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 ma
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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
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