool for curriculum mapping when designing
More informationAssessment Report. Level 2, Mathematics
Assessment Report Level 2, 2006 Mathematics Manipulate algebraic expressions and solve equations (90284) Draw straightforward non-linear graphs (90285) Find and use straightforward derivatives and integrals
More informationRearrange m ore complicated formulae where the subject may appear twice or as a power (A*) Rearrange a formula where the subject appears twice (A)
Moving from A to A* A* Solve a pair of simultaneous equations where one is linear and the other is non-linear (A*) Rearrange m ore complicated formulae may appear twice or as a power (A*) Simplify fractions
More informationTopic test on first 3 units Problem solving task
SUBJECT Mathematics Year 8 HOD: C Thenuwara TERM 1 UNIT TITLES Fractions &Decimals LEARNING OBJECTIVES Pupils should be able to solve problem questions involving: One number as a fraction of another Fractions
More informationIntegers, Fractions, Decimals and Percentages. Equations and Inequations
Integers, Fractions, Decimals and Percentages Round a whole number to a specified number of significant figures Round a decimal number to a specified number of decimal places or significant figures Perform
More informationYEAR 10 PROGRAM TERM 1 TERM 2 TERM 3 TERM 4
YEAR 10 PROGRAM TERM 1 1. Revision of number operations 3 + T wk 2 2. Expansion 3 + T wk 4 3. Factorisation 7 + T wk 6 4. Algebraic Fractions 4 + T wk 7 5. Formulae 5 + T wk 9 6. Linear Equations 10 +T
More informationGCSE Linear Targeting Grade A*
GCSE Linear Targeting Grade A* Notes This scheme of work includes all the topics that make up the AQA GCSE Specification 800. It is aimed at classes that will fast-track their GCSE, completing the course
More informationCheck boxes of Edited Copy of Sp Topics (was 261-pilot)
Check boxes of Edited Copy of 10023 Sp 11 253 Topics (was 261-pilot) Intermediate Algebra (2011), 3rd Ed. [open all close all] R-Review of Basic Algebraic Concepts Section R.2 Ordering integers Plotting
More informationKing s Year 12 Medium Term Plan for LC1- A-Level Mathematics
King s Year 12 Medium Term Plan for LC1- A-Level Mathematics Modules Algebra, Geometry and Calculus. Materials Text book: Mathematics for A-Level Hodder Education. needed Calculator. Progress objectives
More informationGCSE (9 1) Mathematics
GCSE (9 1) Mathematics New topics sample questions (1MA1) First teaching from September 2015 First certification from June 2017 Issue 2 Contents About this booklet 3 1. Number 5 2. Algebra 8 3. Ratio,
More informationAlgebra. CLCnet. Page Topic Title. Revision Websites. GCSE Revision 2006/7 - Mathematics. Add your favourite websites and school software here.
Section 2 Page Topic Title 54-57 12. Basic algebra 58-61 13. Solving equations 62-64 14. Forming and solving equations from written information 65-67 15. Trial and improvement 68-72 16. Formulae 73-76
More informationUnderstand the difference between truncating and rounding. Calculate with roots, and with integer and fractional indices.
The assessments will cover the following content headings: 1. Number 2. Algebra 3. Ratio, and rates of change 4. Geometry and measures 5. Probability 6. Statistics Higher Year 7 Year 8 Year 9 Year 10 Year
More informationA Level Maths summer preparation work
A Level Maths summer preparation work Welcome to A Level Maths! We hope you are looking forward to two years of challenging and rewarding learning. You must make sure that you are prepared to study A Level
More informationCore A-level mathematics reproduced from the QCA s Subject criteria for Mathematics document
Core A-level mathematics reproduced from the QCA s Subject criteria for Mathematics document Background knowledge: (a) The arithmetic of integers (including HCFs and LCMs), of fractions, and of real numbers.
