Number 1

? How to do long multiplication and long division with and without
a calculator.
? How to work out equivalent fractions.
? How to find a fraction of a quantity.
? How to add, subtract, multiply and divide with fractions.
? How to add, subtract, multiply and divide with negative numbers.
? How to round off to the nearest ten, hundred, thousand.
? How to round off to significant figures and to decimal places.
? How to approximate the value of a calculation.

Fractions

? Calculate a percentage of a given amount.
? Express one quantity as a percentage of another.
? Increase or decrease a given amount by a certain percentage.
? Calculate the original amount when a certain percentage of it is
known.
? Calculate compound interest on a given amount.

Ratio

? How to divide any amount in a given ratio.
? The relationships between speed, time and distance.
? That density is a rate. It is the mass of a substance per unit volume
– usually expressed in grams/cm3.

Shape

? Area of a rectangle is Length × Breadth.
? Area of a triangle is half × Base length × Vertical height.
? Circumference of a circle is pi × D, where D is the diameter.
? Area of a circle is pi × r2, where r is the radius.
? Area of a trapezium is Vertical height (h) × mean of the lengths of
the two parallel sides.

Volume and Surface Area

? The volume of a cuboid is Length × Breadth × Height.
? The volume of a prism is Cross-sectional area × Length.
? The volume of a cylinder is pi × r2 × h, where r is the radius of the
cylinder and h is its height or length.


Algebra 1

? Read and write simple algebraic expressions.
? Substitute fractional and negative values into expressions and
formulae and evaluate them.
? Solve simple linear equations, including those containing brackets.
? Solve equations by trial and improvement.

Geometry

? That vertically opposite angles are equal.
? That the sum of the angles on a straight line is 180°.
? That the sum of angles around a point is 360°.
? That the sum of the three interior angles of a triangle is 180°.
? That a line which intersects parallel lines is called a transversal and
the two sets of equal angles thus formed are called respectively
alternate angles and corresponding angles.
? How to find the sum of the interior angles of a polygon.
? How to find the exterior angle of a regular polygon.
? The properties of equilateral and isosceles triangles, trapeziums,
parallelograms, rhombuses, and kites.

Transformations

? The four conditions for two triangles to be congruent.
? What is meant by the terms ‘translation’, ‘reflection’, ‘rotation’ and
‘enlargement’.
? How to change shapes using translations, reflections, rotations and
enlargements.

Constructions

? What bearings are and how to calculate back bearings.
? The three ways of constructing a triangle: two sides and the
included angle known; two angles and a side known; all three sides
known.
? How to construct a line bisector and an angle bisector.
? How to construct angles of 90° and 60°.

Shape and symmetry

? How to recognise and draw the lines of symmetry of plane
2-D shapes.
? How to recognise whether a plane shape has rotational symmetry,
and how to find its order of rotational symmetry.
? How to draw 2-D representations of 3-D shapes on square grids
and isometric grids.
? How to draw nets of certain common 3-D shapes.
? What tessellations are and how to construct them.
? How to recognise the planes and axes of symmetry of 3-D shapes.

Indices and Standard Form

? Express a number in its prime factors.
? Divide and multiply by powers of 10.
? Calculate the value of a number raised to any power.
? Multiply and divide powers of the same number.
? Write large and small numbers in standard form and compare their
sizes.
? Solve problems using numbers in standard form.

Algebra 2

I can solve:
? Pairs of simultaneous equations.
? Linear inequalities and represent their solutions on the number
line.
? Inequalities of the types x2 < a2 and x2 > a2

Statistics 1

? Find the three averages – mode, median, mean.
? Construct and interpret frequency tables, and find the three
averages from frequency tables of both grouped and ungrouped
data.
? Recognise the difference between discrete data and continuous
data.
? Read and create frequency polygons, bar charts and histograms.
? Read and create pie charts.
? Create a data collection sheet
? Create a questionnaire to test a hypothesis.

Algebra 3

? Expand and simplify expressions containing brackets.
? Factorise an expression into one or two brackets.
? Expand and factorise simple quadratic expressions.
? Solve quadratic equation by factorising.
? Transpose a formula to change its subject.

Graphs 1

? How to use conversion graphs.
? How to draw and interpret distance–time graphs.
? How to find the gradient of a straight-line graph.
? The relevance of the gradient of a straight-line graph.
? How to find the rule or equation represented by a straight-line
graph.

