# Unit 3BMAT – Yr11 (Opt 8-9) Yr12 (Opt 7) Mathematics – Western Australia

### Unit 3BMAT – Yr11 (Opt 8-9) Yr12 (Opt 7) Mathematics

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

1 | Study Plan | Self Assessment – Unit 3BMAT – Yr11 (Opt 8-9) Yr12 (Opt 7) | |

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

2 | 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. | |||

3 | Functions | Notation and evaluations | |

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

4 | 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. | |||

5 | 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. | |||

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 | Algebraic equations | Solving two step equations | |

Objective: On completion of the lesson the student will be able to solve two step equations. | |||

14 | Algebraic equations | Solving equations containing binomial expressions | |

Objective: On completion of the lesson the student will be able to move terms in binomial equations. | |||

15 | Algebraic equations | Equations involving grouping symbols. | |

Objective: On completion of the lesson the student will be able to solve equations using grouping symbols | |||

16 | Algebraic equations | Equations involving fractions. | |

Objective: On completion of the lesson the student will know how to solve equations using fractions. | |||

17 | Algebra- formulae | Equations resulting from substitution into formulae. | |

Objective: On completion of the lesson the student will be able to substitute into formulae and then solve the resulting equations. | |||

18 | Algebra- formulae | Changing the subject of the formula. | |

Objective: On completion of the lesson the student will be able to move pronumerals around an equation using all the rules and operations covered previously. | |||

19 | Algebra-inequalities | Solving Inequalities. | |

Objective: On completion of the lesson the student will understand the ‘greater than’ and ‘less than’ signs, and be able to perform simple inequalities. | |||

20 | Algebra-factorising | Simplifying easy algebraic fractions. | |

Objective: On completion of the lesson the student will understand how to simplify algebraic fractions by factorising. | |||

21 | Simultaneous equns | Simultaneous equations | |

Objective: On completion of the lesson the student will be able to solve 2 equations with 2 unknown variables by the substitution method. | |||

22 | Simultaneous equns | Elimination method | |

Objective: On completion of the lesson the student will be able to solve 2 equations with 2 unknown variables by the elimination method. | |||

23 | Simultaneous equns | Elimination method part 2 | |

Objective: On completion of the lesson the student will be able to solve all types of simultaneous equations with 2 unknown variables by the elimination method. | |||

24 | Simultaneous equns | Applications of simultaneous equations | |

Objective: On completion of this lesson the student will be able to derive simultaneous equations from a given problem and then solve those simultaneous equations. | |||

25 | Simultaneous equations | Number of solutions (Stage 2) | |

Objective: On completion of the lesson of the lesson the student will identify simultaneous equations that are consistent, inconsistent or the same. | |||

26 | Linear systems | Optimal solutions (Stage 2) – Vectors | |

Objective: On completion of the lesson the student will understand the process of linear programming to find optimal solutions. | |||

27 | Linear systems | Linear systems with matrices (Stage 2) | |

Objective: On completion of the lesson the student will process matrices formed from linear systems of equations. | |||

28 | Calculus | Limits | |

Objective: On completion of the lesson the student will be able to solve problems using limiting sum rule. | |||

29 | Calculus=1st prin | Differentiation from first principles. | |

Objective: On completion of the lesson the student will be able apply the first principles (calculus) formula to find the gradient of a tangent at any point on a continuous curve. | |||

30 | Calculus=1st prin | Differentiation of y = x to the power of n. | |

Objective: On completion of the Calculus lesson the student will be able to differentiate a number of expressions involving x raised to the power of n. | |||

31 | Calculus-differential, integ | Meaning of dy over dx – equations of tangents and normals. | |

Objective: On completion of the Calculus lesson the student will be able to apply differentiation and algebra skills to find the equation of the tangent and the normal to a point on a curve. | |||

32 | Calculus-differential, integ | Function of a function rule, product rule, quotient rule. | |

Objective: On completion of the Calculus lesson the student will understand how to use the chain rule, the product rule and the quotient rule. | |||

33 | Calculus-differential, integ | Increasing, decreasing and stationary functions. | |

Objective: On completion of the lesson the student will understand how to find the first derivative of various functions, and use it in various situations to identify increasing, decreasing and stationary functions. | |||