More informationYear 12 Maths C1-C2-S1 2016/2017
Half Term 1 5 th September 12 th September 19 th September 26 th September 3 rd October 10 th October 17 th October Basic algebra and Laws of indices Factorising expressions Manipulating surds and rationalising
More informationAlgebraic. techniques1
techniques Algebraic An electrician, a bank worker, a plumber and so on all have tools of their trade. Without these tools, and a good working knowledge of how to use them, it would be impossible for them
More informationN5 R1.2 and R1.3 Quadratics - Revision
N5 R and R3 Quadratics - Revision This revision pack covers the skills at Unit Assessment and exam level for Quadratics so you can evaluate your learning of this outcome. It is important that you prepare
More informationYou must have: Ruler graduated in centimetres and millimetres, pair of compasses, pen, HB pencil, eraser.
Write your name here Surname Other names Pearson Edexcel Award Algebra Level 3 Calculator NOT allowed Centre Number Candidate Number Tuesday 10 May 2016 Morning Time: 2 hours Paper Reference AAL30/01 You
More informationUNIT 3 MATHEMATICAL METHODS ALGEBRA
UNIT 3 MATHEMATICAL METHODS ALGEBRA Substitution of Values Rearrangement and Substitution Polynomial Expressions Expanding Expressions Expanding Expressions by Rule Perfect Squares The Difference of Two
More informationYou must have: Ruler graduated in centimetres and millimetres, pair of compasses, pen, HB pencil, eraser.
Write your name here Surname Other names Pearson Edexcel Award Algebra Level 3 Calculator NOT allowed Centre Number Candidate Number Thursday 12 January 2017 Morning Time: 2 hours Paper Reference AAL30/01
More informationHaringey Sixth Form Mathematics Department. Algebra Revision SHOW ALL WORKING OUT. Forming Equations
Haringey Sixth Form Mathematics Department Algebra Revision SHOW ALL WORKING OUT Forming Equations 1. A shop sells doughnuts and muffins. Doughnuts cost d pence each. Muffins cost m pence each. Daniel
More informationFree download from not for resale. Apps 1.1 : Applying trigonometric skills to triangles which do not have a right angle.
Apps 1.1 : Applying trigonometric skills to triangles which do not have a right angle. Area of a triangle using trigonometry. Using the Sine Rule. Using the Cosine Rule to find a side. Using the Cosine
More informationCheck boxes of Edited Copy of Sp Topics (was 145 for pilot) Beginning Algebra, 3rd Ed. [open all close all] Course Readiness and
Check boxes of Edited Copy of 10021 Sp 11 152 Topics (was 145 for pilot) Beginning Algebra, 3rd Ed. [open all close all] Course Readiness and Additional Topics Appendix Course Readiness Multiplication
More informationPaper 1 Foundation Revision List
Paper 1 Foundation Revision List Converting units of length 692 Converting units of mass 695 Order of operations 24 Solving one step equations 178 Operations with negative numbers 39, 40 Term to term rules
More informationA-Level Notes CORE 1
A-Level Notes CORE 1 Basic algebra Glossary Coefficient For example, in the expression x³ 3x² x + 4, the coefficient of x³ is, the coefficient of x² is 3, and the coefficient of x is 1. (The final 4 is
More informationQuadratic Equations. All types, factorising, equation, completing the square. 165 minutes. 151 marks. Page 1 of 53
Quadratic Equations All types, factorising, equation, completing the square 165 minutes 151 marks Page 1 of 53 Q1. (a) Factorise x 2 + 5x 24 Answer... (2) (b) Solve x 2 + 5x 24 = 0 Answer... (1) (Total
More informationSolve Quadratics Using the Formula
Clip 6 Solve Quadratics Using the Formula a + b + c = 0, = b± b 4 ac a ) Solve the equation + 4 + = 0 Give our answers correct to decimal places. ) Solve the equation + 8 + 6 = 0 ) Solve the equation =
More informationINDEX UNIT 3 TSFX REFERENCE MATERIALS 2014 ALGEBRA AND ARITHMETIC
