Algebra Skills Required for Entry to a Level Two Course in Mathematics
|
|
- Hope Ball
- 5 years ago
- Views:
Transcription
1 Algebra Skills Required for Entr to a Level Two Course in Mathematics This is a list of Level One skills ou will be required to demonstrate if ou are to gain entr to the Level Two Achievement Standard Course in Year. To demonstrate that ou have gained these skills ou will be required to attend school and sit an Algebra test. If ou can demonstrate master of out of the Achieved skills and out of of the Merit skills then this will count as satisfing the Merit in Algebra criterion for entr to the Year course. Level of Achievement Skill Eample Simplif epressions involving indices Simplif Achieved Simplif epressions involving brackets Epand and simplif Epand a pair of brackets Epand and simplif Factorise a quadratic epression Factorise 0 Solve a linear equation Solve Solve a factorised quadratic equation Solve 0 Achieved with Merit Factorise, then solve, a quadratic equation Rearrange, then solve, a quadratic equation Solve simultaneous linear equations Rearrange a formula Solve, b factorising, Solve: Solve this pair of equations: 00 0 Rearrange the formula A a bh to make a the subject of the formula Simplif a fractional algebraic epression Simplif Add or subtract algebraic fractions Simplif Worked eamples, practice questions, and practice assessments with answers are provided in the following pages.
2 Achieved Skill Simplif epressions involving indices Eample a: Method: Answer: Simplif Cancel the fraction part. You can use the fraction ke on our calculator to do this. Or just divide both and b, giving the fraction. Now subtract the powers, so =. Eample b: Simplif Method: Multipl the numbers. So = 0 Now add the powers, so + =. Answer: 0 Eample c: Simplif Method: Answer: Work out. This is. Now multipl the powers. So becomes And becomes Achieved Skill Practice questions Simplif these: 0 0 a b 0 d p p d d a a a a a m n d e Go to List of Required Skills (page )
3 Achieved Skill Simplif epressions involving brackets Eample a: Epand and simplif Method: Multipl each term inside the bracket b the number that is outside. Remember = +. Then gather like terms = Answer: = Eample b: Epand and simplif Method: If there is just a sign in front, make it into Answer: = = Achieved Skill Practice questions Simplif these: ( ) + ( ) ( + ) ( ) ( ) ( ) ( ) ( ) + ( ) 0 ( ) + ( ) + ( ) ( ) ( ) ( ) + + ( ) ( + ) ( ) + ( ) ( ) ( + ) ( ) ( ) ( + ) Go to List of Required Skills (page )
4 Achieved Skill Epand a pair of brackets Eample a: Epand and simplif Method: Multipl each term inside the second bracket first b the and then b the. Remember + =. Then gather like terms. = Answer: = Eample b: Epand and simplif Method: Multipl each term inside the second bracket first b the and then b the. Remember = +. = 0 Answer: = 0 Achieved Skill Practice questions Epand the bracket and then simplif: ( )( ) ( + )( ) ( )( ) ( )( ) ( )( + ) 0 ( )( ) ( )( ) ( )( + ) ( )( + ) ( )( + ) ( + )( ) ( )( ) ( + )( ) ( )( + ) Go to List of Required Skills (page )
5 Achieved Skill Factorise a quadratic epression Eample a: Factorise 0 Method: Draw a pair of skeleton brackets, then put at the start of each bracket. Write down pairs of numbers that multipl to give 0. Choose the pair of numbers that also add together to give. Put these numbers into the brackets. Check that ou get 0 if ou epand the brackets. 0 = Answer: = Eample b: Factorise Method: Draw a pair of skeleton brackets, and put at the start of each bracket. Find the pair of numbers that multipl to give + and add together to give. Put these numbers into the brackets. Check that ou get if ou epand the brackets. = Answer: = Eample c: Factorise (This tpe is called the difference of two squares) Method: Draw a pair of skeleton brackets, and put at the start of each bracket. Our pair of numbers must multipl to give and add together to give zero (there is no term). The numbers are + and Check that ou get if ou epand the brackets. Answer: = Achieved Skill Practice questions Factorise: Go to List of Required Skills (page )
