Below there are 163 Algebra Topics
Algebra is probably the most misunderstood area in GCSE Maths
This area is very important for solving problems and getting the higher grades!
Step 01
Algebra
Key Stage 2 - GCSE Basics
- Topic does not start until Step 03
Step 02
Algebra
Key Stage 2 - GCSE Basics
- Topic does not start until Step 03
Step 03
Algebra
Key Stage 2 - GCSE Basics
- Find outputs of more complex functions expressed in words (e.g. add 6 then multiply by 3)
- Find the inputs of simple functions expressed in words by using the output and inverse operations
- Use function machines to find coordinates
- Discuss and interpret line graphs and graphs of functions from a range of sources
- Read values from straight-line graphs for real-life situations
- Draw, straight-line graphs for real-life situations
- Use conventions and notation for 2-D co-ordinates in all four quadrants.
- Draw, label and scale axes
- Use the correct notation to show inclusive and exclusive inequalities
- Describe simple functions in words (e.g. add 3, multiply by 6, subtract 4)
- Generate terms of a simple sequence using term to term rules like +3, -2
- Find the next term in a sequence, including negative values
- Generate and describe simple integer sequences – square and triangle numbers
- Generate terms of a simple sequence arising from practical contexts
- Generate terms of a more complex sequence arising from practical contexts
- Use notation and symbols correctly
Step 04
Algebra
Key Stage 3 - Pre GCSE
- Substitute positive integers into simple formulae expressed in letter symbols, e.g. a+/- b, a × b
- Substitute integers into more complex formulae expressed in letter symbols, e.g. a/b, ax +/- b
- Identify variables and use letter symbols, e.g. 'the cost of hiring a van...', c = cost, v = van
- Identify formulae and functions
- Identify the unknowns in a formula and a function
- Explain the distinction between equations, formulae and functions
- Simplify algebraic expressions by collecting like terms
- Create basic expressions from worded examples e.g 6 more than x
- Find outputs of more complex functions and inputs using inverse operations
- Construct functions to describe mappings (completing a number machine)
- Plot a simple distance-time graph (straight-line graphs)
- Read x and y coordinate in all four quadrants
- Identify points with given coordinates and coordinates of a given point in all four quadrants
- Plot and draw graphs of y = a, x = a, y = x and y = -x
- Show inequalities on a number line
- Find a term given its position in a sequence like tenth number in 4 × table is 40 (one operation on n)
- Find a term of a practical sequence given its position in the sequence
- Generate terms of a linear sequence using term-to-term using positive or negative integers.
- Find a specific term in the sequence using term-to-term rules
- Generate and describe integer sequences such as powers of 2 and growing rectangles
- Know that an arithmetic sequence is generated by a starting number , then adding a constant number
- Write the term-to-term definition of a sequence in words
- Know that expressions can be written in more than one way, e.g. 2 × 3 + 2 × 7 = 2(3 + 7)
- Use arithmetic operations with algebra
- Multiply together two simple algebraic expressions, e.g. 2a × 3b
Step 05
Algebra
Key Stage 3 - Pre GCSE
- Substitute positive and negative integers into simple formulae
- Write expressions to solve problems representing a situation
- Understand the difference between an expression and an equation and the meaning of the key vocabulary 'term'
- Understand the different role of letter symbols in formulae and functions
- Select an expression/ equation/ formula from a list
- Express simple functions in symbols
- Generate four quadrant coordinate pairs of simple linear functions
- Draw and use graphs to solve distance-time problems.
- Interpret information from a complex real life graph (fixed charge/unit cost), read values and discuss trends
- Find the coordinates of points identified by geometrical information in 2D ( all four quadrants) for simple shapes e.g. squares and rectangles
- Plot a graph of a simple linear function in the first quadrant.
- Plot and draw graphs of straight lines using a table of values
- Drawing and recognising lines parallel to axes, plus y = x and y = -x
- Generate terms of a linear sequence using position to term with positive integers.
