Sequences, functions and graphs

Home

Algebra

Geometry and Measures

Numbers and the number system

Statistics

Sequences, functions and graphs

Year 7	Year 8	Year 9	Year 10	Year 11	Extension
Describe integer sequences; generate terms of a simple sequence, given a rule (e.g. finding a term from the previous term, finding a term given its position in the sequence). Alien functions	Generate terms of a linear sequence using term-to-term and position-to-term rules, on paper and using a spreadsheet or graphics calculator. Linear Sequences	Generate terms of a sequence using term-to-term and position-to-term rules, on paper and using ICT.
Generate sequences from patterns or practical contexts and describe the general term in simple cases. Algebra with matchsticks	Use linear expressions to describe the nth term of a simple arithmetic sequence, justifying its form by referring to the activity or practical context from which it was generated. The Rich Aunt Problem Excel	Generate sequences from practical contexts and write and justify an expression to describe the nth term of an arithmetic sequence. Seven squares	Find the next term and the nth term of quadratic sequences and explore their properties; deduce properties of the sequences of triangular and square numbers from spatial patterns. Quadratic sequences
Express simple functions in words, then using symbols; represent them in mappings. Number machines Excel	Express simple functions algebraically and represent them in mappings or on a spreadsheet. Magic Squares Excel (It adds up, Magic Squares)	Find the inverse of a linear function.	Plot the graph of the inverse of a linear function. Function and inverse tutorial graphical calculator
Generate coordinate pairs that satisfy a simple linear rule; plot the graphs of simple linear functions, where y is given explicitly in terms of x, on paper and using ICT; recognise straight-line graphs parallel to the x-axis or y-axis. Exploring graphs with Omnigraph	Generate points in all four quadrants and plot the graphs of linear functions, where y is given explicitly in terms of x, on paper and using ICT; recognise that equations of the form y = mx + c correspond to straight-line graphs. y=mx+c with autograph Linking Co-ordinates, Tables, Graphs & Equations graphing calculator Graph Matching y=mx+c graphing calculator	Generate points and plot graphs of linear functions, where y is given implicitly in terms of x (e.g. ay + bx = 0, y + bx + c = 0), on paper and using ICT; find the gradient of lines given by equations of the form y = mx + c, given values for m and c.	Understand that equations in the form y = mx + c represent a straight line and that m is the gradient and c is the value of the y-intercept; investigate the gradients of parallel lines and lines perpendicular to these lines. Find the function Linear Graphing using Cameras Curve Stitching graphing calculators	Identify the equations of straight-line graphs that are parallel; find the gradient and equation of a straight-line graph that is perpendicular to a given line.
Plot and interpret the graphs of simple linear functions arising from real-life situations, e.g. conversion graphs. Conversion graphs Excel (pdf) Conversion graphs Excel (excel)	Construct linear functions arising from real-life problems and plot their corresponding graphs; discuss and interpret graphs arising from real situations, e.g. distance–time graphs. Archimedes bath	Construct functions arising from real-life problems and plot their corresponding graphs; interpret graphs arising from real situations, e.g. time series graphs.	Understand that the point of intersection of two different lines in the same two variables that simultaneously describe a real situation is the solution to the simultaneous equations represented by the lines.	Find approximate solutions of a quadratic equation from the graph of the corresponding quadratic function.	Know and understand that the intersection points of the graphs of a linear and quadratic function are the approximate solutions to the corresponding simultaneous equations.
					Construct the graphs of simple loci, including the circle x2 + y2 = r2; find graphically the intersection points of a given straight line with this circle and know this represents the solution to the corresponding two simultaneous equations.
			Explore simple properties of quadratic functions; plot graphs of simple quadratic and cubic functions, e.g. y = x2, y = 3x2 + 4, y = x3. Find the function	Plot graphs of more complex quadratic and cubic functions; estimate values at specific points, including maxima and minima.	Plot and recognise the characteristic shapes of graphs of simple cubic functions (e.g. y = x3), reciprocal functions (e.g. y = 1/x, x ≠ 0), exponential functions (y = kx for integer values of x and simple positive values of k) and trigonometric functions, on paper and using ICT.
				Identify and sketch graphs of linear and simple quadratic and cubic functions; understand the effect on the graph of addition of (or multiplication by) a constant.	Apply to the graph y = f(x) the transformations y = f(x) + a, y = f(ax), y = f(x+a) and y = af(x) for linear, quadratic, sine and cosine functions. Transforming functionsAutograph Function transformations
		Use ICT to explore the graphical representation of algebraic equations and interpret how properties of the graph are related to features of the equation, e.g. parallel and perpendicular lines.
		Interpret the meaning of various points and sections of straight-line graphs, including intercepts and intersection, e.g. solving simultaneous linear equations.