## Number

Number 1 Review Questions

You need be able to:

- Order positive numbers
- Order negative numbers
- Order decimal numbers
- Order fractions
- Use the symbols =, ≠, <, >, ≤, ≥

You will need to be able to:

- Add, subtract, multiply and divide whole numbers
- Add, subtract, multiply and divide fractions (proper and improper)
- Add, subtract, multiply and divide mixed numbers
- Add, subtract, multiply and divide negative numbers
- Add, subtract, multiply and divide decimal numbers

You will need to be able to:

- Use BIDMAS
- Use Inverse operations
- Understand reciprocals

You will need to be able to:

- Identify and explain prime numbers
- Identify and explain factors
- Identify and explain multiples
- Identify and explain highest common factors
- Identify and explain lowest common multiple
- Identify and explain prime factors

You will need to be able to:

- Systematic listings

You will need to be able to:

- know square numbers
- know square roots
- know cube numbers
- recognise numbers to the power of 4 and 5

You will need to be able to:

- Complete calculations with roots
- Complete calculations with indices

You will need to be able to:

- Complete calculations with fractions
- Complete calculations with multiples of π

You will need to be able to:

- Complete calculations including standard form

You will need to be able to:

- Recognise and explain terminating and recurring decimals
- Convert terminating decimals to fractions and vice versa

You will need to be able to:

- Identify and work with fractions in ratio problems

You will need to be able to:

- Interpret fractions and percentages as operators

You need to be able to:

- Use units of mass
- Use units of length
- Use units of time
- Use units of money

You need to be able to:

- Use estimation and approximation

You need to be able to:

- Round numbers and measures using decimal places
- Round numbers and measures using significant figures
- Identify error intervals due to truncation
- Identify error intervals due to rounding

You need to be able to:

- Apply and interpret limits of accuracy

## Algebra

You need be able to:

- Use and interpret algebraic manipulation

You will need to be able to:

- Substitute numerical values into formulae and expressions

You will need to be able to:

- Explain the term “expressions”
- Explain the term “equations”
- Explain the term “formulae”
- Explain the term “identities”
- Explain the term “factors”

You will need to be able to:

- Simplify expressions
- Expand a single bracket
- Expand double brackets
- Factorise a quadratic expression
- Factorise using difference of two squares
- Simply expressions using laws of indices

You will need to be able to:

- Use mathematical formulae
- Rearrange formulae to change the subject

You will need to be able to:

- Explain the difference between an equation and an identity
- Argue mathematically to show algebraic expressions are equivalent

You will need to be able to:

- Interpret simple expressions as functions with inputs and outputs

You will need to be able to:

- work with coordinates in all four quadrants

You will need to be able to:

- Plot straight line graphs
- Identify parallel lines
- Find the equation of a line given one point and gradient
- Find the equation of the line through two given points

You will need to be able to:

- Identify and interpret gradients and intercepts of linear functions graphically and algebraically.

You will need to be able to:

- Identify and interpret roots of quadratic graphs
- Identify intercepts of quadratic graphs
- Identify turning points of quadratic graphs
- Deduce roots graphically

You will need to be able to:

- Recognise, sketch and interpret quadratic graphs

You need to be able to:

- Plot and interpret reciprocal graphs
- Plot and interpret real-life graphs

You need to be able to:

- Solve linear equations with an unknown on one side
- Solve linear equations with the unknown on both sides
- Find approximate solutions using a graph

You need to be able to:

- Solve quadratic equations using factorising
- Find approximate solutions using a graph

You need to be able to:

- Solve two simultaneous equations
- Find approximate solutions using a graph

You need to be able to:

- Form expressions and equations
- Derive simultaneous equations and solve.

You need to be able to:

- Solve linear inequalities
- Represent and interpret inequalities on a number line

You need to be able to:

- generate a term to term rule from a given sequence
- generate a position to term rule from a given sequence

You need to be able to:

- Recognise and use sequences of triangular numbers
- Recognise and use sequences of square numbers
- Recognise and use sequences of cube numbers
- Recognise and use Fibonacci sequences
- Recognise and use simple geometric progressions

You need to be able to:

- Find expressions to calculate the nth term of linear sequences

## Geometry

You need be able to:

- Understand these terms: points, lines, vertices, edges, planes, parallel lines, perpendicular lines, right angles, polygons, regular polygons
- Label sides and angles of a triangle
- Draw diagrams from written descriptions

You will need to be able to:

- Construct a perpendicular bisector of a line
- Construct a perpendicular bisector to a given line from a given point
- Bisect a given angle
- Solve loci problems
- Know that the perpendicular distance from a point to a line is the shortest distance to the line.

You will need to be able to:

- Apply the properties of angles at a point
- Apply the properties of angles on a straight line
- Apply the properties of vertically opposite angles
- Understand and use corresponding angles
- Understand and use alternate angles
- Derive and use the sum of angles in a triangle
- Find the sum of angles in any polygon

You will need to be able to:

- Derive and apply the properties and definitions of special types of quadrilaterals; including square, rectangle, parallelogram, trapezium, kite, and rhombus.
- Derive and apply the properties of all types of triangles

You will need to be able to:

- Use the basic congruence criteria for triangles (SSS, SAS, ASA, RHS)

You will need to be able to:

- Apply angle facts
- Apply triangle congruence
- Apply similarity and properties of quadrilaterals
- Apply Pythaoras’ theorem
- Know the base angles of an isosceles triangle are equal
- Show simple proofs

You will need to be able to:

- Identify, describe and construct congruent and similar shapes
- Identify congruent and similar shapes by considering rotation, reflection, translation, and enlargement (including fractional scale factors)

You will need to be able to:

- Identify and apply circle definitions and properties; centre, radius, chord, diameter, circumference, tangent, arc, sector and segment

You will need to be able to:

- Solve geometrical problems on coordinate axes

You will need to be able to:

- Identify properties of the faces, surfaces, edges and vertices of: cubes, cuboids, prisms, cylinders, pyramids, cones and spheres.