- Recognise arithmetic sequences from diagrams and draw the next term in a pattern sequence
- Predict how the sequence should continue and test for several more terms
- Recognise simple sequences including triangular, square, cube numbers and Fibonacci-type sequences
- Begin to use linear expressions to describe the nth term in a one-step arithmetic sequence (e.g. nth term is 3n or n + 5)
- Begin to use linear expressions to describe the nth term in a two-step arithmetic sequence (e.g. nth term is 3n + 1 or n/2 − 5)
Step 06
Algebra
Key Stage 3 - Pre GCSE
- Substitute positive integers into expressions involving small powers (up to 3)
- Select an expression/ equation/ formula/identity from a list
- Use the distributive law to take out numerical common factors, e.g. 6a + 8b = 2(3a + 4b)
- Manipulate expressions by taking out common factors, not necessarily the highest e.g. 4x + 8 = 2(2x + 4)
- Change the subject of a formula in one step e.g. y = x + 4
- Begin to consider the features of graphs of simple linear functions, where y is given explicitly in terms of x, e.g. y = x, y = 2x, y = 3x are all straight lines that pass through the origin,
vary in steepness depending on the function
- Use gradients to interpret how one variable changes in relation to another
- Discuss and interpret linear and non linear graphs from a range of sources
- Draw distance-time graphs and velocity-time graphs
- Find the coordinates of the midpoint of a line from a given graph
- Plot the graphs of simple linear functions in the form y = mx + c in four quadrants
- Recognise that equations of the form y = mx + c correspond to straight-line graphs in the coordinate plane
- Write down whole number values that satisfy an inequality
- Find a specific term in the sequence using position-to-term rules
- Recognise sequences including those for odd and even numbers
- Begin to use formal algebra to describe the nth term in an arithmetic sequence.
- Know that expressions involving repeated multiplication can be written as n, n², n³
- Understand the difference between 2n and n²
Step 07
Algebra
KS4 - Foundation GCSE
- Use systematic trial and improvement to find the approximate solution to one decimal place of equations such as x³ = 29
- Construct and solve equations that involves multiplying out brackets by a negative number (e.g. 4(2a - 1) = 32 - 3(2a - 2))
- Derive a simple formula, including those involving squares, cubes and roots
- Multiply out brackets involving positive terms such as (a + b)(c + d) and collect like terms
- Substitute positive and negative integers into linear expressions and expressions involving powers
- Know and understand the meaning of an identity and use the ≠ sign
- Factorise to one bracket by taking out the highest common factors for all terms e.g. 2x²y + 6xy² = 2xy(x + 3y)
- Find an unknown where it is not the subject of the formula and where an equation must be solved.
- Rearrange simple equations
- Know that the gradient of a line is the change in y over change in x.
- Without drawing the graphs, compare and contrast features of graphs such as y = 4x, y = 4x + 6, y = x + 6, y = -4x, y= x - 6
- Identify parallel lines from their equations
- Generate points and plot graphs of simple quadratic functions, then more general functions
- Construct a table of values, including negative values of x for a function such as y = ax²
- Recognise a graph which represents a quadratic function
- Plot the graphs of linear functions in the form y = mx + c and recognise and compare their features
- Recognise that linear functions can be rearranged to give y explicitly in terms of x e.g. rearrange y + 3x - 2 = 0 in the form y = 2 - 3x
- Solve simple linear inequalities in one variable and represent the solution on a number line e.g. 3n + 2 <11 and 2n - 1 >1
- Represent the solution set for inequalities using set notation
- Argue mathematically to show algebraic expressions are equivalent e.g 2x(x + 3) - 4(3x - x²) = 6x(x - 1)
- Find and use the nth term of an arithmetic sequence
- Simplify simple expressions involving index notation
Step 08
Algebra
KS4 - Foundation GCSE
- Find the equation of a straight-line from its graph
- Identify the line of symmetry of a quadratic graph
- Recognise that when the linear and inverse of a linear function such as y = 2x, y = 3x are plotted, they are a reflection in the line y = x
- Interpret distance-time graphs and calculate the speed of individual sections, total distance and total time
- Interpret gradient as rate of change in distance-time and speed-time graphs, containers emptying and filling and unit price graphs
- Identify and interpret roots, intercepts and turning points of a quadratic graph
- Given the coordinates of points A and B, calculate the length of AB
- Plot and draw graphs of straight lines WITHOUT using a table of values (use intercept and gradient)
- Write down the equation of a line parallel to a given line
- Recognise a quadratic function from its equation and explain the shape of it's graph