INDEX UNIT 3 TSFX REFERENCE MATERIALS 2014 ALGEBRA AND ARITHMETIC Surds Page 1 Algebra of Polynomial Functions Page 2 Polynomial Expressions Page 2 Expanding Expressions Page 3 Factorising Expressions
More informationPURE MATHEMATICS AM 27
AM Syllabus (014): Pure Mathematics AM SYLLABUS (014) PURE MATHEMATICS AM 7 SYLLABUS 1 AM Syllabus (014): Pure Mathematics Pure Mathematics AM 7 Syllabus (Available in September) Paper I(3hrs)+Paper II(3hrs)
More informationCAMBRIDGE IGCSE MATHS EXAMINATION BOARD COVERAGE
CAMBRIDGE IGCSE MATHS EXAMINATION BOARD COVERAGE TIER TOPIC HEADING SUB HEADING Both Number Integers Ordering numbers Both Number Integers Rounding numbers Both Number Integers Adding and subtracting whole
More informationCandidate Name Centre Number Candidate Number MATHEMATICS UNIT 2: CALCULATOR-ALLOWED HIGHER TIER SPECIMEN PAPER SUMMER 2017
GCSE MATHEMATICS Specimen Assessment Materials 61 Candidate Name Centre Number Candidate Number 0 GCSE MATHEMATICS UNIT 2: CALCULATOR-ALLOWED HIGHER TIER SPECIMEN PAPER SUMMER 2017 1 HOUR 45 MINUTES ADDITIONAL
More informationDepartment Curriculum Map
Department Curriculum Map 2018-19 Department Mathematics Subject Specific Skills Wider key skills To be able to involving: Number Algebra Ratio, Proportion & Rates of Change Logic skills Problem solving
More informationSection A Plotting Straight Line Graphs Grade D / C
Name: Teacher Assessment Section A Plotting Straight Line Graphs Grade D / C 1. (a) Complete the table of values for = 3x + x 0 1 3 5 10 16 19 (b) On the grid draw the graph of = 3x + for values of x from
More informationCheck boxes of Edited Copy of Sp Topics (was 217-pilot)
Check boxes of Edited Copy of 10024 Sp 11 213 Topics (was 217-pilot) College Algebra, 9th Ed. [open all close all] R-Basic Algebra Operations Section R.1 Integers and rational numbers Rational and irrational
More informationC1 (EDEXCEL) GlosMaths Resources. C1 Mindmap
Bring on the Maths () Algebra C1 Mindmap Prior knowledge: Use index laws to simplify calculate the value of expressions involving multiplication division of integer powers, zero powers, fractional negative
More informationYear 12 Maths C1-C2-S1 2017/2018
Half Term 1 5 th September 12 th September 19 th September 26 th September 3 rd October 10 th October 17 th October Basic algebra and Laws of indices Factorising expressions Manipulating surds and rationalising
More informationC-1. Snezana Lawrence
C-1 Snezana Lawrence These materials have been written by Dr. Snezana Lawrence made possible by funding from Gatsby Technical Education projects (GTEP) as part of a Gatsby Teacher Fellowship ad-hoc bursary
More information2009 Assessment Report. Mathematics Level 2
National Certificate of Educational Achievement 2009 Assessment Report Mathematics Level 2 90284 Manipulate algebraic expressions and solve equations 90285 Draw straightforward non linear graphs 90286
More informationYear 10 Mathematics - Student Portfolio Summary
Year 10 - Student Portfolio Summary WORK SAMPLE PORTFOLIOS These work sample portfolios have been designed to illustrate satisfactory achievement in the relevant aspects of the achievement standard. The
More informationGCSE MATHEMATICS GCSE Teaching guidance For teaching from September 2015 onwards For GCSE exams in June 2017 onwards. Version 1.
GCSE MATHEMATICS GCSE 8300 Teaching guidance For teaching from September 2015 onwards For GCSE exams in June 2017 onwards Version 1.0, August 2014 Our specification is published on our website (www.aqa.org.uk).
More informationMATHS Learning Ladder Year 7
MATHS Learning Ladder Year 7 Key Learning Ladders The Learning Ladders are split into Year 7, 8 and 9 on different pages, and are colour coded to indicate the expected progress the students should be making.