6 Achieved Skill Solve a linear equation Eample a: Method: Eample b: Method: + + Achieved Skill Practice questions Solve these equations: 0... Go to List of Required Skills (page )
7 Achieved Skill Solve a factorised quadratic equation Eample a: Solve: 0 Method: Answer: Let each bracket equal zero. This gives two equations, so there are two solutions. 0 or 0 or Eample b: Solve: 0 Method: Let each part equal zero. Again there are two solutions. 0 or 0 Answer: 0 or Achieved Skill Practice questions Solve these equations: ( + )( ) = 0 ( ) = 0 ( )( + ) = 0 ( )( + ) = 0 ( )( + ) = 0 0 ( ) = 0 ( )( ) = 0 ( )( + ) = 0 ( )( + ) = 0 ( + )( ) = 0 ( + )( + ) = 0 ( ) = 0 ( ) = 0 ( + ) = 0 Go to List of Required Skills (page )
8 Merit Skill Factorise and solve a quadratic equation Eample a: Solve: Method: Answer: 0 or 0 Eample b: Solve: 0 0 Method: 0 0 Answer: or Merit Skill Practice questions Solve these equations: Go to List of Required Skills (page )
9 Merit Skill Rearrange, then solve a quadratic equation Eample a: Solve: Method: 0 0 Answer: or Eample b: Solve: 0 Method: Answer: or Eample c: Solve: Method: 0 0 Answer: or Merit Skill Practice questions Solve these equations: Go to List of Required Skills (page )
10 0 Merit Skill Solve simultaneous linear equations Eample a: Solve: 00 0 Method: Substitute + 0 in place of in the first equation ( +0) + = = 0 = 0 = 00 Now substitute this into the second equation to find out what is. Answer: 0 and Eample b: Solve: Method: The equations have to be arranged this wa if ou are using a graphics calculator. Rearrange the second equation so that it matches the first one Divide the first equation b 0 (or multipl the second equation b 0) Add the equations to eliminate the variable 0 0 Substitute 0 into one of the original equations, and solve for Answer: and 0 Merit Skill Practice questions Solve these pairs of simultaneous equations: Go to List of Required Skills (page )
11 Merit Skill Rearrange a formula Eample a: Make a the subject of the formula A a bh Method: a bh A Answer: a a bh A A a b h A h b Eample b: Make a the subject of the formula v u at Method: u at v at v u Answer: v u a t Merit Skill Practice questions The formula for the perimeter of a rectangle is P l b. Rearrange the formula to make b the subject. Make n the subject of the formula 0n S. Make h the subject of the formula A bh. The formula for the distance around a running track is D l w. Rearrange the formula to make w the subject. The formula for the area of a square with an equilateral triangle on one of its sides is A.. Rearrange the formula to make the subject. The formula for the volume of a clinder is V r h. Rearrange the formula to make (i) h (ii) r the subject. Make d the subject of the formula Make v the subject of the formula A d. E mv. Make d the subject of the formula T a n d. 0 The equation of a straight line is. Rearrange the equation to make the subject. Go to List of Required Skills (page )
12 Merit Skill Simplif a fractional algebraic epression Eample a: Simplif: Method: = = Answer: = Eample b: Simplif: Method: = = Answer: = Merit Skill Practice questions Simplif: pq q p q p 0 Go to List of Required Skills (page ) Factorise top, or bottom, or both. Then cancel.
13 Merit Skill Add or subtract algebraic fractions Eample a: Simplif: Method: = = Answer: = Use the method for adding fractions Eample b: Simplif: Method: = = Answer: = Merit Skill Practice questions Simplif: 0 m m p p 0 z z a a d d 0 k k Go to List of Required Skills (page )
14 Practice Assessment One Simplif a b Solve: 0 Simplif Solve these simultaneous equations: a b 0 a b Epand and simplif Factorise 0 Make h the subject of the formula V r h Solve: Simplif a b a ab b Solve: 0 Solve: 0 0 Simplif Go to List of Required Skills (page )
15 Simplif a a Practice Assessment Two Solve: Simplif p q p q Solve these simultaneous equations: Epand and simplif Factorise 0 Make r the subject of the formula A r Solve: Simplif Solve: 0 Simplif m m Solve: 0 Go to List of Required Skills (page )
16 Simplif a a Practice Assessment Three Solve: Simplif a a Solve these simultaneous equations: Epand and simplif d d Factorise 0 Make t the subject of the formula C k nt Solve: Simplif Solve: 0 Solve: 0 0 Simplif Go to List of Required Skills (page )
