GCSE Mathematics Specification for first teaching in 2015
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GCSE Mathematics8300
Specification8300
8300
Appendix: mathematical formulae
1. Students are expected to know the following formulae included in the subject content; they will not be given in the exam. Refer to the Subject content section to determine the tier at which these formulae could be used.
The quadratic formula
The solutions of
, where
Circumference and area of a circle
Where
is the radius and
is the diameter:
Circumference of a circle =
=
Area of a circle =
Pythagoras’ theorem
In any right-angled triangle where
,
and
are lengths of the sides and
is the hypotenuse:
Trigonometry formulae
In any right-angled triangle
where
,
and
are lengths of the sides and
is the hypotenuse:
,
,
In any triangle
where
,
and
are lengths of the sides:
sine rule:
cosine rule:
Area =
2. Students are expected to know the following formulae or be able to derive them; they will not be given in the exam. Refer to the Subject content section to determine the tier at which these formulae could be used.
Perimeter, area, surface area and volume formulae
Where
and
are the lengths of the parallel sides and
is their perpendicular separation:
Area of a trapezium =
Volume of a prism = area of cross section x length
Compound interest
Where
is the principal amount,
is the interest rate over a given period and
is number of times that the interest is compounded:
Total accrued =
Probability
Where
is the probability of outcome
and
is the probability of outcome
:
3. Students are not expected to memorise the following formulae; they will be given in the exam in the relevant question. Refer to the Subject content section to determine the tier at which these formulae could be used.
Perimeter, area, surface area and volume formulae
Where
is the radius of the sphere or cone,
is the slant height of a cone and
is the perpendicular height of a cone:
Curved surface area of a cone =
Surface area of a sphere =
Volume of a sphere =
Volume of a cone =
Kinematics formulae
Where
is constant acceleration,
is initial velocity,
is final velocity,
is displacement from the position when
and
is time taken: