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1. Functions

1.1. Understand function terminology

1.2. Find domains and ranges of functions

1.3. Use function notation

1.4. Relate y = f(x) and y = |f(x)|

1.5. Explain when inverses do not exist

1.6. Find inverse functions

1.7. Form and use composite functions

1.8. Sketch functions and inverses

2. Quadratic functions

2.1. Find maximum and minimum values

2.2. Use vertex values to sketch or find range

2.3. Use discriminant conditions

2.4. Solve quadratic equations

2.5. Solve quadratic inequalities

3. Factors of polynomials

3.1. Use remainder and factor theorems

3.2. Find polynomial factors

3.3. Solve cubic equations

4. Equations, inequalities and graphs

4.1. Solve modulus equations

4.2. Solve modulus inequalities

4.3. Use substitution for related equations

4.4. Sketch cubic polynomials and moduli

4.5. Solve cubic inequalities graphically

5. Simultaneous equations

5.1. Solve simultaneous equations

6. Logarithmic and exponential functions

6.1. Use logarithmic and exponential graphs

6.2. Use laws of logarithms

6.3. Solve exponential equations

7. Straight-line graphs

7.1. Use straight-line equations

7.2. Use parallel and perpendicular gradients

7.3. Solve midpoint, length and bisector problems

7.4. Transform relationships to straight-line form

8. Coordinate geometry of the circle

8.1. Use circle equations

8.2. Solve line-circle intersection problems

8.3. Solve tangent problems

8.4. Solve circle-circle intersection problems

9. Circular measure

9.1. Solve arc length and sector area problems

10. Trigonometry

10.1. Use the six trigonometric functions

10.2. Use amplitude and period

10.3. Draw and use trigonometric graphs

10.4. Use trigonometric identities

10.5. Solve trigonometric equations

10.6. Prove trigonometric relationships

11. Permutations and combinations

11.1. Distinguish permutations and combinations

11.2. Use n! and nPr/nCr expressions

11.3. Solve arrangement and selection problems

12. Series

12.1. Use the binomial theorem

12.2. Use the general binomial term

12.3. Recognise arithmetic and geometric progressions

12.4. Use finite progression formulas

12.5. Use convergence and sum to infinity

13. Vectors in two dimensions

13.1. Use vector notation

13.2. Use position and unit vectors

13.3. Calculate and combine vectors

13.4. Compose and resolve velocities

14. Calculus

14.1. Understand derived functions

14.2. Use differentiation notation

14.3. Differentiate standard functions

14.4. Differentiate products and quotients

14.5. Find gradients, tangents and normals

14.6. Find stationary points

14.7. Apply differentiation to rates and approximations

14.8. Apply differentiation to maxima and minima

14.9. Use derivative tests for maxima and minima

14.10. Understand integration as reverse differentiation

14.11. Integrate powers of x

14.12. Integrate standard composite functions

14.13. Evaluate definite integrals and areas

14.14. Apply calculus to kinematics

14.15. Use kinematics graphs

IGCSE Additional Math 12.5. Use convergence and sum to infinity Topic Practice

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