More informationYear 9 Mastery Statements for Assessment 1. Topic Mastery Statements - I can Essential Knowledge - I know
Year 9 Mastery Statements for Assessment 1 Topic Mastery Statements - I can Essential Knowledge - I know Whole Numbers and Decimals Measures, perimeter area and volume Expressions and formulae Indices
More informationYou must have: Ruler graduated in centimetres and millimetres, pair of compasses, pen, HB pencil, eraser.
Write your name here Surname Other names Pearson Edexcel Award Algebra Level 3 Calculator NOT allowed Centre Number Candidate Number Monday 8 May 017 Morning Time: hours Paper Reference AAL30/01 You must
More informationPreCalculus. Curriculum (447 topics additional topics)
PreCalculus This course covers the topics shown below. Students navigate learning paths based on their level of readiness. Institutional users may customize the scope and sequence to meet curricular needs.
More information6 x. x y
Higher tier unit 19a check in test Calculator [Q1 Q2 linked] Q1. Complete the table of values for 6 y = x x 0.5 1 2 3 4 5 6 y 6 3 1.5 1 Q2. On the grid, draw the graph of 6 y = for 0.5 x 6 x Q3. The graph
More informationDRAFT. WJEC Eduqas GCSE (9-1) in MATHEMATICS. For teaching from 2015 For award from Summary of assessment 2
GCSE MATHEMATICS 1 WJEC Eduqas GCSE (9-1) in MATHEMATICS For teaching from 2015 For award from 2017 Summary of assessment 2 1. Introduction 3 1.1. Aims and objectives 3 1.2 Prior learning and progression
More informationPaper collated from year 2007 Content Pure Chapters 1-13 Marks 100 Time 2 hours
1. Paper collated from year 2007 Content Pure Chapters 1-13 Marks 100 Time 2 hours 4. 5. 6. 7. 8. 9. 10. 11. 12. 13. 14. Mark scheme Question 1 Question 2 Question 3 Question 4 Question 5 Question 6 Question
More informationMaths A Level Summer Assignment & Transition Work
Maths A Level Summer Assignment & Transition Work The summer assignment element should take no longer than hours to complete. Your summer assignment for each course must be submitted in the relevant first
More informationMesaieed International School
Mesaieed International School SUBJECT: Mathematics Year: 10H Overview of the year: The contents below reflect the first half of the two-year IGCSE Higher course which provides students with the opportunity
More informationWJEC LEVEL 2 CERTIFICATE 9550/01 ADDITIONAL MATHEMATICS
Surname Centre Number Candidate Number Other Names 0 WJEC LEVEL 2 CERTIFICATE 9550/01 ADDITIONAL MATHEMATICS A.M. MONDAY, 22 June 2015 2 hours 30 minutes S15-9550-01 For s use ADDITIONAL MATERIALS A calculator
More information4751 Mark Scheme June fraction line; accept to power ½ with denominator appropriate brackets answer M1 for a triple decker fraction or for
1 Question Answer Marks Guidance A A 2 square root symbol must extend below condone missing end bracket in [ r ] or [ r ] as final fraction line; accept to power ½ with denominator x y x y appropriate
More informationSummer Work for students entering PreCalculus
Summer Work for students entering PreCalculus Name Directions: The following packet represent a review of topics you learned in Algebra 1, Geometry, and Algebra 2. Complete your summer packet on separate
More informationMyMathLab for School Precalculus Graphical, Numerical, Algebraic Common Core Edition 2016
A Correlation of MyMathLab for School Precalculus Common Core Edition 2016 to the Tennessee Mathematics Standards Approved July 30, 2010 Bid Category 13-090-10 , Standard 1 Mathematical Processes Course
More informationFurther Mathematics Summer work booklet
Further Mathematics Summer work booklet Further Mathematics tasks 1 Skills You Should Have Below is the list of the skills you should be confident with before starting the A-Level Further Maths course:
More informationRegion 16 Board of Education. Precalculus Curriculum
Region 16 Board of Education Precalculus Curriculum 2008 1 Course Description This course offers students an opportunity to explore a variety of concepts designed to prepare them to go on to study calculus.
More informationCore Mathematics C12
Write your name here Surname Other names Pearson Edexcel International Advanced Level Centre Number Candidate Number Core Mathematics C12 Advanced Subsidiary Tuesday 10 January 2017 Morning Time: 2 hours
More informationPre AP Algebra. Mathematics Standards of Learning Curriculum Framework 2009: Pre AP Algebra
Pre AP Algebra Mathematics Standards of Learning Curriculum Framework 2009: Pre AP Algebra 1 The content of the mathematics standards is intended to support the following five goals for students: becoming
More informationMark = / Exam Questions. My Working. 1 Evaluate. 2 Find the equation of the line. 3 Express. in its simplest form. 4 Solve.
100 Exam Questions 1 Evaluate Mark = /10 My Working 6 1 5 2 1 3 2 Find the equation of the line 3 Express a 2 (2a 1 2 + a) in its simplest form 4 Solve x 2(x 1) = 8 5 Solve 4sinx = 2 for 0 < x < 360 6
More informationGrade 9 type questions. GCSE style questions arranged by topic
Write your name here Surname Other names In the style of: Pearson Edexcel Level 1/Level 2 GCSE (9-1) Centre Number Mathematics Grade 9 type questions GCSE style questions arranged by topic Candidate Number
More informationLCA Maths Department
Name: LCA Maths Department Unit 19 Higher Check-in test 1 Calculator Q1. Complete the table of values for 6 y x x 0.5 1 2 3 4 5 6 y 6 3 1.5 1 Q2. On the grid, draw the graph of 6 y for 0. x x Q3. The graph
More informationMath Prep for College Physics
Math Prep for College Physics This course covers the topics outlined below. You can customize the scope and sequence of this course to meet your curricular needs. Curriculum (190 topics + 52 additional
More informationCurriculum Area: Mathematics A Level - 2 year course (AQA) Year: 12. Aspire Learn Achieve
Topics Core 1 - Algebra Core 1 - Coordinate Geometry Core 1 - Differentiation Core 1 - Integration Year Curriculum - Use and manipulate surds - Quadratic functions and their graphs - The discriminant of
More informationMATHEMATICS SPECIFICATION GCSE. WJEC Eduqas GCSE in. Teaching from 2015 For award from Version 2 August 2018 ACCREDITED BY OFQUAL
GCSE WJEC Eduqas GCSE in MATHEMATICS ACCREDITED BY OFQUAL SPECIFICATION Teaching from 2015 For award from 2017 Version 2 August 2018 This Ofqual regulated qualification is not available for candidates
More informationYEAR 12 - Mathematics Pure (C1) Term 1 plan
Week YEAR 12 - Mathematics Pure (C1) Term 1 plan 2016-2017 1-2 Algebra Laws of indices for all rational exponents. Use and manipulation of surds. Quadratic functions and their graphs. The discriminant
More informationMEI Core 1. Basic Algebra. Section 1: Basic algebraic manipulation and solving simple equations. Manipulating algebraic expressions
MEI Core Basic Algebra Section : Basic algebraic manipulation and solving simple equations Notes and Examples These notes contain subsections on Manipulating algebraic expressions Collecting like terms
More informationPLC Papers Created For:
PLC Papers Created For: Quadratics intervention Deduce quadratic roots algebraically 1 Grade 6 Objective: Deduce roots algebraically. Question 1. Factorise and solve the equation x 2 8x + 15 = 0 Question
More informationSummer Work for students entering PreCalculus
Summer Work for students entering PreCalculus Name Directions: The following packet represent a review of topics you learned in Algebra 1, Geometry, and Algebra 2. Complete your summer packet on separate
More informationcorrelated to the Washington D.C. Public Schools Learning Standards Algebra I
correlated to the Washington D.C. Public Schools Learning Standards Algebra I McDougal Littell Algebra 1 2007 correlated to the Washington DC Public Schools Learning Standards Algebra I NUMBER SENSE AND
More informationKey competencies (student abilities)
Year 9 Mathematics Cambridge IGCSE Mathematics is accepted by universities and employers as proof of mathematical knowledge and understanding. Successful Cambridge IGCSE Mathematics candidates gain lifelong
More informationMaths Assessment Framework Year 10 Higher
Success Criteria for all assessments: Higher Tier 90% 9 80% 8 70% 7 60% 6 50% 5 Please note the GCSE Mathematics is one of the first GCSEs which will be graded by number rather than A*, A, B, C etc. Roughly,
More informationUnit 2: Number, Algebra, Geometry 1 (Non-Calculator)
Write your name here Surname Other names Edexcel GCSE Centre Number Mathematics B Unit 2: Number, Algebra, Geometry 1 (Non-Calculator) Tuesday 21 June 2011 Morning Time: 1 hour 15 minutes Candidate Number
More informationA Level Summer Work. Year 11 Year 12 Transition. Due: First lesson back after summer! Name:
A Level Summer Work Year 11 Year 12 Transition Due: First lesson back after summer! Name: This summer work is compulsory. Your maths teacher will ask to see your work (and method) in your first maths lesson,
More informationWhat you may need to do: 1. Formulate a quadratic expression or equation. Generate a quadratic expression from a description or diagram.
