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Key Maths phrases, explanations and Formula
Algebra (C1 and C2)
SHOW THAT:
Find equation of a line

starting with the information you are given, show all the steps
of working until you get to the answer
write in form 𝑦 = 𝑚𝑥 + 𝑐, with m gradient and c intercept
or use 𝑦 – 𝑦1 = 𝑚(𝑥 – 𝑥1 ) with (𝑥1,y1) a point on the line
1

Perpendicular line

gradient is −

Intersects the 𝑥-axis:
Intersects the y-axis:
Coordinates of intersection of lines:
Give exact solutions:

make y = 0
make 𝑥 = 0
solve the equations simultaneously
leave as a surd and/or fraction (or in term of π or a log)
No decimal answers for exact solutions
divide the polynomial by (𝑥 – 2)
Prove that the discriminant is negative (b2 – 4ac < 0)
Make the equations of the line and curve equal to form a new
quadratic and show there is only 1 solution
Or show discriminant is zero (b2 – 4ac = 0)
Make a right angled triangle and use Pythagoras
Must be parallel – same gradient
Solve simultaneously E
...
Make the equations of the line and
curve equal to form a new quadratic – show there is no
solution Or show discriminant is negative
Solve when 𝑑𝑦/𝑑𝑥 = 0
Decide whether a maximum, minimum or inflection point
𝑑2 𝑦⁄
by using
𝑑𝑥 2

If 𝑥 = 2 is a root, find the other roots:
Prove no real roots:
Prove it is a tangent:

Distance between 2 points
Prove 2 lines don’t intersect
Prove line and curve don’t intersect

Turning point/Stationary point
Determine Nature of turning point

Increasing function
Area of a Triangle
Area of a Sector
Arc Length
Calculate gradient at a point
Calculate the area under a curve

𝑚

If < 0 →Max, If > 0 →Min, if =0 then need to compare 𝑑𝑦/𝑑𝑥
for 𝑥 -values either side of turning point
When 𝑑𝑦/𝑑𝑥 > 0
Either ½ x base x height OR ½ x a x b x sin C
½ r2 θ (where θ is in radians)
S = rθ (where θ is in radians)
Substitute 𝑥 into 𝑑𝑦/𝑑𝑥
Use integration between two limits



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