# Unit 2CMAT – Yr11 (Opt 7) Yr12 (Opt 6) Mathematics – Western Australia

### Unit 2CMAT – Yr11 (Opt 7) Yr12 (Opt 6) Mathematics

# | TOPIC | TITLE | |
---|---|---|---|

1 | Study Plan | Self Assessment – Unit 2CMAT – Yr11 (Opt 7) Yr12 (Opt 6) | |

Objective: On completion of the course formative assessment a tailored study plan is created identifying the lessons requiring revision. | |||

2 | Significant figures | Significant figures | |

Objective: On completion of the lesson the student will be able to observe how many significant figures are in a number and how to express a number to a certain level of significant figures. | |||

3 | Scientific notation | Scientific notation with larger numbers | |

Objective: On completion of the lesson the student will be able to change numbers greater than 1 to scientific notation. | |||

4 | Scientific notation | Scientific notation with small numbers | |

Objective: On completion of the lesson the student will be able to change numbers between zero and 1 to scientific notation. | |||

5 | Scientific notation | Changing scientific notation to numerals | |

Objective: On completion of the lesson the student will be able to change numbers written in scientific notation to basic numerals and be capable of solving problems on the calculator in scientific notation. | |||

6 | Coordinate Geometry-gradient | Gradient | |

Objective: On completion of the lesson the student will be able to calculate the gradient of a line given its inclination, or angle to the positive direction of the x-axis; or its rise and run. | |||

7 | Coordinate Geometry-gradient | Gradient formula. | |

Objective: On completion of the lesson the student will be able to calculate the gradient of a line given any two points on the line and also be capable of checking whether 3 or more points lie on the same line and what an unknown point will make to parallel lines. | |||

8 | Coordinate Geometry-straight line | The straight line. | |

Objective: On completion of the lesson the student will be able to draw a line which is parallel to either axis and comment on its gradient, where that gradient exists. | |||

9 | Coordinate Geometry-slope, etc. | Lines through the origin. | |

Objective: On completion of the lesson the student will be able to draw a line which passes through the origin of the form y=mx and comment on its gradient compared to the gradients of other lines through the origin and use the information to solve problems. | |||

10 | Coordinate Geometry-equation of line | General form of a line and the x and y Intercepts. | |

Objective: On completion of the lesson the student will be able to change the equation of a straight line from the form, written as y=mx+c, into the general form and vice versa. | |||

11 | Coordinate Geometry-intercept | Slope intercept form of a line. | |

Objective: On completion of the lesson the student will be able to find the slope and intercept given the equation and given the slope and intercept, derive the equation. | |||

12 | Coordinate Geometry-point slope | Point slope form of a line | |

Objective: On completion of the lesson the student will understand how to derive the equation of a straight line given the gradient and a point on the line. | |||

13 | Geometry-parabola | The parabola: to describe properties of a parabola from its equation | |

Objective: On completion of the lesson the student will be able to predict the general shape and important features of a parabola and then graph the parabola to check the predictions. | |||

14 | Functions and graphs | Quadratic polynomials of the form y = ax. + bx + c. | |

Objective: On completion of the lesson the student will be able to predict the general shape of a parabola and verify the predictions by sketching the parabola. The student will also be introduced to the discriminant and the axis. | |||

15 | Functions and graphs | Graphing perfect squares: y=(a-x) squared | |

Objective: On completion of the lesson the student will be able to analyse a curve and then check their work by graphing the curve. | |||

16 | Graphing roots | Graphing irrational roots | |

Objective: On completion of the lesson the student will be able to solve any polynomial which has real roots, whether they are rational or irrational. | |||

17 | Coordinate geometry | Solve by graphing | |

Objective: On completion of the lesson students will use the slope intercept form of a line to create graphs and find points of intersection. | |||

18 | Functions | Definition, domain and range | |

Objective: On completion of this lesson the student will be able to select functions from relations by referring to the domain and range. | |||

19 | Functions | Notation and evaluations | |

Objective: On completion of the lesson the student will be understand different notations for functions. | |||

20 | Functions | More on domain and range | |

Objective: On completion of the lesson the student will be able to describe the domain and range using appropriate set notation. | |||

21 | Functions | Domain and range from graphical representations | |

Objective: On completion of the lesson the student will be able to describe the domain and range using appropriate set notation from graphical representations. | |||

22 | Quadratic equations | Introduction to quadratic equations. | |

Objective: On completion of the lesson the student will understand simple quadratic equations. | |||

23 | Quadratic equations | Quadratic equations with factorisation. | |

Objective: On completion of the lesson the student will be able to find both roots of a quadratic equation by factorising. | |||

24 | Quadratic equations | Solving quadratic equations. | |

Objective: On completion of the lesson the student will have gained more confidence in working with quadratic equations. | |||

25 | Quadratic equations | Completing the square | |

Objective: On completion of the lesson the student will understand the process of completing the square. | |||

26 | Quadratic equations | Solving quadratic equations by completing the square | |

Objective: On completion of the lesson the student will understand the reasoning behind completing the square. | |||

27 | Quadratic equations | The quadratic formula | |

Objective: On completion of the lesson the student will be familiar with the quadratic formula. | |||

28 | Quadratic equations | Problem solving with quadratic equations | |

Objective: On completion of the lesson the student will be able to express a problem as a quadratic equation and then solve it. | |||

29 | Quadratic equations | Solving simultaneous quadratic equations graphically | |

Objective: On completion of the lesson the student will better understand why quadratic equations have two solutions and will be capable of solving quadratic equations and problems graphically.. | |||

