The quadratic formula:
The solutions of ax2+bx+c=0 , where a≠0
x= ( -b±√(b2-4ac) ) / 2a

Circumference and area of a circle:
Where r is the radius and d is the diameter:
Circumference of a circle = 2πr = πd
Area of a circle = πr2

Pythagoras' theorem:
In any right-angled triangle where a , b and c are lengths of the sides and c is the hypotenuse:
a2+b2=c2

Trigonometry formulae:
In any right-angled triangle ABC, where a , b and c are lengths of the sides and c, is the hypotenuse:
sinA = a/c , cosA = b/c , tanA = a/b
In any triangle ABC where a , b and c are lengths of the sides:
sine rule: a/sinA = b/sinB = c/sinC
cosine rule: a2=b2+c2-2bc cosA
Area = 0.5xaxbxsinC

Perimeter, area, surface area and volume formulae:
Where a and b are the lengths of the parallel sides and h is their perpendicular separation:
Area of a trapezium = 0.5(a+b)h
Volume of a prism = area of cross-section x length

Compound interest:
Where P is the principal amount, r is the interest rate over a given period and n is number of times that the interest is compounded:
Total accrued = P(1+r/100)^n

Probability:
Where P(A) is the probability of outcome A and P(B) is the probability of outcome B :
P(A or B)=P(A)+P(B)-P(A and B)
P(A and B)=P(A given B)P(B)
Not needed to be memorised, they will be given in the exam

Perimeter, area, surface area and volume formulae:
Where r is the radius of the sphere or cone, l is the slant height of a cone and h is the perpendicular height of a cone:
Curved surface area of a cone = πrl
Surface area of a sphere = 4πr2
Volume of a sphere = 4/3xπxr3
Volume of a cone = 1/3xπxr2xh

Kinematics formulae:
Where a is constant acceleration, u is initial velocity, v is final velocity, s is displacement from the position when t=0 and t is time taken:
v = u+at
s = ut+1/2xaxt
v2 = u2+2as

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AQA GCSE Mathematics Topics

AQA GCSE Mathematics Equations