Intermediate 2 Mind Maps Fractions Volume Straight Line Circle Simultaneous Equations Trigonometry Trig Functions & Equations Comparing Data Standard Deviation Quadratic Functions

Multiplication 15 Adding Basic Rules of Fraction Simple fractions Subtracting Multiplication Division Flip and change the sign Harder fractions Subtracting 6 1 Deal with whole numbers first 1 1 Same idea for addition Division 9 10 Top-heavy first Flip and change the sign 8 Top-heavy first 8 7 1

Area & Volume of a Prism Simple Areas Simple Volume Composite Areas Composite Volume Volume = Area x Height V = L x B x H A = L x BA = πr 2 A = ½bh A = B x h h A = ½(a + b) h h h V = πr 2 h made up of basic areas A = L x B + h V = (L x B x H) + h L B H B L a b B L r made up of basic volumes L B H h (½BhL) ½bh

Straight Line y = mx + c m = gradient c = y intercept Possible values for gradient m > 0 m < 0 m = 0 m = undefined Parallel lines have same gradient m > 0 Two points needed (x 1,y 1 ) and (x 2,y 2 ) to calculate gradient Graph of y = mx + c (0,c) (0, c ) Note : 2y + 4x = 8 rearrange into correct form y = -2x + 4

Area is Summary of Circle Topic Circumference is Sector area Arc length is Diameter Radius line that bisects a chord 1.Splits the chord into 2 equal halves. 2.Makes right-angle with the chord. 3.Passes through centre of the circle Pythagoras Theorem SOHCAHTOA Semi-circle angle is always 90 o Tangent touches circle at one point and make angle 90 o with point of contact radius

Simultaneous Equations Graphically Where two lines intersect (crossover) Algebraically y = -2x + 6 y = 0.5x + 1 y = -2x + 6 2y = x + 2 -x + 2y = 2 2x + y = 6 (A) (B) 1. Rearrange & Label 2. Scale and Eliminate -2x + 4y = 4 2x + y = 6 (C) (D) 2 x (A) then added 5y = 10 y = 2 Sub y = 2 into (A) -x + 2 x 2 = 2 -x = -2 x = 2 (2,2) (2,2) Remember to use the check

Right - Angle Triangle ONLY ! a b c Ratio values for sin and cos are between 0 and 1 Used for lengths only Pythagoras Theorem Used for finding length and angles S O HC A HT O AConverse is also true ! Isosceles 2 sides & 2 angles equal Equilateral All lengths & Angles equal (60 o ) Special Triangles For Any triangle Angles in a triangle add up to 180 o Triangle & Trig. Sine Rule Cosine Rule Right - Angle 90 o Scalene No angle the same Max / Mini values for sin and cos are 1 and - 1 SG Any triangle a b c A B C opp adj hyp xoxo a = stretches / squashes graph in y direction b = how times it repeats in 360 o c = moves graph up / down SAS

Trig Functions and Solving Trig Equations Basic Strategy for Solving Trig Equations Basic Graphs 360 o o o 90 o sin x cos x Exact Value Table 1.Rearrange into sin = 2.Find solution in the Quads Amplitude Period Amplitude Period Complex Graph o 180 o 270 o 360 o 3 y = 2sin4x + 1 Max. Value = = 3 Mini. Value = = -1 Period = 360 ÷ 4 = 90 o Amplitude = 2 C A S T 0o0o 180 o 270 o 90 o Period tan x Period Amplitude 180 o - x o 180 o + x o x o 360 o + x o

Things to note Things to note Q 1 = 25% of data Q 2 =Median = 50% of data Q 3 = 75% of data Interquartile range Q 3 - Q 1 Semi – Interquartile ÷ 2 Ways of comparing data Boxplots Key 1|9 = 19 n = Median Mode Mean Range Q1Q1 Q2Q2 Q3Q3 LH Q1Q1 Q2Q2 Q3Q3 LH Mean and standard deviation See separate mindmap Order data Back to back stem leaf

xx2x Standard Deviation “a measure of spread only ” S = standard deviation n = number of data points (Σx) 2 = Sum of data squared Σx 2 = Sum of squared data Σx = 15 (Σx) 2 = 225 Σx 2 = Note

Quadratic Functions y = ax 2 + bx + c SAC e.g. (x+1)(x-2)=0 Graphs Evaluating Decimal places Factorisation ax 2 + bx + c = 0 Cannot Factorise Roots x = -1 and x = 2 Roots x = -1.2 and x = 0.7 Roots Mini. Point (0, ) (0, ) Max. Point Line of Symmetry half way between roots Line of Symmetry half way between roots a > 0 a < 0 f(x) = x 2 + 4x + 3 f(-2) =(-2) x (-2) + 3 = -1 x = x = cc