Edexcel Maths Pure Paper 2 A+ Graded 100% Verified

Edexcel Maths Pure Paper 2 A+ Graded 100% Verified (Yr1) Expanding (a+B) ^n using the binomial expansion formula? ANS: (3-2x)^8 Find the binomial expansions up to x^2 1.) 8C0 x(-2x)x(3^8) + 8C1x(-2x)x(3^7) + 8C2x(-2x)^2x(3^6) 2. (1 + 2x)^30 up to x^3 =30C0x(2x) + 30C1x(2x) + 30C2x(2x)^2 xeg( 1^28)+ 30C3x(2x)^3 Powers (x) go up Coefficient (eg 1) goes down Binomial expansion formula when n(power) is a negative number or a fraction ANS: (1+x)^n = 1 + nx + n(n-1)/2 (x^2) + n(n-1)(n-2)/3 (x^3) +... Example (1+x)^-3 up to x^3 =1 - 3x +(-3(-3-1)/2 (x^2) + (-3(-3-1)(-3-2) /3 (x^3) =1 - 3x + 6x^2 - 10x^3 (if it is not 1 take it outside of the bracket, everything inside will be divisible by that ) How do you calculate modulas functions? ANS: X? = solve for x algebraicly Y? = line crosses Y axis, so sub x for 0 | Negatives | become | Positives | | Positives | become | Negatives | V Shape Negative parts are reflected in the x axis REMEMBER: What is outside the bracket affects the Y axis What is inside the bracket affects the X axis Calculating inequalities in modulas functions? ANS: Bndk What is the equation for differentiation from first principles? ANS: F'(x) = f(x+H) - f(X) / H Lim H>0( H becomes 0) 1. Sub for f(X) and f(X+H) 2. Multiply the brackets 3. Simplify 4. Divide by H 5. Apply the limit, make H= 0 iterative sequences ANS: a = first term d = common ratio n = term a + (n-1) x d Eg write down the first 6 terms in the sequence defined by xn = 2x(n-1) + 3, where x1 = 2 BE CAREFUL THE (N-1) IS A SUBSCRIPT AND NOT INVOLVED WITH THE CALCULATION X2 = 2 x (2) (n-1) + 3 = 7 X3 = 2 x (7) (n-1) + 3 = 17 X4 = 2 x (17) (n-1) + 3 = 77 Use the previous term in the sequence to work out the next term in the sequence Previous term = Xn - 1 What is the domain? ANS: Values on the x axis (x values touching the start and the finish of a graph) What is the range? ANS: Values on the Y axis (Y values touching the start and the finish of a graph) What is the form of the Exponential function? ANS: Y = a^x Eg, the growth of a population Y = c x a^x = Exponential growth Model will eventually break down C x a^-kx Negative Exponential decay What is meant by proof by deduction? ANS: A set of logical steps Even = 2n Odd = 2n + 1 What is meant by Proof by counter example? ANS: To Disprove a conjecture, you need to find a single instance where the conjecture is not true What is meant by Direct proof? ANS: Expressing the problem algebraiclly. Simple algebraic manipulation is required. Integers (not decimals or fractions) What is meant by proof by contradiction? ANS: U assume the opposite of the conjecture and show how it leads to a contradiction What is meant by proof by Exhaustion? ANS: Testing a number of possible subset of cases