17 Answers Achieved Skill Simplif epressions involving indices 00 0 a b 0 d p a 0 d a m n d e 0 Answers Achieved Skill Simplif epressions involving brackets ( ) + ( ) = + = ( ) ( ) = + = + + ( ) = + = 0 + ( ) = + = ( ) + + = + + = + + ( ) + ( ) = = ( + ) ( ) = + = + ( + ) ( ) = + + = + 0 ( ) ( ) = + + = 0 ( ) + ( ) = + = ( ) ( ) = 0 + = ( ) ( + ) = = ( ) = + = + ( ) ( + ) = + = Go to List of Required Skills (page )
18 Answers Achieved Skill Epand a pair of brackets ( )( ) = + = + ( )( ) = + = + ( )( + ) = + = + ( )( ) = 0 + = + ( )( + ) = + = ( + )( ) = + = ( + )( ) = + = + ( + )( ) = + = ( )( ) = + = + 0 ( )( ) = + 0 = + 0 ( )( + ) = + 0 = + ( )( + ) = + = + ( )( ) = 0 + = + ( )( + ) = + 0 = 0 + Answers Achieved Skill Factorise a quadratic epression = ( )( + ) 0 = ( + )( ) 0 = ( 0)( ) = ( )( ) 0 = ( + )( ) = ( + )( ) 0 = ( )( ) = ( + )( ) 0 = ( )( + ) = ( + )( ) = ( + )( ) 0 = ( + )( + ) = ( + )( ) = ( )( + ) = ( )( + ) Go to List of Required Skills (page )
19 Answers Achieved Skill Solve a linear equation Answers Achieved Skill Solve a factorised quadratic equation or or or or or or 0 or 0 or or 0 0 or or or 0 or 0 or Go to List of Required Skills (page )
20 Answers Merit Skill Factorise and solve a quadratic equation or or or or or or or or or or 0 0 or or or or or (twice) 0 0 or 0 0 (twice) (twice) or or 0 0 or or or 0 Go to List of Required Skills (page )
21 Answers Merit Skill Rearrange, then solve, a quadratic equation or or 0 0 or or 0 0 or 0 0 or or or or or or 0 0 or or or or or 0 0 Go to List of Required Skills (page )
22 Answers Merit Skill Solve simultaneous linear equations 0 and and 0 0 and 0 subtract then eqn, Rearrange Now substitute intoeqn 0 and and eqn Rearrange subtract then, Double eqn Now substituteintoeqn and and Rearrangeequation 0 0 eqn b Multipl 0 b eqn Multipl 0 Now substitute intoeqn Subtracting equations Go to List of Required Skills (page )
23 Answers Merit Skill Rearrange a formula b l P l P b l P b P b l 0 n S 0 0 this : or ou can do S n S n S n S n S n S n bh A b A h A bh A bh w l D l D w l D w D w l. A... A A A h r V r V h V h r h V r h V r V h r d A A d A d A d mv E m E v m E v E mv E mv d n a T n a T d a T d n T d n a 0 Go to List of Required Skills (page )
24 Answers Merit Skill Simplif a fractional algebraic epression pq q p q p q p pq q q p 0 Go to List of Required Skills (page )
25 Answers Merit Skill Add or subtract algebraic fractions m m m m 0 m a a a a a k k k 0k k k 0 0 p p 0p p p z z z z z d d 0 d d 0 0 d 0 Go to List of Required Skills (page )
26 Practice Assessment Answers Assessment One Assessment Two Assessment Three a b a a 0 0 or 0 or or a and b 0 h ab 0 V r p q 0 or or or and 0 r m A a d d 0 or or or and 0 t C k n Go to List of Required Skills (page )
Section J Venn diagrams
Section J Venn diagrams A Venn diagram is a wa of using regions to represent sets. If the overlap it means that there are some items in both sets. Worked eample J. Draw a Venn diagram representing the
More informationHigher Tier - Algebra revision
Higher Tier - Algebra revision Contents: Indices Epanding single brackets Epanding double brackets Substitution Solving equations Solving equations from angle probs Finding nth term of a sequence Simultaneous
More informationSOLVING QUADRATICS. Copyright - Kramzil Pty Ltd trading as Academic Teacher Resources
SOLVING QUADRATICS Copyright - Kramzil Pty Ltd trading as Academic Teacher Resources SOLVING QUADRATICS General Form: y a b c Where a, b and c are constants To solve a quadratic equation, the equation
More informationPreparing for A-Level Mathematics Summer 2017
Preparing for A-Level Mathematics Summer 017 INTRODUCTION TO A LEVEL MATHS Thank you for choosing to study Mathematics in the sith form. You will sit two modules in Pure Mathematics (C1 and C) as well
More informationUNCORRECTED SAMPLE PAGES. 3Quadratics. Chapter 3. Objectives
Chapter 3 3Quadratics Objectives To recognise and sketch the graphs of quadratic polnomials. To find the ke features of the graph of a quadratic polnomial: ais intercepts, turning point and ais of smmetr.
More informationHow can I prepare for the Mathematics entrance examination test?
