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GCSE learning Objectives

Clicking on the links as indicated by BLUE UNDERLINING BELOW will take you to FREE INDIVIDUAL VIDEO resources – these will be added throughout 2011/2012 academic year.

THE OVERVIEW VIDEOS are older videos which are gradually being replaced over time,

Gifted and Talented links will also be added in due course. These are indicated by a [G&T].

These will be useful for refining your APP within your school and will help your students make GOOD or EXCELLENT progress in Mathematics.

If you are a teacher who would like a FREE WORD copy of the following to edit, please contact me at info@mathslearn.co.uk with your school and details

You may wish to print a copy of this off and make notes in the third column- this has been left blank on purpose

 

Shape and Space

Grade

Reflection points

Angles in Triangles and Polygons, overview video

·         I understand angles in a triangle add up to 180

·         I can solve algebraic problems, where the three angles in a triangle are given in terms of

·         I understand that exterior angles add up

·         I understand that

·         I can find the interior angle of a regular polygon

·         I can find the number of sides of a polygon

 

 

Circle Theorems:

 I can solve problems involving the following

·         I know the angle at the centre is twice that at the circumference

·         I know the angle in a semicircle is a right-angle

·         I know angles in the same segment are equal

·         I know opposite angles in a cyclic quadrilateral add up to 180

·         I know that a tangent is at right-angles to the radius

·         I know the alternate segment theorem

 

 

 

Fundamental Area and Volume, old overview video

·         I can find the area of triangles, trapeziums and parallelograms

·         I can find the area of composite shapes

·         I know associated language facts about circles

·         I can find the area and circumference of a circle

·         I can find the radius of a circle given its area or circumference

·         I can find the volume of a range of prisms, including cylinders

·         I can find the surface area of a cuboid

·         I can find the surface area of a cylinder

·         I can use density to find the mass of a cuboid

I can convert between different units of area

 

 

Transformations

·         I can reflect shapes in lines vertical lines and horizontal lines

·         I can reflect in the lines  and

·         I can translate by a given vector

·         I can rotate about a given point

·         I can describe a given rotation

·         I can enlarge a shape by a positive or negative scale factor

 

 

Similar shapes part 1 and enlargements

·         I understand that similar shapes are enlargements

·         I can find the ratio of enlargement or scale factor as a fraction

·         I can deduce whether shapes are similar

·         I can enlarge by a negative scale factor

 

 

Similar shapes part 2

·         I understand how enlargement effects area

·         I understand how enlargement effects volume

 

 

Area of parts of circles plus further cylinders

·         I can find the area of a sector

·         I can find the length of an arc

·         I can find the area of a segment of a circle

·         I can find the volume of parts of cylinders

 

 

Volumes of pyramids and spheres

·         I can find the volume of a pyramid

·         I can find the volume of a cone

·         I can find the volume of a frustum

·         I can find the volume of a sphere

·         I can re-arrange to find the radius of a sphere

 

 

Loci

·         can find the loci of points a fixed distance from a line

·         I can construct the perpendicular bisector

·         I can find the shortest route from a point to a line

·         I can bisect an angle

 

 

Fundamental Trigonometry, overview1 and overview2

·         I can use trigonometry to find sides

·         I can use trigonometry to find missing angles

·         I can solve problems requiring multiply trigonometry calculations

 

 

Sine and Cosine Rule

·         I can use the sine-rule to find sides

·         I can use the sine-rule to find lengths

·         I can use the cosine-rule to find sides

·         I can use the cosine-rule to find angles

·         I can use the sine-rule to find the area of a triangle

 

 

Vectors

·         I understand vector notation

·         I can add vectors

·         I can subtract vectors

·         I can find fractions of vectors

·         I can use vector algebra

·         I can do vector proof

 

 

Further Trigonometry in 3D

·         I can solve 3d problems involving trigonometry

 

 

Dimensional analysis

·         I understand when an  expression represents a length, area of volume by considering its dimensions

 

 

 

 

 

Algebra

Grade

Reflection points

Solving Equations

·         I can solve equations the form ax+b=c

·         I can solve equations with terms on both sides

·         I can solve equations with linear brackets

·         I can form and solve equations related to angles in polygons and perimeter

