1. Foundations Basics: Notation, and other things Algebraic manipulations Indices, Logs, Roots and Surds Binomial expansion Trigonometric functions Trigonometric identities Functions Types of function Solving equations

2. Sets of numbers the set of Natural numbers the set of Integers R is the set of Real Numbers the set of Rational Numbers Interval notation Order of Operations B Brackets O Order: Exponentials, Powers, Roots D M A S Division & Multiplication Addition & Subtraction Set notation is an element of is not an element of the set whose members are Intersection Union Subset Foundations Basics Index page

3. Difference of two squares Fraction equivalence Fraction arithmetic Splitting the numerator Squaring brackets Partial fractions Foundations Algebraic manipulation Index page

4. Laws of Logarithms Laws of Indices Laws of Surds Rationalising the denominator Indices notation Foundations Indices, logs, roots & surds Index page

5. Sigma Notation Binomial coefficients Factorial notation Binomial Theorem Binomial coefficients in Pascal’s triangle 1 1 2 1 1 3 3 1 1 4 6 4 1 15 10 10 5 1..... 1 n............n 1 General term Foundations Binomial Expansion Index page

6. Exact values General solutions Trigonometric ratios Radians Complementary angles and are complementary angles S A T C Symmetries of trig functions Foundations Trigonometry functions Index page

7. Addition formula etc. See formula sheet Double angle formulae etc. See formula sheet Pythagorean identities etc. See formula sheet Wave functions - cosine So and so Squares of sin and cos So and so Wave functions - sine Foundations Trigonometry identities Index page

8. Definitions A function is a rule which associates each member of a set, A, the domain a unique element of a set, B, the range Composite functions If then is a composite function. Function is calculated first on and function is calculated on the result. Function diagram Range Domain Natural Domain This is the set of all real numbers that can be used in a function Points to note: One-to-one Functions/ inverses A B A B A one-to-one function has an inverse If then rearrange to write. Interchanging and gives. Graph of a Function Domain [a,b]= Range [d,e] Foundations Functions Index page

9. Modulus Function Linear function Quadratic function Polynomial functions If the degree of the polynomial is i.e. where and are polynomials. is a proper fraction if Otherwise the fraction is improper. Rational functions Odd & Even Functions A function is even if A function is odd if The graph of an odd function has rotation symmetry about the origin and that of an even function has reflection symmetry in the axis. Foundations Types of Functions Index page

10. Quadratic Factorise or use Polynomial: Remainder theorem & Factor Theorem If is a factor of If then the remainder when is divided by is Exponential 1 Exponential 2 Simultaneous –non linear Try: 1)Solve one equation for (or ) in terms of or for (or ) in terms of and substitute in the other equation 2)Factorise or and set the factors equal to zero. Foundations Solving equations Index page

11. Foundations That’s all folks!!!