How can I prepare for the Mathematics entrance examination test? The mathematics entrance examination test is designed to help ou find out how suitable ou will be to stud A level mathematics. It uses algebra-based
More informationMaths Department. A Level Induction Booklet
Maths Department A Level Induction Booklet CONTENTS Chapter 1 Removing brackets page Chapter Linear equations 4 Chapter 3 Simultaneous equations 8 Chapter 4 Factors 10 Chapter 5 Change the subject of the
More informationA-LEVEL MATHS Bridging Work 2017
A-LEVEL MATHS Bridging Work 017 Name: Firstly, CONGRATULATIONS for choosing the best A-Level subject there is. A-Level Maths at Wales is not only interesting and enjoyable but is highly regarded by colleges,
More informationQuadratics NOTES.notebook November 02, 2017
1) Find y where y = 2-1 and a) = 2 b) = -1 c) = 0 2) Epand the brackets and simplify: (m + 4)(2m - 3) To find the equation of quadratic graphs using substitution of a point. 3) Fully factorise 4y 2-5y
More informationAQA Level 2 Further mathematics Number & algebra. Section 3: Functions and their graphs
AQA Level Further mathematics Number & algebra Section : Functions and their graphs Notes and Eamples These notes contain subsections on: The language of functions Gradients The equation of a straight
More informationMaths Department. A Level Induction Booklet
Maths Department A Level Induction Booklet One of the most important things if you are to succeed at A Level Maths is to ensure you understand all the algebra you met at GCSE. Working through the eamples
More informationIntermediate Tier - Algebra revision
Intermediate Tier - Algebra revision Contents : Collecting like terms Multiplying terms together Indices Expanding single brackets Expanding double brackets Substitution Solving equations Finding nth term
More informationIntroduction to A-Level Maths (Bridging Unit)
Introduction to A-Level Maths (Bridging Unit) What is infinity + infinity? To infinity and beyond! SUMMER 017 Tuford Academy Faculty of Mathematics 1 INTRODUCTION TO A LEVEL MATHS AT TUXFORD ACADEMY Thank
More informationFurther factorising, simplifying, completing the square and algebraic proof
Further factorising, simplifying, completing the square and algebraic proof 8 CHAPTER 8. Further factorising Quadratic epressions of the form b c were factorised in Section 8. by finding two numbers whose
More informationAlgebra Revision Guide
Algebra Revision Guide Stage 4 S J Cooper 1st Edition Collection of like terms... Solving simple equations... Factorisation... 6 Inequalities... 7 Graphs... 9 1. The straight line... 9. The quadratic curve...
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 informationSimultaneous equations
Get started Simultaneous equations This unit will help ou to solve two equations simultaneousl, where one equation is linear and the other non-linear. AO1 Fluenc check 1 Make the subject of each equation.
More informationChapter XX: 1: Functions. XXXXXXXXXXXXXXX <CT>Chapter 1: Data representation</ct> 1.1 Mappings
978--08-8-8 Cambridge IGCSE and O Level Additional Mathematics Practice Book Ecerpt Chapter XX: : Functions XXXXXXXXXXXXXXX Chapter : Data representation This section will show you how to: understand
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 information4Cubic. polynomials UNCORRECTED PAGE PROOFS
4Cubic polnomials 4.1 Kick off with CAS 4. Polnomials 4.3 The remainder and factor theorems 4.4 Graphs of cubic polnomials 4.5 Equations of cubic polnomials 4.6 Cubic models and applications 4.7 Review
More informationMay 27, QUADRATICS.notebook. Apr 26 17:43. Apr 26 18:27. Apr 26 18:40. Apr 28 10:22. Apr 28 10:34. Apr 28 10:33. Starter
1. Factorise: 2 - - 6 2. Solve for : 2( + 1) = - 1 3. Factorise: 2-25 To solve quadratic equations.. Factorise: 2 2-8 5. State the gradient of the line: + 12 = 2 Apr 26 17:3 Apr 26 18:27 Solving Quadratic
More informationQUADRATIC GRAPHS ALGEBRA 2. Dr Adrian Jannetta MIMA CMath FRAS INU0114/514 (MATHS 1) Quadratic Graphs 1/ 16 Adrian Jannetta
QUADRATIC GRAPHS ALGEBRA 2 INU0114/514 (MATHS 1) Dr Adrian Jannetta MIMA CMath FRAS Quadratic Graphs 1/ 16 Adrian Jannetta Objectives Be able to sketch the graph of a quadratic function Recognise the shape
More informationLinear And Exponential Algebra Lesson #1
Introduction Linear And Eponential Algebra Lesson # Algebra is a very powerful tool which is used to make problem solving easier. Algebra involves using pronumerals (letters) to represent unknown values
More informationA11.1 Areas under curves
Applications 11.1 Areas under curves A11.1 Areas under curves Before ou start You should be able to: calculate the value of given the value of in algebraic equations of curves calculate the area of a trapezium.
More informationUnit 2: Rational Expressions
Rational Epressions Pure Math 0 Notes Unit : Rational Epressions -: Simplifing Rational Epressions Rational Epressions: - fractions with polnomials as numerator and / or denominator. To Simplif (Reduce)
More informationTHOMAS WHITHAM SIXTH FORM
THOMAS WHITHAM SIXTH FORM Algebra Foundation & Higher Tier Units & thomaswhitham.pbworks.com Algebra () Collection of like terms. Simplif each of the following epressions a) a a a b) m m m c) d) d d 6d
More informationGeometry and Honors Geometry Summer Review Packet 2014
Geometr and Honors Geometr Summer Review Packet 04 This will not be graded. It is for our benefit onl. The problems in this packet are designed to help ou review topics from previous mathematics courses
More informationCoordinate geometry. + bx + c. Vertical asymptote. Sketch graphs of hyperbolas (including asymptotic behaviour) from the general
A Sketch graphs of = a m b n c where m = or and n = or B Reciprocal graphs C Graphs of circles and ellipses D Graphs of hperbolas E Partial fractions F Sketch graphs using partial fractions Coordinate
More informationILLUSTRATIVE EXAMPLES
CHAPTER Points to Remember : POLYNOMIALS 7. A symbol having a fied numerical value is called a constant. For e.g. 9,,, etc.. A symbol which may take different numerical values is known as a variable. We
More informationZETA MATHS. Higher Mathematics Revision Checklist
ZETA MATHS Higher Mathematics Revision Checklist Contents: Epressions & Functions Page Logarithmic & Eponential Functions Addition Formulae. 3 Wave Function.... 4 Graphs of Functions. 5 Sets of Functions
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 informationA polynomial expression is the addition or subtraction of many algebraic terms with positive integer powers.