·         I can solve equations involving fractions

·         I can solve equations involving cross-multiplying

·         I can solve equations with more than one fraction, over-view video

·         Functions machines and equations

 

 

Algebraic manipulations

BRACKET OVERVIEW

·         I can collect like terms

·         I can multiply and divide expressions

·         I can factorise simple expressions

·         I can substitute into expressions with more than one variable

·         I can multiply expressions with more than one letter

·         I can divide expressions with more than one letter

·         I can expand and factorise expressions with more than one letter

·         I can find simple expressions for algebraic area and volume

 

 

Re-arranging equations: part 1

·         I can re-arrange simple formulae

·         I can re-arrange formulae containing more than two letters

I can re-arrange formulae containing squares and roots

 

 

Re-arranging equations: part 2

·         I can re-arrange simple formulae

·         I can simplify squares and square roots

·         I can re-arrange formulae containing squares and roots

·         I can factorise to re-arrange where the new subject appears more than once

·         I can form and manipulate formulae

 

 

Quadratic Brackets

Bracket Overview

Factorising Overview

 

 

·         I can expand quadratic brackets of the form

 

·         I can expand brackets of the form

 

·         I can factorise quadratic expressions

 

·         I can recognise perfect squares

 

·         I can solve quadratic equations by factorising; exam q1

 

·         I can sketch quadratic graphs

Simultaneous Equations: part 1

·         I can set up simultaneous equations

·         I can solve simultaneous equations using the elimination or substitution method

·         I understand that simultaneous equations sometimes needs to be pre-multiplied before solving

·         I understand that solving simultaneous equations finds the intersection of two graphs which I can show graphically

 

 

Further Quadratic Brackets

·         I can expand expressions for the form

·         I can factorise quadratics where the coefficient of , alternative method

·         I can solve harder quadratics by factorising

·         I can expand expressions with more than one letter

·         I can use the difference of two squares

 

 

Algebraic fractions

·         I can simplify simple algebraic fractions

·         I can factorise to simplify algebraic fractions

·         I can add or subtract algebraic fractions

·         I can multiply algebraic fractions

·         I can divide algebraic fractions

·         I can solve equations with fractions that lead to quadratic equations

 

 

 

Quadratic equations

·         I can use perfect squares to solve certain quadratics

·         I can complete the square

·         I can use the quadratic formula

·         I can solve quadratic simultaneous equations

 

 

Further algebraic fractions

·         I can add algebraic fractions

·         I can solve equations involving fractions

·         I can re-arrange equations involving fractions

·         I can do algebraic proof

 

 

Inequalities

·         I can represent inequalities on number lines

·         I can solve linear inequalities

·         I understand that dividing by a negative reverses the inequality sign

·         I can find integer solutions of combined inequalities

·         I can represent inequalities in 2D

·         I can represent overlapping inequalities in 2D

·         I understand when to use a dotted or solid line

 

 

Sequences

·         I can find the nth term of a linear sequence

·         I can use algebra to deduce patterns and terms in sequences

·         I can find the nth term of quadratic sequences

·         I can find terms of sequences for a given formula

·         I can analyse spatial patterns

 

 

 

 

 

Handling Data

Grade

Reflections points

Averages

·         I can use averages to compare discrete distributions

·         I can find the mean from a grouped frequency table

·         I can construct frequency polygons

 

 

Cumulative Frequency

·         I can construct cumulative frequency polygons

·         I can use cumulative frequency polygons to find an estimate for the median and quartiles

·         I can use cumulative frequency diagrams to compare two distributions

·         I can construct a box and whisker plot for a cumulative frequency graph

 

 

Questionnaires and surveys

·         I can critically evaluate questionnaires and surveys

·         I can improve questions

·         I can critically evaluate experiment design

 

 

Probability: part 1

·         I understand relative frequency

·         I understand equally likely outcomes

·         I can list outcomes

·         I can show outcomes on a grid

 

 

Probability: part 2

·         I understand when events are mutually exclusive

·         I can find the probability of mutually exclusive events

·         I can find the probability of non-mutually exclusive events

·         I understand when events are independent and can use the multiplicative rule

·         I can construct tree diagrams for independent events

·         I can construct tree diagrams for dependent events

 

 