You need to be able to:

- Construct and interpret plans and elevations of 3D shapes

You need to be able to:

- Use standard units of measures

You need to be able to:

- Measure line segments and angles in geometric figures
- Interpret maps
- Interpret scale drawings
- Interpret use of bearings

You need to be able to:

- Know and apply formulae to calculate areas of triangles
- Know and apply formulae to calculate areas of parallelograms
- Know and apply formulae to calculate areas of trapezium
- Know and apply formulae to calculate volume of cuboids
- Know and apply formulae to calculate volume of prisms
- Know and apply formulae to calculate volume of cylinders

You need to be able to:

- Calculate circumference
- Calculate area of a circle
- Calculate perimeters of 2d shapes
- Calculate perimeter of composite shapes
- Calculate surface area and volume of spheres
- Calculate surface area and volume of pyramids
- Calculate surface area and volume of cones
- Calculate surface area and volume of composite solids

You need to be able to:

- Calculate arc lengths of circles
- Calculate angles of sectors
- Calculate areas of sectors

You need to be able to:

- Apply the concept of congruence and similarity

You need to be able to:

- Know the Pythagoras’ theorem
- Know the trigonometric ratios
- Use trigonometry to find angles and lengths in right angled triangles

You need to be able to:

- Know the exact values of Sin 0, 30, 45, 60 and 90 degrees
- Know the exact values of Cos 0, 30, 45, 60 and 90 degrees
- Know the exact values of Tan 0, 30, 45, and 60 degrees

You need to be able to:

- Describe translations as 2D vectors

You need to be able to:

- Apply addition and subtraction of vectors
- Calculate multiplication of vectors by a scalar
- Apply column representations of vectors

## Ratio

You need be able to:

- Change between units (time, length, area, volume, mass).
- Change between compound units (speed, rates of pay, prices, density, pressure).

You will need to be able to:

- Use scale factors, scale diagrams and maps

You will need to be able to:

- Express one quantity as a fraction of another (fraction is less than one)
- Express one quantity as a fraction of another (fraction is greater than one)

You will need to be able to:

- Simplify ratios

You will need to be able to:

- Divide a given quantity by a ratio

You will need to be able to:

- Express a multiplicative relationship between two quantities as a ratio or a fraction

You will need to be able to:

- Understand and use proportion as equality of ratios

You will need to be able to:

- Relate ratios to fractions and to linear functions

You will need to be able to:

- Interpret percentages and percentage changes as a fraction or a decimal
- Express one quantity as a percentage of another
- Compare two quantities using percentages
- Work with percentages greater than 100%
- Solve problems involving percentage change
- Solve problems involving percentage increase/ decrease
- Calculate simple interest

You will need to be able to:

- Solve problems involving direct proportion
- Solve problems involving indirect proportion

You will need to be able to:

- Calculate speed, rates of pay, unit pricing, density and pressure

You will need to be able to:

- Compare lengths
- Compare areas and volumes using ratio notation
- Recognise and identity similarity including trigonometry ratios
- Use scale factors

You need to be able to:

- Understand that X is inversely proportional to Y is equivalent to X is proportional to 1/Y
- Interpret equations that describe direct and inverse proportion

You need to be able to:

- Interpret the gradient of a straight line graph as a rate of change
- Recognise and interpret graphs that illustrate direct and inverse proportion

You need to be able to:

- Solve problems involving compound interest
- Solve problems including growth and decay

## Probability

You need be able to:

- Record, describe and analyse the frequency of outcomes of probability experiments using tables and frequency trees

You will need to be able to:

- Apply ideas of randomness, fairness and equally likely events to calculate expected outcomes of multiple future events.

You will need to be able to:

- Express one quantity as a fraction of another (fraction is less than one)
- Express one quantity as a fraction of another (fraction is greater than one)

You will need to be able to:

You will need to be able to:

- Understand that empirical unbiased samples tend towards theoretical probability distributions, with increasing sample size.

You will need to be able to:

- Enumerate sets and combinations of sets systematically, using tables, grids, Venn diagrams and tree diagrams.

You will need to be able to:

- Construct theoretical possibility spaces for single and combined experiments with equally likely outcomes and use these to calculate theoretical probabilities.

You will need to be able to:

- Calculate the probability of independent and dependent combined events
- Interpret and use tree diagrams

## Statistics

You need be able to:

- Infer properties of populations or distributions from a sample, while knowing the limitations of sampling.

You will need to be able to:

- Interpret and construct tables, charts and diagrams including frequency tables, bar charts, pie charts, and pictograms.
- Interpret and construct vertical line charts for ungrouped discrete numerical data.
- Interpret and construct tables and line graphs for time series data

You will need to be able to:

- Interpret, analyse and compare the distributions of data sets involving discrete, continuous or grouped data.
- Interpret, analyse and compare median, mean, mode and modal class
- Interpret, analyse and compare range (including consideration of outliers)

You will need to be able to:

- Apply statistics to describe a population

You will need to be able to:

- Use and interpret scatter graphs
- Recognise correlation and know that it does not indicate causation
- Draw estimated lines of best fit
- Make predications, interpolate and extrapolate apparent trends while knowing the dangers of so doing.