Changes to GCSE Mathematics
7
© Cambridge University Press, 2015
Calculate or estimate gradients
of graphs and areas under
graphs (including quadratic
and other non-linear graphs),
and interpret results in cases
such as distance-time graphs,
velocity-time graphs and
graphs in financial contexts.
A15 Chapter 29 (F) and 30
(H)
There is an increased emphasis on
interpreting the information presented
in graphs and in addition to the new
requirement for students to calculate the
gradient of curves at given points they
will also have to interpret this in given
situations.
Find the equation of a tangent
to a circle at a given point.
A16 Chapter 28 (F) and 29
(H), Chapter 37 (F) and
39 (H)
This topic does not require calculus as the
gradient can be found by considering the
negative reciprocal of the gradient of the
radius connecting the centre of the circle
to a given point. It is a challenging addition
and requires strong knowledge of linear
equations and an ability to work with
equations of circles.
solve … quadratic inequalities
in one variable; represent the
solution set on a number line,
using set notation and on a
graph.
A22 Chapter 37 (F) and 39
(H)
Solving quadratic inequalities was
previously a topic reserved for A level.
In addition, higher students are also
expected to represent their solutions with
set notation and graphically.
Recognise and use sequences
of triangular, square and cube
numbers, simple arithmetic
progressions, Fibonacci
type sequences, quadratic
sequences, and simple
geometric progressions (r n
where n is an integer, and r is a
rational number > 0, or a surd)
and other sequences
A24 Chapter 18 These dierent types of sequences have
had more emphasis placed on them in
the new specification. ‘Fibonacci type
sequences’ implies students now may
have to work with sequences defined by a
recurrence relation. In addition for higher
pupils the common ratio of a geometric
sequence may also be an irrational
number.
deduce expressions to calculate
the nth term of linear and
quadratic sequences.
A25 Chapter 18 The addition here is finding an expression
for the nth term of quadratic sequences.
Use compound units such as …
pressure.
R11 Chapter 21 (F) and 22
(H)
Pressure is a new compound measure to
both tiers.
Interpret the gradient at
a point on a curve as the
instantaneous rate of change;
apply the concepts of average
and instantaneous rate of
change (gradients of chords
and tangents) in numerical,
algebraic and graphical
contexts.
R15 Chapter 29 (F) and 30
(H)
This addition to the higher tier introduces
students to the idea that a non-linear
curve can have a dierent gradient at
dierent points and that these gradients
can be found by investigating the tangent
to the curve at that point. It is not the
reintroduction of calculus to the GCSE
curriculum but does introduce some
important ideas that will be studied for
students continuing Mathematics at A
level.
Derive and use the sum of angles
in a triangle.
G3 Chapter 9 The important word here being ‘derive’ as
previously there was only an expectation
students understood a proof that the sum
of angles in a triangle is 180 degrees.
Changes to GCSE Mathematics