LEAVING CERT Honours Maths notes on Algebra. A polynomial expression is the addition or subtraction of many algebraic terms with positive integer powers. The degree is the highest power of x. 3x 2 + 2x
More informationUNCORRECTED. To recognise the rules of a number of common algebraic relations: y = x 1 y 2 = x
5A galler of graphs Objectives To recognise the rules of a number of common algebraic relations: = = = (rectangular hperbola) + = (circle). To be able to sketch the graphs of these relations. To be able
More informationN5 R1.1 Linear Equations - Revision
N5 R Linear Equations - Revision This revision pack covers the skills at Unit Assessment and eam level for Linear Equations so ou can evaluate our learning of this outcome. It is important that ou prepare
More informationMathematics Revision Guide. Algebra. Grade C B
Mathematics Revision Guide Algebra Grade C B 1 y 5 x y 4 = y 9 Add powers a 3 a 4.. (1) y 10 y 7 = y 3 (y 5 ) 3 = y 15 Subtract powers Multiply powers x 4 x 9...(1) (q 3 ) 4...(1) Keep numbers without
More informationMath 154 :: Elementary Algebra
Math :: Elementar Algebra Section. Section. Section. Section. Section. Section. Math :: Elementar Algebra Section. Eponents. When multipling like-bases, ou can add the eponents to simplif the epression..
More informationReview of Essential Skills and Knowledge
Review of Essential Skills and Knowledge R Eponent Laws...50 R Epanding and Simplifing Polnomial Epressions...5 R 3 Factoring Polnomial Epressions...5 R Working with Rational Epressions...55 R 5 Slope
More informationChapter 18 Quadratic Function 2
Chapter 18 Quadratic Function Completed Square Form 1 Consider this special set of numbers - the square numbers or the set of perfect squares. 4 = = 9 = 3 = 16 = 4 = 5 = 5 = Numbers like 5, 11, 15 are
More informationOne Solution Two Solutions Three Solutions Four Solutions. Since both equations equal y we can set them equal Combine like terms Factor Solve for x
Algebra Notes Quadratic Systems Name: Block: Date: Last class we discussed linear systems. The only possibilities we had we 1 solution, no solution or infinite solutions. With quadratic systems we have
More informationF6 Solving Inequalities
UNIT F6 Solving Inequalities: Tet F6 Solving Inequalities F6. Inequalities on a Number Line An inequalit involves one of the four smbols >,, < or The following statements illustrate the meaning of each
More informationContents. Useful formulae. iv Glossary
Contents Useful formulae iv Glossar v Unit 1 Histograms with equal class widths Get started 1 1 Drawing histograms with equal class widths Estimating the mean from a histogram 4 Practise the methods 6
More informationAlperton Community School. Preparation for. A Level Mathematics. This induction booklet is for students who wish to start AS Level Maths in Year 12.
Alperton Community School Preparation for A Level Mathematics This induction booklet is for students who wish to start AS Level Maths in Year 1. You are epected to know these topics before your first maths
More informationPure Core 1. Revision Notes
Pure Core Revision Notes Ma 06 Pure Core Algebra... Indices... Rules of indices... Surds... 4 Simplifing surds... 4 Rationalising the denominator... 4 Quadratic functions... 5 Completing the square....
More informationDay 3: Section P-6 Rational Expressions; Section P-7 Equations. Rational Expressions
1 Day : Section P-6 Rational Epressions; Section P-7 Equations Rational Epressions A rational epression (Fractions) is the quotient of two polynomials. The set of real numbers for which an algebraic epression
More informationTeddington School Sixth Form
Teddington School Sith Form AS / A level Maths Induction and Key Course Materials 016-018 Introduction The Mathematics Department at Teddington School are delighted that you would like to continue your
More informationUNIT 6 MODELING GEOMETRY Lesson 1: Deriving Equations Instruction
Prerequisite Skills This lesson requires the use of the following skills: appling the Pthagorean Theorem representing horizontal and vertical distances in a coordinate plane simplifing square roots writing
More informationCubic and quartic functions
3 Cubic and quartic functions 3A Epanding 3B Long division of polnomials 3C Polnomial values 3D The remainder and factor theorems 3E Factorising polnomials 3F Sum and difference of two cubes 3G Solving
More informationCoordinate goemetry in the (x, y) plane
Coordinate goemetr in the (x, ) plane In this chapter ou will learn how to solve problems involving parametric equations.. You can define the coordinates of a point on a curve using parametric equations.
More informationLines, Conics, Tangents, Limits and the Derivative
Lines, Conics, Tangents, Limits and te Derivative Te Straigt Line An two points on te (,) plane wen joined form a line segment. If te line segment is etended beond te two points ten it is called a straigt
More informationAlgebra Mat: Working Towards Year 6
Algebra Mat: Working Towards Year 6 at 3 and adds 3 each time. 5, 10, 15, 20, Use simple formulae. The perimeter of a rectangle = a + a + b + b a = a b = 2, cd = 6, find 2 different pairs of numbers for
More informationSNAP Centre Workshop. Solving Systems of Equations
SNAP Centre Workshop Solving Systems of Equations 35 Introduction When presented with an equation containing one variable, finding a solution is usually done using basic algebraic manipulation. Example
More informationAlgebra Review. 1. Evaluate the expression when a = -3 and b = A) 17 B) 1 C) Simplify: A) 17 B) 29 C) 16 D)
Algebra Review a b. Evaluate the epression when a = - and b = -. A) B) C). Simplify: 6 A) B) 9 C) 6 0. Simplify: A) 0 B) 8 C) 6. Evaluate: 6z y if =, y = 8, and z =. A) B) C) CPT Review //0 . Simplify:
More informationMath Intermediate Algebra
Math 095 - Intermediate Algebra Final Eam Review Objective 1: Determine whether a relation is a function. Given a graphical, tabular, or algebraic representation for a function, evaluate the function and
More information6.6 General Form of the Equation for a Linear Relation
6.6 General Form of the Equation for a Linear Relation FOCUS Relate the graph of a line to its equation in general form. We can write an equation in different forms. y 0 6 5 y 10 = 0 An equation for this
More informationTHE DISTRIBUTIVE LAW. Note: To avoid mistakes, include arrows above or below the terms that are being multiplied.
THE DISTRIBUTIVE LAW ( ) When an equation of the form a b c is epanded, every term inside the bracket is multiplied by the number or pronumeral (letter), and the sign that is located outside the brackets.
More informationTrigonometric. equations. Topic: Periodic functions and applications. Simple trigonometric. equations. Equations using radians Further trigonometric
Trigonometric equations 6 sllabusref eferenceence Topic: Periodic functions and applications In this cha 6A 6B 6C 6D 6E chapter Simple trigonometric equations Equations using radians Further trigonometric
More informationTECHNIQUES IN FACTORISATION
TECHNIQUES IN FACTORISATION The process where brackets are inserted into an equation is referred to as factorisation. Factorisation is the opposite process to epansion. METHOD: Epansion ( + )( 5) 15 Factorisation
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 informationSystems of Linear Equations: Solving by Graphing
8.1 Sstems of Linear Equations: Solving b Graphing 8.1 OBJECTIVE 1. Find the solution(s) for a set of linear equations b graphing NOTE There is no other ordered pair that satisfies both equations. From
More informationFormulae Using an algebraic formula CHAPTER. A h(a b) F 22
Formulae 18 CHAPTER A formula is a way of describing a fact or a rule. A formula can be written using algebraic expressions. A formula must have an sign. In Section 9.6 the area (A) of a trapezium was
More informationAre You Ready? Find Area in the Coordinate Plane
SKILL 38 Are You Read? Find Area in the Coordinate Plane Teaching Skill 38 Objective Find the areas of figures in the coordinate plane. Review with students the definition of area. Ask: Is the definition
More information2017 SUMMER REVIEW FOR STUDENTS ENTERING GEOMETRY
2017 SUMMER REVIEW FOR STUDENTS ENTERING GEOMETRY The following are topics that you will use in Geometry and should be retained throughout the summer. Please use this practice to review the topics you
More informationSample Problems For Grade 9 Mathematics. Grade. 1. If x 3
Sample roblems For 9 Mathematics DIRECTIONS: This section provides sample mathematics problems for the 9 test forms. These problems are based on material included in the New York Cit curriculum for 8.
More informationWCGS Mathematics Lower Sixth Bridging Work 2018
WCGS Mathematics Lower Sith Bridging Work 08 To be successful in Mathematics, students need to be confident in certain aspects of algebra, coordinate geometry and trigonometry before starting the course.
More informationAlgebra 1 Skills Needed for Success in Math
Algebra 1 Skills Needed for Success in Math A. Simplifing Polnomial Epressions Objectives: The student will be able to: Appl the appropriate arithmetic operations and algebraic properties needed to simplif
More informationThe standard form of the equation of a circle is based on the distance formula. The distance formula, in turn, is based on the Pythagorean Theorem.