30 | Algebra-highest common factor | Highest common factor. | |

Objective: On completion of the lesson the student will be capable of turning a simple algebraic expression into the product of a factor in parentheses and identifying the highest common factors of the whole expression. | |||

31 | Factors by grouping | Factors by grouping. | |

Objective: On completion of the lesson the student will be able to complete the process given just two factors for the whole expression. | |||

32 | Difference of 2 squares | Difference of two squares | |

Objective: On completion of the lesson the student understand the difference of two squares and be capable of recognising the factors. | |||

33 | Common fact and diff | Common factor and the difference of two squares | |

Objective: On completion of the lesson the student will be aware of common factors and recognise the difference of two squares. | |||

34 | Quadratic trinomials | Quadratic trinomials [monic] – Case 1. | |

Objective: On completion of the lesson the student will understand the factorisation of quadratic trinomial equations with all terms positive. | |||

35 | Sequences and Series-Compound interest | Compound interest | |

Objective: On completion of the G.P. lesson the student will understand the compound interest formula and how to use it and adjust the values of r and n, if required, for different compounding periods. | |||

36 | Coordinate Geometry-the plane | Distance formula. | |

Objective: On completion of the lesson the student will be able to calculate the distance between any two points on the number plane and interpret the results. | |||

37 | Co-ordinate Geometry-Intercept form | Intercept form of a straight line: find the equation when given x and y | |

Objective: On completion of the lesson the student will have an effective and efficient method for calculating the equation of a straight line. | |||

38 | Co-ordinate Geometry-Parallel lines equations | Parallel lines: identify equation of a line parallel to another | |

Objective: On completion of the lesson the student will be able to decide if two or more lines are parallel or not and to solve problems involving parallel lines. | |||

39 | Co-ordinate Geometry-Perpendicular lines | Perpendicular lines. | |

Objective: On completion of the lesson the student will be able to derive the equation of a line, given that it is perpendicular to another stated line. | |||

40 | Statistics | Frequency distribution table | |

Objective: On completion of the lesson the student will be able to construct a frequency distribution table for raw data and interpret the table. | |||

41 | Statistics | Frequency histograms and polygons | |

Objective: On completion of the lesson the student will be able to construct and interpret frequency histograms and polygons. | |||

42 | Statistics | Relative frequency | |

Objective: On completion of the lesson the student will be able to collect, display and make judgements about data. | |||

43 | Statistics | The range. | |

Objective: On completion of the lesson the student will be able to determine the range of data in either raw form or in a frequency distribution table. | |||

44 | Statistic-probability | The mode | |

Objective: On completion of the lesson the student will understand how to find the mode from raw data, a frequency distribution table and polygon. | |||

45 | Statistic-probability | The mean | |

Objective: On completion of the lesson the student will be able to calculate means from raw data and from a frequency table using an fx column. | |||

46 | Statistic-probability | The median | |

Objective: On completion of the lesson the student will be able to determine the median of a set of raw scores | |||

47 | Statistic-probability | Calculating the median from a frequency distribution | |

Objective: On completion of the lesson the student will be able to determine the median from a cumulative frequency polygon. | |||

48 | Statistics – grouped data | Calculating mean, mode and median from grouped data | |

Objective: On completion of the lesson the student will be capable of identifying class centres, get frequency counts and determine the mean and mode values. | |||

49 | Statistics using a calculator | Statistics and the student calculator | |

Objective: On completion of the lesson the student will be capable of using a scientific calculator in statistics mode to calculate answers to statistical problems. | |||

50 | Statistics – Range and dispersion | Range as a measure of dispersion | |

Objective: On completion of the lesson the student will be able to determine the range and using it in decision making. | |||

51 | Statistics – Interquartile range | Measures of spread: the interquartile range | |

Objective: On completion of the lesson the student will be able to find the upper and lower quartiles and the interquartile range | |||

52 | Statistics | Stem and Leaf Plots along with Box and Whisker Plots | |

Objective: On completion of the lesson the student will be familiar with vocabulary for statistics including quartiles, mode, median, range and the representation of this information on a Box and Whisker Plot. | |||

53 | Statistics | Scatter Diagrams | |

Objective: On completion of the lesson the student will be able to construct scatter plots and draw conclusions from these. | |||

54 | Statistic-probability | Probability of Simple Events | |

Objective: On completion of the lesson the student will be able to understand the probability of simple events. | |||

55 | Statistic-probability | Rolling a pair of dice | |

Objective: On completion of the lesson the student will be capable of ascertaining the probability of certain results when 2 dice are thrown simultaneously. | |||

56 | Statistic-probability | Experimental probability | |

Objective: On completion of this lesson the student will be able to find the probabilities in an experimental trial. | |||

57 | Statistic-probability | Tree diagrams – not depending on previous outcomes | |

Objective: On completion of the lesson the student will be confident in drawing tree diagrams to list outcomes of a multi stage probability problem and then finding probabilities of certain events not depending on previous outcomes. | |||

58 | Statistic-probability | Tree diagrams – depending on previous outcomes | |

Objective: On completion of the lesson the student will be confident in drawing tree diagrams to list outcomes of other multi stage probability problems and then finding probabilities of certain events depending on previous outcomes. | |||

59 | Statistic-probability | The complementary result .. | |

Objective: On completion of the lesson the student will be capable of ascertaining the probability of certain results where the complementary event is involved. | |||

60 | Statistic-probability | P[A or B] When A and B are both mutually and NOT mutually exclusive | |

Objective: On completion of this lesson the student will be able to distinguish between mutually exclusive and non mutually exclusive events and be able to find the probabilities of both. | |||

61 | Exam | Exam – Unit 2CMAT – Yr11 (Opt 7) Yr12 (Opt 6) | |

Objective: Exam |