Edexcel IGCSE Maths EXAM WITH 100% CORRECT ANSWERS

Solving Simultaneous Equations: Elimination Method Multiple one, or both, of the equations by suitable multiplier, until they have a matching number of x's or y's 2 variants of method: If the matching terms have one + and one - signs, then use add equations. If signs are the same then subtract equations. Remember: DASS : Different, Add; Same, Substract! Solving Simultaneous Equations: Graphical Method Use if answers are whole numbers. Example: 4x + y = 6 equation(1) 5x-4y = 18 equation(2) Use equation(1), when x=0 then 4x0 +y =6, giving y=6. Thus graph passes through (0,6). When y=0 then 4x + 0 = 6, giving x =1.5 Thus graph passes through (1.5,0) Repeat above with equation(2) then plot lines, where they cross is the solution. Probability: Number of likely outcomes Probability = no. of favourable outcomes/ total no. of possible outcomes Probability: With test data Probability = no. of tests with favourable outcome/ total number of tests conducted Probability of an event not happening Probability Event(x) doesn't happen = 1- Probability Event(x) does happen Combined Probability of 2 events happening, when they can't happen at the same time. P [A or B] = P [A] + P [B] Combined Probability of 2 events happening when they are independent. P [A or B] = P[A] x P [B] Probabilities with multiple tests Use tree diagrams Venn Diagrams Differentiation: General Rule y = ax^n dy/dx = anx^n-1 Differentiation: Useful Examples 1/x becomes -1/x^2 1/x^2 becomes -2/x^3 Differentiation: Finding Max, Min values of Graphs Max, min values are known as turning points and occur when dy/dx = 0 Surds: √ab = √ab = √a x √b Surds: (√a)^2 = (√a)^2 = a Surds: Rules When multiplying or dividing: calculate whole numbers first then surds When adding and subtracting: only collect like terms Surds: Special products: (a+b)^2 = (a+b)^2 = a^2 + 2ab + b^2 first term squared + double the product +second term squared Surds: Special products: (a+b)(a-b) (a+b)(a-b) = a^2 - b^2 1st term squared - 2nd term squared (√a+√b)(√a-√b) = a - b