M May Maths Revision Notes Intermediate 2

M May Reminder : to _ significant figuresto _ decimal places = 340 to 2sf = to 1dp Percentages non-calccalculator interest: 10% = 1 / 10 25% = 1 / / 3 % = 1 / / 2 % = simple or compound? eg interest rate = 3% new balance = original x 1.03 appreciation depreciation increases decreases 6% x 1.06 x 0.94

M May Volumes Substitute carefully into formulae Use calculator carefully!(remember brackets) V = 4 πr 2 h 3 V = 4πx7x7x94πx7x7x9 3 r = 7cmh = 9cm V = V = 1850cm 3 correct to 3sf (remember units) show this step V = Ah for prism, A is Area of cross section / base eg

M May Area of rectangle Area of triangle Area of circle A = l x b A = 1 / 2 base x ht A = πr 2 C = πd Part of the circumference - arc Part of the circle area - sector 360 arc C sector A == Angle in semicircle = 90˚ Angle tangent / radius = 90˚ Radii equal => isosceles chord cut in half => 90˚ from centre 

M May Trigonometry SohCahToa p q r sinP = cosP = tanP = p/rp/r q/rq/r p/qp/q sin  = cos  = tan   = y/ry/r x/rx/r y/xy/x (x, y)  r 360˚ 360 ˚ y = sinx period amplitude 360 ˚ 180 ˚ y = tanx Pythagoras’ Theorem r 2 = p 2 + q 2

M May Area of triangle A C B a b c = 1 / 2 ab sin C Sine Rule a sin A = b sin B = c sin C Cosine Rule a 2 = b 2 + c 2 - 2bc cos A a sin A = b sin B = c sin C cos A b 2 + c 2 - a 2 2bc =

M May Graph / Equations Plot points from table (x, y) x y y = ax 2 + bx + cparabola y = mx + c straight line ax + by + c = 0 gradient = vertical length horizontal length gradient = m intercept (0, c) simultaneous equations - true at the same time point of intersection of two lines algebraic - by substitution algebraic - by “adding” (a, b) x = a y = b ax + by = c y = px + q ax + b(qx + q) = c ax + by = c px - by = r (a + p)x = c + r equation of best fit line on a scattergraph. y 2 - y 1 x 2 - x 1 m =

M May Algebramultiply out bracketsfactorise 7(3x + 4) = 21x x + 15 = 5(7x + 3) common factor x = (x + 9)(x - 9) x 2 + 9x + 14 = (x + 7)(x + 2) difference of 2 squares (2x - 5)(3x + 4) = 6x 2 + 8x - 15x - 20 = 6x 2 - 7x - 20 eg Simplify 2x 2 - 6x - 20 x x 2 - 6x - 20 x = 2(x 2 - 3x - 10) = 2(x - 5)(x + 2) 2(x - 5)(x + 2) = (x - 5)(x + 5) (x - 5)(x + 5) = = 2(x + 2) (x + 5)

M May Statistics mean mode median upper quartile lower quartile Highest Lowest Range semi-interquartile range standard deviation x _ most frequent middle one in order n / 4 = _ R _ H L Q1Q1 Q2Q2 Q3Q3 = H - L = 1 / 2 (Q 3 - Q 1 ) => table of values circle 1/2/3 of Qs each of 4 groups contains _ Probability P( ) = no. of favourable no. of possible Σ (x - x) 2 s = n - 1 √ _ Box plot

M May Stem and Leaf => n = 14 1| 0 represents 10 ‘ things’ Quartiles: 14 4 = 3 R 2 so Q 1 and Q 3 )( Pie Chart x x / total then x 360˚ dot plot Cumulative frequency x fc f symmetrical / skewed toward “tail”

M May Read each question carefully. Show all steps of working. Remember no working = no marks. Leave enough time to attempt all questions. Re-read questions when you finish to make sure you have answered all parts. Having prepared thoroughly, ensure a good night’s sleep before the exam.