Dealing with a quadratic What it is: A quadratic expression is an algebraic expression containing an x 2 term, as well as possibly an x term and/or a number, but nothing else - eg, no x 3 term. The general
More informationMathematics OBJECTIVES FOR ENTRANCE TEST - YEAR 7. Numbers
Mathematics OBJECTIVES FOR ENTRANCE TEST - YEAR 7 1. Adding and subtracting Integers 2. Multiplying and Dividing Integers 3. Adding and Subtracting Decimals 4. Multiplying and Dividing by 10, 100 and 1000
More informationMATH Spring 2010 Topics per Section
MATH 101 - Spring 2010 Topics per Section Chapter 1 : These are the topics in ALEKS covered by each Section of the book. Section 1.1 : Section 1.2 : Ordering integers Plotting integers on a number line
More informationStudent. Teacher AS STARTER PACK. September City and Islington Sixth Form College Mathematics Department.
Student Teacher AS STARTER PACK September 015 City and Islington Sixth Form College Mathematics Department www.candimaths.uk CONTENTS INTRODUCTION 3 SUMMARY NOTES 4 WS CALCULUS 1 ~ Indices, powers and
More informationCore Mathematics C12
Write your name here Surname Other names Pearson Edexcel International Advanced Level Centre Number Candidate Number Core Mathematics C12 Advanced Subsidiary Monday 10 October 2016 Morning Time: 2 hours
More informationAS PURE MATHS REVISION NOTES
AS PURE MATHS REVISION NOTES 1 SURDS A root such as 3 that cannot be written exactly as a fraction is IRRATIONAL An expression that involves irrational roots is in SURD FORM e.g. 2 3 3 + 2 and 3-2 are
More informationCourse outline Mathematics: Methods ATAR Year 11
Course outline Mathematics: Methods ATAR Year 11 Unit 1 Sequential In Unit 1 students will be provided with opportunities to: underst the concepts techniques in algebra, functions, graphs, trigonometric
More informationThe Not-Formula Book for C1
Not The Not-Formula Book for C1 Everything you need to know for Core 1 that won t be in the formula book Examination Board: AQA Brief This document is intended as an aid for revision. Although it includes
More informationCore Mathematics C12
Write your name here Surname Other names Core Mathematics C12 SWANASH A Practice Paper Time: 2 hours 30 minutes Paper - E Year: 2017-2018 The formulae that you may need to answer some questions are found
More informationMathematics. SCEGGS Darlinghurst. Centre Number. Student Number. Preliminary Course Semester 2 Examination
Centre Number SCEGGS Darlinghurst Student Number 010 Preliminary Course Semester Examination Outcomes Assessed: P P8 Task Weighting: 40% General Instructions Reading time 5 minutes Working time hours Write
More informationA marks are for accuracy and are not given unless the relevant M mark has been given (M0 A1 is impossible!).
NOTES 1) In the marking scheme there are three types of marks: M marks are for method A marks are for accuracy and are not given unless the relevant M mark has been given (M0 is impossible!). B marks are
More information