1. Higher Maths Question Types

2. Functions & Graphs TYPE questions (Trig, Quadratics) Sketching Graphs Composite Functions Steps : 1.Outside function stays the same EXCEPT replace x terms with a ( ) 2.Put inner function in bracket You need to learn basic movements Exam questions normally involve two movements Remember order BODMAS Restrictions : 1.Denominator NOT ALLOWED to be zero 2.CANNOT take the square root of a negative number

3. Differentiation TYPE questions (Fractions / Surds /Indices) Basic and Format Function Increasing or Decreasing Tangent Line Steps : 1.Differentiate 2.f’(x) = 0 (statement) 3.Factorise 4.Nature Table 5.Sub x = to original equation to find y coordinate. Stationary Points Gradient f’(x) Optimization Steps : 1.Differentiate 2.Sub x = into f’(x) to find gradient 3.Use a point on the line and y – b = m(x – a) f’(x) > 0 f’(x) < 0 Max / Mini in closed intervals Steps : 1.Find Max / Mini points 2.Find end values 3.Decide Max / Mini Points

4. Recurrence Relations TYPE questions (Fractions / Sim Equations) Wordy question Finding Constants Steps : 1.Setup recurrence relation 2.State if limit exists 3.Find limit Steps : 1.Using information given setup two equations 2.Use simultaneous equation method to find constants

5. Quadratic Theory questions (Circle, Function Graphs) Completing the square Harder discriminant Steps 1.Identify a, b and c. 2.Discriminant.... = 0 and factorise. 3.Sketch and identify solution based on question asked. 2x 2 - 8x + 9 f(x) = a(x + b) 2 + c 2x 2 - 8x + 9 2(x - 2) 2 + 9 f(x) = 2(x - 2) 2 + 1 - 8 2(x 2 - 4x) + 9 Sketch See Function & Graphs Discriminant b 2 – 4ac 3 scenarios > 0 = 0 tangent !!! < 0 (1 - 2k)x 2 - 5kx - 2k > 0 Factorising cubic's polynomials (x+2) is a factor since no remainder Factor Theorem 1 4 5 2-2 -4-2 2101 e.g. use coefficients to factorise further if possible !! Remember to answer question f(x) = ( ) ( ) ( ) Harder Finding coefficients simultaneous equations

6. Integration TYPE questions (Fractions / Surds /Indices) Basic 2 Simple Area under the curve 014 Area above & below x-axis Do separately and remember statement for below x-axis A T = A 1 + A 2 Area between two curves -2 3 Steps : 1.For limits make equal to each other. 2.Integrate Top – (bottom) Original Equation

7. Trigonometry TYPE questions (Quadratic, Function Graphs) Expansion With Triangles Equation from Graph and solving Steps 1.Write down equation using graph 2.Using balance method to solve Sketching Substitution and solving β α 3 4 12 5 Steps 1.Pythagoras Theorem 2.Expansion 3.SOHCAHTOA 4.Solve. Sub for cos2x Factorise Solve See A3 sheet given out in Unit 1 For more solving techniques f(x) = sinxf(2x) = sin2x 3f(2x) = 3sin2xf(2x) + 1 = 3sin2x + 1 See A3 sheet given out in Unit 1 For more solving techniques Basic Exact values and radians !!!

8. Circle TYPE questions (Straight Line, Quadratics) Equation from graph Finding centre and radius from circle equation Is equation a circle ? Intersection points between line and circle Steps 1.Sub line equation y =... into circle. 2.Discriminant to establish how many points. 3.Factorise for x coordinates and sub into line equation for y coordinates (x - a) 2 + (y - b) 2 = r 2 x 2 + y 2 + 2gx + 2fy + c =0 centre = (-g,-f) radius = (a,b) r > 0 3 possible scenarios Equation of tangent Steps 1.Find gradient of centre to point 2.Use m 1 x m 2 = -1 to find gradient of line 3.Use y – b = m(x - a) Does circles touch externally or internally ? (a,b)

9. B Vector Theory Magnitude & Direction Points A, B and C are said to be Collinear if Parallel AND B is a point in common. C A Section formula properties n m a c b O A B C Angle between two vectors θ a b Tail to tail

10. Differentiations Question Type see Basic Differentiation. Harder functions Use Chain Rule Integration Question Type see Basic Integration. Differentiation Further Calculus Integration Trig

11. Logs & Exp Question Types Functions & Graphs Straight Line log A + log B = log AB log A - log B = log B A log a 1 = 0 log a a = 1 log (A) n = n log A log y = x log b + log a C = log am = log b (0,C) log y x log y = b log x + log a C = log am = b (0,C) log y log x Y = bX + C Y = (log b) X + C Y = mX + C Y = mX + C y = ab x Graph 1 y = ax b Graph 2 Solving Log Equations Solving Exp Equations ( half – life) Remember ln e -kt = -kt

12. Wave Function Type Questions (Functions & Graphs) f(x) = a sinx + b cosx compare to required trigonometric identities f(x) = k sin(x + β) = k sinx cos β + k cosx sin β Changing format Part (a) of question Solving Equation Normally Part (b) of question UNIT 2 3sin(x + 45 o ) = 1 Sketching Wave Function Normally Part (b) of question UNIT 1 Find Max / Mini Value Normally Part (b) of question AS TC Arrange into x =.......