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# AQA GCSE Higher Modular Mathematics – Module 5 by dfsiopmhy6

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```									                       AQA GCSE Higher Modular Mathematics – Module 5

2-D & 3-D SHAPES                              D     Find angles in triangles & quadrilaterals
D      Calculate Circumference & Area of Circles     C     Find interior & exterior angles of polygons
D      Calculate the Area of a Trapezium             B     Find angles in circles
C      Calculate Volume of Prisms & Cylinders        A     Find angles in circles using the alternate
B      Calculate Arc Lengths & Sector Areas                segment theorem
B      Calculate Surface Area of                    A*     Use circle theorems to prove geometrical
Cylinders/Cones/Spheres                             results.
B      Calculate Volume of                                 TRANSFORMATIONS
Pyramids/Cones/Spheres                       D      Reflect a 2-D shape in lines x = … & y = …
A      Calculate Volume & Surface Area of           D      Rotate a 2-D shape about the origin
compound 3-D shapes                          D      Enlarge a 2-D shape by a whole number
GEOMETRICAL REASONING                               scale factor
C      Use Pythagoras Theorem in right-angle        C      Translate a 2-D shape by a vector
triangles                                    C      Reflect a 2-D shape in lines y = x & y = -x
C      Solve 2-D problems using Pythagoras          C      Rotate a 2-D shape about any point
Theorem                                      C      Enlarge a 2-D shape by a fractional scale
B      Solve 3-D problems using Pythagoras                 factor
Theorem                                      C      Enlarge a 2-D shape about any point
B      Use Trigonometry to find sides and angles    B      Know the conditions for congruence of 2
in right-angle triangles                            triangles
B      Solve problems using Trigonometry            B      Enlarge a 2-D shape by a negative scale
factor
A      Prove 2 triangles are congruent               1
CONSTRUCTIONS                                         VECTORS
C      Construct angle and line bisectors             A      Solve problems using addition &
C      Draw & describe the locus on a point from a           subtraction of vectors
given rule                                     A*     Solve complex geometrical problems in
C      Solve problems using loci                             terms of vectors
B      Construct a perpendicular from a point on a           ALGEBRA 1
line                                           D      Expand a single linear bracket
B      Construct a perpendicular from a point to a    D      Substitute numbers into a linear
line.                                                 expression
B      Compass construct of an angle of 60o           D      Factorise simple linear expressions
SIMILARITY                                     D      Solve linear equations (inc. ones with
C      Understand why two shapes are similar                 variable inside a bracket)
C      Work out unknown sides using scale factors     D      Solve linear equations with the variable as
& ratios                                              a numerator of a fraction
B      Set up equations to find missing sides in      D      Solve linear equations with the variable on
similar triangles                                     both sides of the equals sign
A      Solve problems using area and volume scale     C      Expand & simplify expressions
factors                                        C      Solve equations using trial & improvement
A      Solve problems using similar triangles         C      Rearrange simple formulae
A*     Use area and volume scale factors to solve     B      Solve 2 linear simultaneous equations
related problems i.e. capacity                 B      Rearrange more complex formulae
DIMENSIONS ANALYSIS                            A      Set up and solve simultaneous equations in
D      Work out a formula for                                a practical context
perimeter/area/volume of simple shapes                ALGEBRA 2
C      Work out a formula for                         C      Expand a pair of linear brackets (to result
perimeter/area/volume of complex shapes               in a quadratic expression)
C      Work out whether an expression/formula is      B      Factorise a quadratic expression of the
dimensionally consistent & whether it                 form x2 + ax + b
represents a length, area or volume
2
B   Solve a quadratic expression of the form x2      A*   Use sine & cosine rules to solve more
+ ax + b = 0                                          complex problems involving non-right-angled
A   Factorise a quadratic expression of the               triangles
form ax2 + bx + c                                A*   Solve 3-D problems using Pythagoras’
A   Solve a quadratic expression of the form              theorem and trigonometry
ax2 + bx + c = 0 by factorisation                A*   Find two angles 0o to 360o for any given
A   Solve a quadratic expression of the form              value of a trigonometric ratio (positive or
ax2 + bx + c = 0 by the quadratic formula             negative)
A*   Solve quadratic equations by Completing          A*   Solve simple equations where the
the Square                                            trigonometric ratio is the subject
A*   Solve real-life problems that lead to a               LINEAR GRAPHS AND EQUATIONS
quadratic equation                                D   Draw straight line graphs by plotting points
REAL-LIFE GRAPHS                                  C   Draw straight-line graphs using the
D   Draw and read information from a distance-            gradient/intercept method
time graph                                        B   Solve a pair of simultaneous equations from
C   Calculate the gradient of a straight line and         their graphs
use it to find speed from a distance-time         A   Find equations of linear graphs parallel and
graph                                                 perpendicular to other linear graphs, that
B   Interpret real-life graphs                            pass through specific points
A   Interpret & draw complex real-life graphs             OTHER GRAPHS
HIGHER TRIGONOMETRY                               B   Plot cubic graphs using a table of values
A   Solve complex problems using Pythagoras &         B   Recognise the shapes of the graphs y = x3
Trigonometry                                          and y = 1/x
A   Use sine & cosine rules to calculate missing      A   Draw a variety of graphs such as
angles/sides in non-right-angled triangles            exponential, reciprocal using a table of
A   Find the area of a triangle using                     values
Area = ½ ab sin C                                A*   Solve equations using the intersection of
two graphs

3
Grade                     Details                           INEQUALITIES AND REGIONS
A*   Use trigonometric graphs to solve sine and       C    Solve inequalities such as 3x + 2 < 5 and
cosine problems                                       represent the solution on a number line
ALGEBRA 3                                        B    Represent a region that satisfies a linear
D   Substitute numbers into an nth term rule              inequality graphically
D   Understand how odd and even numbers              B    Solve more complex linear inequalities
interact in addition, subtraction &              B    Represent a region that simultaneously
multiplication problems                               satisfies more that one linear inequality
C   Give the nth term of a linear sequence                graphically
C   Give the nth term of a sequence of powers        A    Translate a problem into an inequality
of 2 or 10                                            TRANSFORMATIONS OF GRAPHS
B   Find the nth term of a quadratic sequence        A*   Transform the graph of a given function
B   Solve linear equations where the subject         A*   Identify the equation of a function from
appears as the numerator                              its graph, which has been formed by a
A   Rearrange a formula where the subject                 transformation on a known function
appears twice                                         PROOF
A   Combine algebraic fractions using the four       B    Verify results by substituting numbers
rules of addition, subtraction, multiplication        into them
& division                                       B    Understand the proofs of simple theorems
A*   Rearrange more complicated formulae                   such as exterior angle of a triangle is the
where the subject may appear twice or as a            sum of the two opposite interior angles
power                                            A    Show that an algebraic statement is true,
A*   Solve a quadratic equation obtained from              using both sides of the statement to
algebraic fractions where the variable                justify your answer
appears as the denominator                       A*   Prove algebraic and geometric results with
A*   Simplify algebraic fractions by                       rigorous and logical mathematical
factorisation & cancellation                          arguments
A*   Solve a pair of simultaneous equations
where one is linear and the other is non-
linear
4

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