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Includes integers, algebraic indices, surds and rationalising denominators, functions such as domain/range, asymptotes, composite and inverse functions, and algebraic manipulation. Also lists equation and inequality skills (linear, quadratic, simultaneous, algebraic fractions, and inequalities), graphs (linear, quadratic, cubic/quartic, and trigonometric), plus Pythagoras and trigonometry, probability, transformations, and proof by 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Certificate Revision Checklist  \n\n| Unit  \u003Cbr>1 Number   | Topic  \u003Cbr>Integers  \u003Cbr>Use index notation including fractional and negative indices  \u003Cbr>1.1  \u003Cbr>Solve equations where the unknown is a power   | RAG   | RAG  \u003Cbr>Topic  \u003Cbr>Unit  \u003Cbr>Functions   |  |  |\n| --- | --- | --- | --- | --- | --- |\n|  |  |  | 5Functions   | Identify the domain and range of a function  \u003Cbr>5.1  \u003Cbr>Identify if a function has asymptotes and if so where they are   |  |\n|  |  |  |  |  |  |\n|  | Surds  \u003Cbr>Simplify surd expressions  \u003Cbr>1.2  \u003Cbr>Expand and simplify with surds  \u003Cbr>Calculate exactly with surds   |  |  | Composite functions  \u003Cbr>Understand and find composite functions  \u003Cbr>5.2  \u003Cbr>Sketch the graphs of composite functions   |  |\n|  |  |  |  |  |  |\n|  |  |  |  |  |  |\n|  | Rationalising denominators  \u003Cbr>Rationalise the denominator involving simple surds  \u003Cbr>1.3  \u003Cbr>Rationalise the denominator involving surds which require simplifying first   |  |  | Inverse functions  \u003Cbr>Understand and find inverse functions  \u003Cbr>5.3  \u003Cbr>Find inverse functions of quadratic functions by completing the square  \u003Cbr>Sketch the graphs of inverse functions   |  |\n|  |  |  |  |  |  |\n| 2 Algebraic Manipulation   | Algebraic indices  \u003Cbr>2.1  \u003Cbr>Use index notation including fractional and negative indices in expressions   |  |  |  |  |\n|  |  |  |  | Transforming functions  \u003Cbr>Transform functions  \u003Cbr>5.4  \u003Cbr>Write the algebraic equation of transformed functions   |  |\n|  | Expanding brackets  \u003Cbr>2.2  \u003Cbr>Expand two or three expressions  \u003Cbr>Use Pascal's triangle to expand simple binomial expressions  \u003Cbr>Use Pascal's Triangle to expand more complex binomial expansions   |  |  |  |  |\n|  |  |  |  |  |  |\n|  |  |  | 6 Equations and inequaliies   | Solve equations  \u003Cbr>Solve equations with one unknown algebraically(including those with the  \u003Cbr>6.1  \u003Cbr>unknown on both sides of the equation).  \u003Cbr>Solve equations involving algebraic fractions   |  |\n|  |  |  |  |  |  |\n|  | Factorising  \u003Cbr>Factorise quadratic expressions including using difference of two squares  \u003Cbr>2.3  \u003Cbr>Use and understand the factor theorem  \u003Cbr>Factorise cubic expressions(by method of inspection or polynomial division)   |  |  |  |  |\n|  |  |  |  |  |  |\n|  |  |  |  | Solve quadratic equations  \u003Cbr>Solve quadratic equations algebraically by factorising,by completing the  \u003Cbr>square and by using the quadratic formula.  \u003Cbr>6.2  \u003Cbr>Solve quadratic equations which involve trigonometry  \u003Cbr>Solve other 'hidden quadratics'e.g.including √xorx^4   |  |\n|  |  |  |  |  |  |\n|  | Completing the square  \u003Cbr>Understand algebraic perfect squares,a²+2ab+b²  \u003Cbr>2.4  \u003Cbr>Completing the square including where the coefficient of x²is not 1 and the coefficient of x is  \u003Cbr>not even   |  |  |  |  |\n|  |  |  |  |  |  |\n|  |  |  |  |  |  |\n|  |  |  |  | Solve simultaneous equations  \u003Cbr>Solve simultaneous equations by substitution  \u003Cbr>Solve simultaneous equations where one equation is a quadratic graphically  \u003Cbr>6.3  \u003Cbr>Solve simultaneous equations where one equation is a quadratic  \u003Cbr>algebraically   |  |\n|  | Algebraic fractions  \u003Cbr>Simplify algebraic fractions  \u003Cbr>2.5  \u003Cbr>Add,subtract,multiply and divide algebraic fractions   |  |  |  |  |\n|  |  |  |  |  |  |\n| shparG3   | Linear graphs  \u003Cbr>Understand and use the equation of a straight line,including the forms y-y₁=m(x-x₁)and  \u003Cbr>3.1  \u003Cbr>ax+by+c=0.  \u003Cbr>Generate equations of parallel and perpendicular lines  \u003Cbr>Solve problems involving parallel and perpendicular lines   |  |  |  |  |\n|  |  |  |  |  |  |\n|  |  |  |  | Solving inequalities  \u003Cbr>Use set notation  \u003Cbr>Solve linear and quadratic inequalities  \u003Cbr>6.4  \u003Cbr>Represent linear and quadratic inequalities graphically  \u003Cbr>Solve problems involving linear programming   |  |\n|  |  |  |  |  |  |\n|  | Quadratic graphs  \u003Cbr>Indentify and interpret roots,intercepts &turning points of a quadratic graph  \u003Cbr>Indentify and interpret roots,intercepts &turni","cbCaijCKuq7KbHGA","https://ap.wps.com/l/cbCaijCKuq7KbHGA","pdf",141565,"English","# Unit 1 Number\n## Integers\n## Surds\n## Rationalising denominators\n# Unit 2 Algebraic Manipulation\n## Expanding brackets\n## Factorising\n## Completing the square\n## Algebraic fractions\n# Unit 3 Graphs\n## Linear graphs\n## Quadratic graphs\n## Cubic and quartic graphs\n## Trigonometric graphs\n# Unit 4 More graphs\n## Translating and reflecting graphs\n## Stretching graphs\n# Unit 5 Functions\n## Composite functions\n## Inverse functions\n## Transforming functions\n# Unit 6 Equations and inequalities\n## Solve equations\n## Solve quadratic equations\n## Solve simultaneous equations\n## Solving inequalities\n# Unit 7 Pythagoras and trigonometry\n## Exact trig values\n## Trigonometry in 3D\n## Sine and cosine rules and triangle area\n# Unit 8 Probability\n## Probability language\n## Venn diagrams and set notation\n## Tree diagrams\n## Conditional probability\n# Unit 9 Proof\n## Proof by deduction","[{\"question\":\"What topics are covered under Unit 1 Number?\",\"answer\":\"Unit 1 focuses on integers and surds, including simplifying surd expressions, expanding/simplifying with surds, and calculating exactly with surds, plus rationalising denominators.\"},{\"question\":\"Which function skills are included in Unit 5 Functions?\",\"answer\":\"Unit 5 includes identifying the domain and range, asymptotes, working with composite functions and sketching their graphs, finding inverse functions (including completing the square), and transforming functions by writing equations.\"},{\"question\":\"How does the checklist approach equations and inequalities in Unit 6?\",\"answer\":\"Unit 6 covers solving equations (including algebraic fractions and one unknown on either side), factorising and solving quadratic equations, solving simultaneous equations by substitution/graphically/algebraically, and representing and solving linear and quadratic inequalities using set notation and graphical methods.\"}]","Level 2 Extended Mathematics Certificate Revision Checklist | PDF",1792473553]