- Solve more complex linear inequalities in one variable and represent the solution on a number line e.g. -6 < 2n+4 or -9 < 2n + 3 < 7
- Use algebra to support proofs e.g. show that the volume of a cube with side lengths of (2x - 1)cm is (8x³ - 12x² + 6x - 1)cm³
- Use algebra to support and construct arguments
- Generate arithmetic sequences of numbers , squared integers and sequences derived from diagrams
- Identify which terms cannot be in a sequence
- Generate the sequence of triangle numbers by considering the arrangement of dots and deduce that T(n) = 1 + 2 + 3 + .... + n, the sum of the series
- Recognise and use simple geometric progressions (rn where n is an integer and r is a rational number number > 0 or a surd)
- By looking at the spatial patterns of triangular numbers, deduce that the nth term is 1/2n(n + 1)
- Use function machines to find terms of sequence
- Solve exactly, by elimination of an unknown, linear/linear simultaneous equations, including where both need multiplying
- Solve linear/linear simultaneous equations graphically
- Solve simultaneous equation, linear/linear simultaneous equations,where neither or one equation needs multiplying
- Write simultaneous equations to represent a situation
- Set up and solve a pair of simultaneous equations in two variables
- Solve simultaneous equations representing a real-life situation graphically and interpret the solution in the context of the question
Step 09
Algebra
KS4 - Foundation GCSE
- Change the subject of a complex formula that involves fractions, e.g. make u or v the subject of the formula 1/v + 1/u =1/t
- Identify and interpret gradient from an equation ax + by = c
- Find approximate solutions of a quadratic equation from the graph of the corresponding quadratic function
- Recognise, sketch and interpret graphs of simple cubic functions
- Recognise, sketch and interpret reciprocal graphs
- Find the coordinates of the midpoint of a line from coordinates using a formula
- Solve linear inequalities in two variables graphically
- Solve two simultaneous inequalities algebraically and show the solution set on a number line
- Answer simple proof and 'show that' questions using consecutive integers (n, n+ 1), squares a², b², even numbers 2n, and odd numbers 2n + 1
- Continue a quadratic sequence and use the nth term to generate terms
- Use finite /infinite and ascending / descending to describe sequences
- Distinguish between arithmetic and geometric sequences
- Continue geometric progression and find term to term rule, including negative, fraction and decimal terms
- Simplify expressions involving brackets and powers e.g. x(x²+x+4), 3(a + 2b) − 2(a + b)
- Square a linear expression and collect like terms
Step 10
Algebra
Key Stage 4 - Higher GCSE
- Use function notation
- Deduce turning points by completing the square
- Sketch a graph of a quadratic by factorising, identifying roots and y-intercept, turning point
- Find the equation of the line through two given points
- Find the equation of the line through one point with a given gradient
- Know that a line perpendicular to the line y = mx + c, will have a gradient of -1/m
- Write down the equation of a line perpendicular to a given line
- Interpret and analyse a straight line graph and generate equations of lines parallel and perpendicular to the given line
- Solve quadratic inequalities in one variable, by factorising and sketching the graph to find critical values
- Simplify and manipulate algebraic expressions involving surds and algebraic fractions
- Solve exactly, by elimination of an unknown, linear/quadratic simultaneous equations
- Find approximate solutions to simultaneous equations formed from one linear function and one non-linear (quadratic or circle) function using a graphical approach
Step 11
Algebra
Key Stage 4 - Higher GCSE
- Apply to the graph of y = f(x) the transformations:
y = -f(x)
y = f(-x)
y = -f(-x) for linear, quadratic, cubic, sine and cosine functions
- Apply to the graph of y = f(x) the transformations:
y = f(x) + a
y = f(ax)
y = f(x + a)
y = af(x) for linear, quadratic, cubic, sine and cosine functions f(x)
- Construct the graphs of simple loci including the circle x² + y² = r² for a circle of radius r centred at the origin of the coordinate plane
- Find the gradient of the radius that meets the circle at a given point
- Find the nth term of a quadratic sequence of the form
n²
an²
an² ± b and
an² ± bn ± c
- Solve exactly, by elimination of an unknown, linear/x² + y² = r² simultaneous equations
Step 12
Algebra
Key Stage 4 - Higher GCSE
- Interpret the gradient of linear or non-linear graphs, and estimate the gradient of a quadratic or non-linear graph at a given point by sketching the tangent and finding its gradient
- Find the equation of a tangent to a circle at a given point
- Interpret coodinates for trigonometric graphs
- Plot graphs of the exponential function y = abx for integer values of x and simple positive values of a and b.
- Use iteration with simple converging sequences
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