Edexcel Pure Maths: A-Level, Content ideas and Formula Already Passed

Document Content and Description Below

Edexcel Pure Maths: A-Level, Content ideas and Formula Already Passed What are the turning point co-ordinates in f(x)=a(x+p)^2 +q ✔✔(-p,q) How many roots are there if the discriminent > 0? ✔�... ��Two distinct roots How many roots are there if the discriminent = 0? ✔✔One/repeated root How many roots are there if the discriminent < 0? ✔✔no real roots What can we use the discriminent to find? ✔✔no. of points of intersection What does the solution of a pair of simultaneous equations represent? ✔✔points of intersection on their graphs What do you use to see/show a linear inequality? ✔✔number line sketch What do you use to see/show a quadratic inequality? ✔✔quadratic curve sketch What type of line do you use to represent ≥ ≤? ✔✔Solid line What type of line do you use to represent > <? ✔✔Dotted line What quadrants are the two curves of the reciprocal graph y=1/x? ✔✔1st and 3rd What quadrants are the two curves of the reciprocal graph y=-1/x? ✔✔2nd and 4th What quadrants are the two curves of the reciprocal graph y= 1/x^2? ✔✔1st and 2nd What quadrants are the two curves of the reciprocal graph y=-1/x^2? ✔✔3rd and 4th How to remember transformations of addition/subtraction and multiplication? ✔✔near x, affects x How to remember transformations of modulus and negatives? ✔✔near x, affects y How does y=f(x)+a affect the graph of f(x)? ✔✔affects y, moves up and down How does y=f(x+a) affect the graph of f(x)? ✔✔affects x, opposite direction sideways How does y=af(x) affect the graph of f(x)? ✔✔y x a How does y=f(ax) affect the graph of f(x)? ✔✔x/a How does y=-f(x) affect the graph of f(x)? ✔✔reflected in x axis How does y=f(-x) affect the graph of f(x)? ✔✔reflected in y axis How to find gradient from two points? ✔✔y2-y1/x2-x1 How to find line parallel? ✔✔same gradient, different y intercept How to find line perpendicular? ✔✔negative reciprocal of gradient, find c How to find the midpoint of two points? ✔✔(x1+x2/2, y1+y2/2) What is a perpendicular bisector to line AB? ✔✔perpendiculare to AB and passes through midpoint of AB Where will the perpendicular bisector of chord pass through? ✔✔centre of circle What is the equation for a circle with centre (0,0) and radius, r? ✔✔x^2 + y^2 = r^2 What is the equation for a circle with centre (a,b) and radius, r? ✔✔(x-a)^2 + (y-b)^2 = r^2 What is the circle with centre (a,b) a translation of? ✔✔x^2 + y^2 = r^2 with vector (a b) Circle theorem about tengents and chords? ✔✔a tangent will meet a chord at 90 degrees Circle theorem subtended arcs and circumference? ✔✔angles subtended by the same arc at the circumference are equal Circle theorem about angles at circumference and centre? ✔✔the angle subtended at the centre is twice the angle at the circumference Circle theorem about triangles in semicircles? ✔✔angle of triangle in a semicircle is 90 degrees Circle theorem about cyclic quadrilaterals? ✔✔opposite angles in a cyclic quadrilateral add up to 180 degrees What is the alternate segment theorem? ✔✔The angle between a tangent and a chord is always equal to the angle in the opposite segment What is the factor theorem? for when f(p)=0 ✔✔then (x-p) is a factor of f(x) What is the factor theorem? for when f(x-p) is a factor of f(x) ✔✔then f(p)=0 What is the Cosine rule for sides? ✔✔a^2 = b^2 + c^2 -2bcCos A What is the Cosine rule for angles? ✔✔CosA = (b^2 + c^2 - a^2)/2bc What do you need to use the Cosine to find a side? ✔✔Two sides and included angle What do you need to use the Cosine to find an angle? ✔✔all three sides What is the Sine Rule for a side? ✔✔a/SinA = b/SinB = c/SinC What is the Sine rule for an angle? ✔✔SinA/a = SinB/b = SinC/c What do you need to use the Sine to find a side? ✔✔one pair of opposite side and angle and angle opposite to side you want to find What do you need to use the Sine to find an angle? ✔✔one pair of opposite side and angle and side opposite to angle you want to find What does sin²θ + cos²θ equal? ✔✔1 what does tan(x) equal? ✔✔sinx/cosx What does it mena for the line segments PQ and RS if vector PQ = vector RS ✔✔they are equal in length and parallel What is the triangle law for vector addition? ✔✔a + b = c What does vector PQ + vector QP equal? ✔✔0 Write vector ( p q) in terms of i and j ✔✔pi + qj How is the magnitude of a vecot written for vecot xi +yj? ✔✔square root x^2 + y^2 [Show More]

Last updated: 1 year ago

Preview 1 out of 7 pages