All of Resource Set 1

3303 kB  Product code: #M1A

Basic Skills

180 kB

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Coordinates

340 kB  Product code: #M1B

- Plotting ordered pairs given coordinates. (Whole numbers only)

- Points on the axes.

- Reading coordinates from a graph
(Whole numbers only)

- Plotting coordinates in a given order.

- Reading coordinates of given landmarks from a map. (Whole numbers only.)

- Reading ordered pairs from a graph.

- Use of four quadrants

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Transformations in the plane, plane shapes, solids

- Area and volume of rectangular prism
- Net of rectangular prism

- Construction of rectangular prism from its net

- Relationship between surface area and shape of a rectangular prism

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Gradient, linear functions, simultaneous solutions

581 kB  Product code: #M1D

- Gradient of a line from the origin to a fixed point

- Gradient of a line segment between two fixed points.

- An investigation of gradient in linear functions

- Correspondence between ‘m’ and steepness of the graph line.

- ‘Increasing’ and ‘decreasing’ gradients.
- Gradient of parallel lines

- An investigation of the ‘y’ intercept of linear functions.

- Correspondence between ‘c’ and the ‘y’ intercept of the graph line.

- Finding the equation of lines through plotted points.

- Includes vertical and horizontal lines.

- Measuring gradients on a photograph of a natural landmark.

- Approximating curves with linear functions.

- Finding simultaneous solutions of linear functions from tables of function values.

- Correspondence between simultaneous solutions and intersection of graph lines.

- Special cases, parallel lines and coincident lines.

- Finding simultaneous solutions of a linear function and a quadratic function from tables of function values.

- Correspondence between simultaneous solutions and intersection of graph lines.

- Special cases, tangential and non intersecting.

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Quadratic functions, polynomials

550 kB  Product code: #M1E

- An investigation of ‘a’ and ‘c’ in equations of type:
          ‘y = ax² + bx + c’

- The effect of the sign of ‘a’ on graph shape.

- The effect of the magnitude of ‘a’ on graph shape.

- Correspondence of ‘c’ and the ‘y’ intercept.

- Hand sketching of functions of type:
          ‘y = ax² + c’.

- Real life applications of quadratics

- Analysis of projectile motion from strobe camera picture.

- Recognising parabolas in nature and man made structures.

- Evaluating quadratic functions

- Finding points that satisfy quadratic functions

- Demonstrating that points satisfying a quadratic function lie on the graph of the function.

- Finding zeros of a quadratic function from a table of values.

- Correspondence of zeros and intersections of a quadratic function graph with the ‘x’ axis.

- Graphs of quadratic functions with 0, 1 and 2 zeros.

- Real roots of quadratic equations.

- An investigation of graphs of functions of type:
      y = xⁿ

- Degree, coefficients, turning points and zeros.

- Determining maximum number of turning points and zeros from the index of the equation.

- Finding accurate zeros and turning points from the graphs.

- Predicting and investigating properties of polynomials up to degree 5.

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Trigonometric Functions

430 kB  Product code: #M1F

- Investigation of amplitude and period of sine functions.

- Magnitude and sign of the amplitude.

- Finding period from the equation and the graph of a sine function.

- Sketching graphs of sine functions of the form:

      y = asin(bx)

- Investigation of phase and vertical position of sine functions.

- Finding phase shift from the equation and the graph of a sine function.

- Sketching graphs of sine functions of the form:

     y = asin(bx + c)

- An investigation of ‘d’ in: 
   y = asin(bx + c) + d

- An investigation of the sine function with the unit circle.

- Relationship between the sine ratio in right triangles and the function y = sinx

- Related trig identities: sin(-x), sin(p ± x)

- An investigation of the cosine function with the unit circle.

- Relationship between the cosine ratio in right triangles and the function y = cosx

- Related trig identities: cos(-x), cos(p ± x)

- An investigation of the tangent function with the unit circle.

- Relationship between the tangent ratio in right triangles and the function y = tanx

- Related trig identities: tan(-x), tan(p ± x)

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Curve fitting

339 kB   Product code: #M1G

- Finding equations of type: y = a/(bx+c) that fit given sets of data points.

- Recognising graphs related to y = 1/x

- Straightening the curve for y = 1/x type functions.

- Finding equations of type: y = a/(bx²+c) that fit given sets of data points.

- Recognising graphs related to y = 1/x²

- Straightening the curve for y = 1/x² functions.

- Finding equations of type: 
y = ae^bx or y = e^ax + b that fit given sets of data points.

- Recognising graphs related to these functions.

- Straightening the curve for these functions.

- Use of index and log rules.

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Calculus

628 kB  Product code: #M1H

- Finding the derivative of a function at a given point by measuring gradients of a secant.

- First principles notation for derivatives.

- Approaching a limit from both sides.

- Plotting a graph of the derivative of a given function from first principles.

- Plotting a graph of the derivative of a given function by direct measurement of gradients around the curve.

- Properties of a function graph when its derivative is: positive, zero, negative, increasing, decreasing.

- Points of inflection.

- Calculating the area under a curved graph by adding rectangles.

- Finding a primitive function by measuring areas on a graph.

- Finding area under a curve by calculating definite integrals.

- Finding area between two curves by subtracting definite integrals.

- Finding intersections of two functions as limits of integration.

- Making sketches of functions and shading areas.

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Statistics

374 kB  Product code: #M1J

- Entering data manually

- Importing a large data file

- Organising data into tables

- Interpreting data from a table.

- Putting data into classes

- Calculating a class midpoint

- Interpreting a huge data set

- Choosing the optimum class width

- Finding quartiles: Q1, Q2 and Q3

- Graphing histograms

- Sketching a histogram by hand

- Using the computer to plot a histogram

- Hints on choice of scales.

- Creating scatter plots

- Multiple scatter plots with vastly different ‘y’ values.

- Using scatter plots to interpret statistical data.

Fun Activity

191 kB

- Spirograph patterns. Create fascinating polar graph patterns.