Unit, Lesson. Deriving the Equation of a Circle The graph of an equation in and is the set of all points (, ) in a coordinate plane that satisf the equation. Some equations have graphs with precise geometric
More informationLearning Goals. College of Charleston Department of Mathematics Math 101: College Algebra Final Exam Review Problems 1
College of Charleston Department of Mathematics Math 0: College Algebra Final Eam Review Problems Learning Goals (AL-) Arithmetic of Real and Comple Numbers: I can classif numbers as natural, integer,
More informationNumerical and Algebraic Fractions
Numerical and Algebraic Fractions Aquinas Maths Department Preparation for AS Maths This unit covers numerical and algebraic fractions. In A level, solutions often involve fractions and one of the Core
More informationMath 030 Review for Final Exam Revised Fall 2010 RH/ DM 1
Math 00 Review for Final Eam Revised Fall 010 RH/ DM 1 1. Solve the equations: (-1) (7) (-) (-1) () 1 1 1 1 f. 1 g. h. 1 11 i. 9. Solve the following equations for the given variable: 1 Solve for. D ab
More informationMathematics. Polynomials and Quadratics. hsn.uk.net. Higher. Contents. Polynomials and Quadratics 1. CfE Edition
Higher Mathematics Contents 1 1 Quadratics EF 1 The Discriminant EF 3 3 Completing the Square EF 4 4 Sketching Parabolas EF 7 5 Determining the Equation of a Parabola RC 9 6 Solving Quadratic Inequalities
More informationAppendices. Appendix A.1: Factoring Polynomials. Techniques for Factoring Trinomials Factorability Test for Trinomials:
APPENDICES Appendices Appendi A.1: Factoring Polynomials Techniques for Factoring Trinomials Techniques for Factoring Trinomials Factorability Test for Trinomials: Eample: Solution: 696 APPENDIX A.1 Factoring
More informationWhich Mathematics Course Should You Take? August 22, 2018 Which mathematics course you should take depends on your current mathematics skill level
Which Mathematics Course Should You Take? August, 018 Which mathematics course you should take depends on your current mathematics skill level and your intended major. This is a conversation you should
More informationAlgebraic Expressions and Identities
9 Algebraic Epressions and Identities introduction In previous classes, you have studied the fundamental concepts of algebra, algebraic epressions and their addition and subtraction. In this chapter, we
More information2 Quadratic. equations. Chapter Contents. Learning Outcomes. ... I just hope it s easy! x 2 8x + 7 = 0 (x 7)(x 1) = 0 x 7 = 0 or x 1 = 0 x = 7 or 1
Quadratic Equations... I just hope it s easy! 8 + 7 = 0 ( 7)( ) = 0 7 = 0 or = 0 = 7 or Chapter Contents :0 Solution using factors PAS5 :0 Solution by completing the square PAS5 :0 The quadratic formula
More informationSTRAND F: ALGEBRA. UNIT F4 Solving Quadratic Equations: Text * * Contents. Section. F4.1 Factorisation. F4.2 Using the Formula
UNIT F4 Solving Quadratic Equations: Tet STRAND F: ALGEBRA Unit F4 Solving Quadratic Equations Tet Contents * * Section F4. Factorisation F4. Using the Formula F4. Completing the Square UNIT F4 Solving
More information12. Quadratics NOTES.notebook September 21, 2017
1) Fully factorise 4y 2-5y - 6 Today's Learning: To find the equation of quadratic graphs using substitution of a point. 2) Epand the brackets and simplify: (m + 4)(2m - 3) 3) Calculate 20% of 340 without
More informationHigher. Polynomials and Quadratics. Polynomials and Quadratics 1
Higher Mathematics Contents 1 1 Quadratics EF 1 The Discriminant EF 3 3 Completing the Square EF 4 4 Sketching Parabolas EF 7 5 Determining the Equation of a Parabola RC 9 6 Solving Quadratic Inequalities
More informationSTUDY KNOWHOW PROGRAM STUDY AND LEARNING CENTRE. Functions & Graphs
STUDY KNOWHOW PROGRAM STUDY AND LEARNING CENTRE Functions & Graphs Contents Functions and Relations... 1 Interval Notation... 3 Graphs: Linear Functions... 5 Lines and Gradients... 7 Graphs: Quadratic
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 informationGCSE style questions arranged by topic
Write our name here Surname Other names In the stle of: Pearson Edecel GCSE Centre Number Candidate Number Mathematics A* tpe questions GCSE stle questions arranged b topic Higher Tier Paper Reference
More information6. This sum can be rewritten as 4( ). We then recall the formula n =
. c = 9b = 3 b = 3 a 3 = a = = 6.. (3,, ) = 3 + + 3 = 9 + + 3 = 6 6. 3. We see that this is equal to. 3 = ( +.) 3. Using the fact that (x + ) 3 = x 3 + 3x + 3x + and replacing x with., we find that. 3
More informationSTRAND: ALGEBRA Unit 2 Solving Quadratic Equations
CMM Suject Support Strand: ALGEBRA Unit Solving Quadratic Equations: Tet STRAND: ALGEBRA Unit Solving Quadratic Equations TEXT Contents Section. Factorisation. Using the Formula. Completing the Square