Sampling techniques

·         I understand sampling

·         I can find a stratified sample

·         I understand bias

 

 

Histograms

·         I can construct a histogram

·         I can read histograms

 

 

 

 

 

Number

Grade

Points of Reflection

Speed, distance and time

·         I can calculate speed

·         I understand and can read distance-time graphs

·         I can calculate distance and time

·         I can convert between units of speed

·         I can calculate with time on a calculator

 

 

Fractions

·         I can add and subtract fractions

·         I can convert between mixed numbers and fractions

·         I can add and subtract mixed numbers

·         I can multiply fractions by fractions and integers

·         I can multiply mixed numbers

·         I can find a reciprocal of an integer and a fraction

·         I can divide a fraction by a fraction

·         I can substitute fractions into expressions

 

 

Percentages

·         I can convert between decimals and percentages

·         I can write a fraction of an amount as a percentage

·         I can increase of decrease by a percentage by multiplication

·         I can convert an increase to a percentage increase

·         I can convert a decrease to a percentage decrease

·         I can find successive percentage changes

·         I understand compound interest

·         I can do percentage change in reverse

 

 

Powers: part 1

·         I can calculate with powers

·         I understand the laws of indices related to positive powers

·         I can multiply expressions involving powers

·         I can divide expressions involving powers

·         I understand negative indices and can add and subtract them

·         I can extend index rules to negative indices

 

 

Standard form

·         I can use standard form to express large numbers

·         I can use standard form to express small numbers

·         I can use a calculator to evaluate expressions involving standard form

·         I can add and subtract numbers in standard form

·         I can multiply and divide numbers in standard form

 

 

 

Powers: part 2

·         I can find roots of integers

·         I can find fractional powers of integers

·         I can find negative fractional powers of integers

·         I can use a calculator to find powers and roots

 

 

Proportionality

·         I understand direct proportionality

·         I understand proportionality involving powers

·         I understand inverse proportionality

·         I can identify proportionality relationships

·         I can sketch graphs to represent proportionality

 

 

SURDS, overview1 or overview2

·         I can convert between recurring decimals and fractions

·         I can multiply surds

·         I can simplify surds

·         I can multiply brackets involving surds

·         I can divide surds

·         I can rationalise

 

 

Error bounds

·         I can estimate calculations

·         I can find the upper and lower bound of a measurements given to 1sf or 1dp

·         I can find upper and lower bounds

·         I can calculate with rounded quantities

·         I can subtract with rounded quantities

·         I can divide with rounded quantities

 

 

Exponentials

·         I understand exponential growth

·         I understand exponential decay

 

 

 

 

 

Graphs

Grade

Points of reflection

Gradients

·         I understand gradient

·         I can find positive and negative gradients

·         I can interpret gradient as a rate of change

 

 

Straight-line graphs

·         I can sketch lines of the form

·         I can sketch lines of the form

·         I can find the y-intercept of a line

·         I can find the gradient of a line

·         I can find the equation of a line

·         I can find the equation of a line through two points

·         I understand fractional gradients

·         I can re-arrange the equation of a graph

·         I understand the relationship between perpendicular gradients and lines

·         I can find the equation of a line of best fit

 

 

Quadratic Graphs

·         I can plot quadratic graphs of the form

·          I can plot quadratic graphs of the form

·         I can plot quadratic graphs of the form

·         I can use quadratic graphs to solve real-life problems

 

 

Cubic Graphs

·         I can sketch cubic graphs

·         I can use trial and improvement to solve cubic equations

 

 

Reciprocal graphs and transformations

·         I understand the word reciprocal

·         I can sketch the reciprocal graph

·         I can transform the reciprocal graph

·         I recognise the quadratic and cubic graphs

 

 

Trigonometry Graphs

·         I can sketch the trigonometry graphs

·         I can transform the trigonometry graphs

·         I can use symmetry to deduce equal trigonometry values

 

 

Using Quadratic Graphs to solve equations

·         I can plot quadratics

·         I can use graphs to solve quadratics

·         I can find the intersection of linear and quadratic graphs

·         I can decide which linear graph to draw to solve a quadratic equation

 

 

The equation of a circle

·         I understand the equation of a circle

·         I can find the intersection between a line and a circle

·         I understand when a line is a tangent algebraically