Module 6 | Graphs & Sequences | |||

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Module | Grade | Topic |
Description |
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6 | 1 | 1 |
Recognise a wider range of sequences. Continue simple sequences; explain how to find the next number in a simple pattern. |
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Creating Simple Sequences |
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6 | 2 | 2 |
Recognise and describe patterns in number. |
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6 | 2 | 3 |
Understand the use of symbols to represent unknowns; use simple function machines to deal with inputs and outputs, recognising basic inverse functions. |
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6 | 2 | 4 |
Use axes and coordinates to specify or locate points in all four quadrants; find the coordinates of points identified by geometrical information. |
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Plotting Co-ordinates in 1st Quadrant |
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Plotting Co-ordinates in all 4 Quadrants |
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6 | 4 | 5 |
Plot graphs of linear functions in which y is given explicitly in terms of x. Relate ratios to linear functions. |
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Plotting Straight Line Graphs |
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6 | 4 | 6 |
Generate sequences from practical contexts and write an expression to describe the nth term of an arithmetic sequence |
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Linear Sequences (nth Term) |
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Generating Sequences |
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6 | 4 | 7 |
Draw and interpret distance-time and speed-time graphs and draw and interpret other real life graphs. |
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Conversion Graphs |
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Real Life Graphs |
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Distance Time Graphs |
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6 | 5 | 8 |
Find the exact solution of two simultaneous equations in two unknowns by interpreting the equations as lines and their common solution as the point of intersection. |
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Solving Simultaneous Equations Graphically |
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6 | 5 | 9 |
Use and justify simple quadratic sequences to generate the nth term of a simple quadratic sequence. Include Fibonacci type sequences and Geometric progressions |
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Geometric Sequences |
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Recognising Sequences |
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6 | 5 | 10 |
Find the gradient of straight lines given by equations of the form y = mx + c given explicitly or implicitly in terms of x.: understand that y = mx + c represents a straight line , interpret the values of m and c; know when lines are parallel. Interpret the gradient as a rate of change. |
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Gradient and Intercept |
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Equation of a Line (Including not in form y = ) |
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Finding the Equation of Lines |
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6 | 6 | 11 |
Plot graphs of a range of quadratic functions and of simple cubic functions and reciprocal functions. Identify and interpret roots, intercepts and turning points of quadratic functions graphically. |
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Plotting Quadratics |
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Key Parts of Quadratic Curves |
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Plotting Quadratics, Cubics, Reciprocals and Exponential Graphs |
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Reciprocal Graphs |
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Recognising the Shapes of Graphs |
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6 | 6 | 12 |
Solve several linear inequalities in two variables and find the solution graphically. |
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Shading Inequalities |
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Quadratic Inequalities |
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Linear Programming |
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6 | 6 | 13 |
Solve quadratic equations by drawing a graph and cubic equations graphically when the graph is given. |
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Solving Quadratics by Drawing a Graph |
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6 | 8 | 14 |
Find gradients of straight lines perpendicular to each other and write equations of straight lines in the form y = mx + c. |
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6 | 8 | 15 |
Draw, sketch and describe the graphs of trigonometric functions (sin, cos and tan) for angles of any size, find trigonometrical solutions e.g. cos(x) = 0.5 |
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Sine and Cosine Graphs |
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Tan Graphs |
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6 | 9 | 16 |
Find the equation of a tangent to a circle at a given point, using the fact that it is perpendicular to the radius |
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6 | 9 | 17 |
Construct
graphs of exponential function, and of the circle x |
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Exponential Graphs |
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Equations of Circles |
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6 | 9 | 18 |
Shortest distance from a point to a straight line |
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6 | 9 | 19 |
Find the nth term of a quadratic sequence |
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Quadratic Sequences |
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6 | 9 | 20 |
Recognise and use Geometric sequences where the common ration may be a surd |
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6 | 9 | 21 |
Apply the concept of instantaneous and average rates of change by looking at the gradients of tangents and chords to a curve |
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Tangents and Chords of Curves |
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6 | 9 | 22 |
Interpret areas under graphs and gradients of graphs in real-life contexts (e.e. recognise that the area under a velocity-time graph represents displacement) |
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Area under a Curve |