More informationPure Core 2. Revision Notes
Pure Core Revision Notes June 06 Pure Core Algebra... Polynomials... Factorising... Standard results... Long division... Remainder theorem... 4 Factor theorem... 5 Choosing a suitable factor... 6 Cubic
More informationModule 3, Section 4 Analytic Geometry II
Principles of Mathematics 11 Section, Introduction 01 Introduction, Section Analtic Geometr II As the lesson titles show, this section etends what ou have learned about Analtic Geometr to several related
More informationA Level Maths. Induction Booklet CONTENTS
A Level Maths Induction Booklet CONTENTS Chapter 1 Removing brackets page Chapter Linear equations page 4 Chapter 3 Simultaneous equations page 8 Chapter 4 Factors page 10 Chapter 5 Change the subject
More informationExponentials and Logs
PSf Eponentials and Logs Paper 1 Section A Each correct answer in this section is worth two marks. 1. Simplif log 4 8 + log 4 2 3 log 5 5. A. 1 2 B. 1 C. log 4 ( 165 ) ( ) D. log 16 4 125 Ke utcome Grade
More informationAMB111F Notes 3 Quadratic Equations, Inequalities and their Graphs
AMB111F Notes 3 Quadratic Equations, Inequalities and their Graphs The eqn y = a +b+c is a quadratic eqn and its graph is called a parabola. If a > 0, the parabola is concave up, while if a < 0, the parabola
More informationJanuary Core Mathematics C1 Mark Scheme
January 007 666 Core Mathematics C Mark Scheme Question Scheme Mark. 4 k or k (k a non-zero constant) M, +..., ( 0) A, A, B (4) 4 Accept equivalent alternatives to, e.g. 0.5,,. M: 4 differentiated to give
More informationFrom the Y9 teaching programme
1 Key Stage Year 8 Unit Title Algebra 1 Duration weeks Use BIDMAS in arithmetical calculations both with & without a calculator Understand that algebraic operations follow the rules of arithmetic MyMaths
More informationQuadratic equationsgraphs
All reasonable efforts have been made to make sure the notes are accurate. The author cannot be held responsible for an damages arising from the use of these notes in an fashion. Quadratic equationsgraphs
More informationSIXTH FORM MATHEMATICS A LEVEL INDUCTION BOOKLET SEPTEMBER Name:
SIXTH FORM MATHEMATICS A LEVEL INDUCTION BOOKLET SEPTEMBER 014 Name: INTRODUCTION TO A LEVEL MATHS Thank you for choosing to study Mathematics in the sixth form at Chelsea Academy. In year 1 you will sit
More informationUNIT 5. SIMULTANEOUS EQUATIONS
3º ESO. Definitions UNIT 5. SIMULTANEOUS EQUATIONS A linear equation with two unknowns is an equation with two unknowns having both of them degree one. Eamples. 3 + 5 and + 6 9. The standard form for these
More informationChapter 8: Algebra Part 2
Chapter 8: Algebra Part 2 Section 8.1 Algebraic Products Expanding brackets means to remove the brackets. How would we expand the following? 5 (x + 2) The term which is outside the brackets must be multiplied
More informationMAIDSTONE GRAMMAR SCHOOL FOR GIRLS DEPARTMENT OF MATHEMATICS
MAIDSTONE GRAMMAR SCHOOL FOR GIRLS DEPARTMENT OF MATHEMATICS Introduction to A level Maths INDUCTION BOOKLET INTRODUCTION TO A LEVEL MATHS AT MGGS Thank you for choosing to study Mathematics in the sith
More informationMathematics Benchmark Achievements Senior Math
Mathematics Benchmark Achievements Senior Math Ages 12+ College Bound Objectives at this age: Continue with a systematic approach to developing math skills. Please note that levels listed below are not
More information2, find c in terms of k. x
1. (a) Work out (i) 8 0.. (ii) 5 2 1 (iii) 27 3. 1 (iv) 252.. (4) (b) Given that x = 2 k and 4 c 2, find c in terms of k. x c =. (1) (Total 5 marks) 2. Solve the equation 7 1 4 x 2 x 1 (Total 7 marks)
More informationHigher. Integration 89
hsn.uk.net Higher Mathematics UNIT UTCME Integration Contents Integration 89 Indefinite Integrals 89 Preparing to Integrate 9 Differential Equations 9 Definite Integrals 9 Geometric Interpretation of Integration
More informationSOLUTION OF QUADRATIC EQUATIONS LESSON PLAN. A3 Topic Overview ALGEBRA
ALGEBRA A Topic Overview A SOLUTION OF QUADRATIC EQUATIONS This topic describes three methods of solving Quadratic equations. assumes you understand and have practised using the algebraic methods described
More information5 3w. Unit 2 Function Operations and Equivalence Standard 4.1 Add, Subtract, & Multiply Polynomials
Unit Function Operations and Equivalence This document is meant to be used as an eample guide for each of the skills we will be holding students accountable for with Standard 4.1. This document should
More informationHigher. Integration 1
Higher Mathematics Contents Indefinite Integrals RC Preparing to Integrate RC Differential Equations A Definite Integrals RC 7 Geometric Interpretation of A 8 Areas between Curves A 7 Integrating along
More information