Module 6 Graphs & Sequences
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Module Grade Topic

Description

6 1 1

Recognise a wider range of sequences. Continue simple sequences; explain how to find the next number in a simple pattern.

     

Creating Simple Sequences

Lesson

Homework

       
6 2 2

Recognise and describe patterns in number.

                   
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.

                   
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.

     

Plotting Co-ordinates in 1st Quadrant

Lesson

Homework

       
     

Plotting Co-ordinates in all 4 Quadrants

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Homework

 

Video

Exam Q

Answers

6 4 5

Plot graphs of linear functions in which y is given explicitly in terms of x. Relate ratios to linear functions.

     

Plotting Straight Line Graphs

Lesson 1

Homework 1

Video

Video

Exam Q

Answers

       

Lesson 2

Homework 2

 
       

Lesson 3

Homework 3

 
6 4 6

Generate sequences from practical contexts and write an expression to describe the nth term of an arithmetic sequence

     

Linear Sequences (nth Term)

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Homework

Video 1

Video

Exam Q

Answers

     

Generating Sequences

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Homework

Video 2

6 4 7

Draw and interpret distance-time and speed-time graphs and draw and interpret other real life graphs.

     

Conversion Graphs

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Homework

 

Video

Exam Q

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Real Life Graphs

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Homework

       
     

Distance Time Graphs

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Homework

 

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Exam Q

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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.

     

Solving Simultaneous Equations Graphically

Lesson

Homework

 

Video

Exam Q

Answers

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

     

Geometric Sequences

Lesson 1

Homework 1

       
       

Lesson 2

Homework 2

       
     

Recognising Sequences

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Homework

       
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.

     

Gradient and Intercept

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Homework

       
     

Equation of a Line (Including not in form y = )

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Homework

       
     

Finding the Equation of Lines

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Homework

Video

     
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.

     

Plotting Quadratics

Lesson

Homework

Video

Video

Exam Q

Answers

     

Key Parts of Quadratic Curves

Lesson

Homework

       
     

Plotting Quadratics, Cubics, Reciprocals and Exponential Graphs

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Homework

       
     

Reciprocal  Graphs

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Homework

       
     

Recognising the Shapes of Graphs

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Homework

       
6 6 12

Solve several linear inequalities in two variables and find the solution graphically.

     

Shading Inequalities

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Homework

 

Video

Exam Q

Answers

     

Quadratic Inequalities

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Homework

 
     

Linear Programming

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Homework

 
6 6 13

Solve quadratic equations by drawing a graph and cubic equations graphically when the graph is given.

     

Solving Quadratics by Drawing a Graph

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Homework

       
6 8 14

Find gradients of straight lines perpendicular to each other and write equations of straight lines in the form y = mx + c.

                   
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

     

Sine and Cosine Graphs

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Homework

       
     

Tan Graphs

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Homework

       
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

                   
6 9 17

Construct graphs of exponential function, and of the circle x2 + y2 = r2; solve problems involving the intersection of straight lines with a curve (including a circle).

     

Exponential Graphs

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Homework

       
     

Equations of Circles

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Homework

       
6 9 18

Shortest distance from a point to a straight line

                   
6 9 19

Find the nth term of a quadratic sequence

     

Quadratic Sequences

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Homework

       
6 9 20

Recognise and use Geometric sequences where the common ration may be a surd

                   
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

     

Tangents and Chords of Curves

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Homework

       
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)

     

Area under a Curve

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Homework