M May Higher Revision Notes Mathematics

M May straight line equations gradient points of intersection parallel lines and perpendicular lines vectors and directed line segments scalar product Notes on Points

M May gradient is vertical / horizontal Straight line equations perpendicular lines parallel lines point of intersection -solve equations simultaneously Distance Formula midpoint

M May Three Dimensions: Distance Formula P p position vector of P component form Scalar product (dot product) magnitude of u perpendicular

M May medians altitudes bisectors join vertex to midpoint of opposite side drop perpendicular from vertex cut in half angles sides m n : A C B B divides AC in the ratio......

M May trigonometric functions radians trigonometric graphs solve trigonometric equations compound angles wave function Notes on Trigonometry

M May 360˚ r r r sin  1 1 radian cos  tan  sin 2  + cos 2  = ˚ 360˚ 180˚ tan  = sin  cos 

M May sin  = n C A S T  = sin -1 (n) two values in 1 complete turn sin(A+B) = sinAcosB + cosA sinB sin(A-B) = sinA cosB - cosA sinB cos(A+B) = cosA cosB - sinA sinB cos(A-B) = cosA cosB + sinA sinB sin(2A) = 2sinA cosA cos(2A) = cos 2 A - sin 2 A cos(2A) = 2cos 2 A - 1 cos(2A) = 1 - 2sin 2 A

M May in form C A S T also in form Reminder: Maximum and Minimum values of sinx or cosx are 1 and -1 SohCahToa for exact values

M May Differerentiation Integration polynomials trigonometric functions Area / Rate of change / Curve sketching chain rule Notes on Calculus

M May rate of change gradient gradient of tangent stationary points: maximum, minimum, inflexion sketch the curve displacement / velocity / acceleration Area under / between curves ‘Undoing’ differentiation

M May Basic functions x in radians

M May Always check your integration by differentiating! x in radians Reminder:

M May at turning points solve equation to give x < ? < ? < ±? 0 0 /?\ _ _ X Y giving turning points maximum?/minimum?

M May Geometry /Symmetry minimum / maximum centre, radius standard equations points of intersection tangents Notes on Parabolae / Circles

M May Parabola polynomial of degree 2 Circles Centre O(0,0) radius r minimum at (a, b) cuts the X-axis at (a,0) and (b,0) Centre radius maximum at (a, b)

M May Sketching graphs Given f(x) f(x) k f(x) f(x) + b f(x - a) f(-x) f(x + a) k stretches b periods in 360˚ or 2 π -a horizontal shift    +a horizontal shift <- ↑ move up ← move left → move right ↕ stretch reflection in X-axis reflection in Y-axis amplitude k period

M May Points of intersection: Solve simultaneous equations (by substitution). It is a Tangent if two solutions are equal. Reminder: find discriminant for a quadratic equation. if zero, then equal roots => tangent if less than 0, then no roots => no points of intersection A tangent to a circle meets the radius at 90˚ (perpendicular). and remember right angles in semicircle.

M May Those bacteria! Napiers shortcuts! / focus on indices Notes on Recurrence Relations Logarithms / Indices

M May Find how ‘long’ til..... After 1 after 2 after Limit exists if Limit State that: Make sure you make most efficient use of your calculator.

M May Logarithms = Indices can use calculator for base e and base 10 non-calculator for other bases

M May Examination Techniques Do read each question carefully. Re-read each question once you have finished to make sure you have answered all parts appropriately. Make sure you leave enough time to attempt all questions. Show all working steps. (particularly the substitution of numbers into formulae) Having prepared thoroughly, get a good night’s sleep before your exam!