Similarity

? Work out the scale factor between two similar shapes.
? Work out the unknown side in a shape when the corresponding side
of a similar shape is known.
? Solve practical problems using similar shapes.

Pythagoras

? Pythagoras’s theorem.
? How to show that I know when to use Pythagoras’s theorem.
? How to use Pythagoras’s theorem to find the hypotenuse or a short
side of a right-angled triangle, given the other two sides.
? How to solve a Pythagoras-type problem without the help of a
calculator.
? How to draw out a right-angled triangle from a problem and label
it with necessary information.

Trigonometry

I know:
? The three basic trigonometric ratios of a right-angled triangle:
sin x = O/H, cos x = A/H , tan x = O/A.
? Given one side and one angle (other than the right angle), how to
calculate the other two sides of a right-angled triangle.
? Given two sides, how to calculate the two angles (other than the
right angle) of a right-angled triangle.
? How to interpret a practical situation to obtain a right-angled
triangle which can be used to solve the problem: examples involve
angles of elevation and depression, bearings and distances, and
isosceles triangles.

Metric Units

? Convert from one metric unit to another.
? Convert from one imperial unit to another.
? Convert between metric and imperial units.
? Use exchange rates in dealing with foreign currencies.
? Compare the prices of products to find the ‘best buys’.

Locus and Circles

? What is meant by a locus.
? How to draw a locus round a point, a line or a plane shape.
? How to draw a locus that depends on the bisecting of lines or
angles or both.
? How to recognise when a locus is being asked for.
? That an angle at the centre of a circle is twice any angle at the
circumference subtended by the same arc.
? That every angle at the circumference of a semicircle that is
subtended by the diameter of the semicircle is a right angle.
? That angles at the circumference in the same segment of a circle
are equal.
? That the sum of the opposite angles of a cyclic quadrilateral
is 180°.
? That a tangent is a straight line that touches a circle at one point
only, which is called the point of contact.
? That a tangent is perpendicular to the radius at the point of contact.

Graphs 2

? Find coordinates using flow diagrams, substitution of values,
gradients and intercepts, and how to use these coordinates to draw
graphs.
? Find the equation of a straight line from its graph.
? Draw the graphs of linear functions.
? Solve two simultaneous linear equations using their graphs.
? Represent a linear inequality on a graph.

Statistics 2

? How to plot points on a scatter diagram.
? What correlation means and how to distinguish between positive
and negative correlations.
? How to recognise positive and negative correlation when looking
at scatter diagrams, and also the condition of no correlation.
? How to draw an accurate line of best fit on a scatter diagram, and
use it to predict.
? How to calculate moving averages and plot them on a graph.
? How to construct cumulative frequency diagrams.
? How to find from a cumulative frequency diagram the median, the
lower and upper quartiles and the interquartile range.
? How to draw and interpret box plots.

Probability

? How to put events in order of likelihood.
? How approximately to place events on the probability scale from 0
to 1.
? How to calculate the experimental probability of an event from
data supplied.
? How to calculate the theoretical probability of an event from
consideration of all outcomes of the event.
? That as the number of trials of an event increases, the experimental
probability of the event gets closer to its theoretical probability.
? How to work out the probability of mutually exclusive and
exhaustive events.
? How to use a probability diagram, such as a tree diagram, to
calculate the probability of combined events.
? How to use AND and OR to solve combined events problems.

Sequences

? Recognise a number pattern and explain how the pattern is made.
? Recognise a linear sequence and find its nth term.
? Form general rules from given number patterns.
? Recognise when a sequence is not linear and therefore look for a
quadratic rule.
? Recognise when a sequence is based on n2 alone.
? Recognise when a sequence is not based on n2 alone and therefore
look for a more complicated quadratic rule.

Graphs 3

? Draw a quadratic graph from its equation, using values of its
coordinates between given limits.
? Draw graphs of reciprocal equations and cubic equations, using
values of their coordinates between given limits.
? Solve quadratic and cubic equations using their graphs.
? Identify quadratic, cubic, and reciprocal graphs.

Dimensions

? Recognise whether a formula represents length, area or volume.
? Recognise when a formula is not consistent and state the
reasons why.

Proof

? The difference between numerical verification of a result and
proving it.
? The meaning of the terms ‘verify that’, ‘show that’ and ‘prove
that’.
? How to prove some standard results in mathematics, such as
Pythagoras’s theorem.
? How to use my knowledge of proof to answer the questions