34 | Calculus | First Derivative – turning points and curve sketching | |

Objective: On completion of the Calculus lesson the student will be able to use the first derivative to find and identify the nature of stationary points on a curve. | |||

35 | Calculus-2nd derivative | The second derivative – concavity. | |

Objective: On completion of the Calculus lesson the student will be able to find a second derivative, and use it to find the domain over which a curve is concave up or concave down, as well as any points of inflexion. | |||

36 | Calculus – Curve sketching | Curve sketching | |

Objective: On completion of the Calculus lesson the student will be able to use the first and second derivatives to find turning points of a curve, identify maxima and minima, and concavity, then use this information to sketch a curve. | |||

37 | Calculus – Maxima minima | Practical applications of maxima and minima | |

Objective: On completion of the lesson the student will be able to apply calculus to a suite of simple maxima or minima problems. | |||

38 | Calculus – Integration | Integration – anti-differentiation, primitive function | |

Objective: On completion of the Calculus lesson the student will be able to use rules of integration to find primitives of some simple functions. | |||

39 | Calculus – Computation area | Computation of an area | |

Objective: On completion of the Calculus lesson the student will be able to select an appropriate formula to calculate an area, re-arrange an expression to suit the formula, and use correct limits in the formula to evaluate an area. | |||

40 | Calculus – Trapezoidal and Simpson’s rules | The Trapezium rule and Simpson’s rule | |

Objective: On completion of the Calculus lesson the student will know how to calculate sub-intervals, set up a table of values, then apply the Trapezoidal Rule, or Simpson’s Rule to approximate an area beneath a curve. | |||

41 | Logic | Inductive and deductive reasoning | |

Objective: On completion of this lesson the student will understand and use the terms hypothesis, conclusion, inductive and deductive. | |||

42 | Logic | Definition and use of counter examples | |

Objective: On completion of this lesson the student will be able to create counter examples to statements. | |||

43 | Logic | Indirect proofs | |

Objective: On completion of the lesson the student will be able to use indirect proofs by assuming the opposite of the statement being proved. | |||

44 | Logic | Conditional statements (converse, inverse and contrapositive) (Stage 2) | |

Objective: On completion of the lesson the student will be able to form related conditional statements. | |||

45 | Geometry | To identify collinear points, coplanar lines and points in 2 and 3 dimensions | |

Objective: On completion of the lesson the student will use correct terms to describe points, lines, intervals and rays. | |||

46 | Geometry – angles | To determine angle labelling rules, naming angles according to size, angle bisector properties and related algebra | |

Objective: On completion of the lesson the student will label angles, use a protractor and perform calculations using algebra involving angles. | |||

47 | Geometry-constructions | Angle bisector construction and its properties (Stage 2) | |

Objective: On completion of the lesson the student will be able to bisect an angle using a pair of compasses and a straight edge. | |||

48 | Geometry-constructions | Circumcentre and incentre (Stage 2) | |

Objective: On completion of the lesson the student will be able geometrically construct the circumcentre and incentre for a triangle and to use Pythagoras’ Theorem to calculate values. | |||

49 | Geometry-constructions | Orthocentre and centroids (Stage 2) | |

Objective: On completion of the lesson the student will be able geometrically construct the orthocentre and centroid for a triangle and to use algebra to calculate values. | |||

50 | Geometry-quadrilaterals | Midsegments of Triangles | |

Objective: On completion of the lesson the student will be able to use coordinate geometry to apply the midsegment properties of a triangle. | |||

51 | Geometry-quadrilaterals | Classifying Quadrilaterals | |

Objective: On completion of this lesson the student will understand the properties that classify quadrilaterals. | |||

52 | Geometry-quadrilaterals | Using the Properties of a Parallelogram | |

Objective: On completion of this lesson the student will be able to use and prove the properties of a parallelogram. | |||

53 | Geometry-quadrilaterals | Proving a Shape is a Parallelogram | |

Objective: On completion of this lesson the student will be able to use properties to prove a given quadrilateral is a parallelogram. | |||

54 | Geometry-quadrilaterals | Properties of the Rectangle, Square and Rhombus | |

Objective: On completion of this lesson students will be able to use the properties of the rectangle, square and rhombus for formal proofs and to find values. | |||

55 | Geometry-quadrilaterals | Properties of the Trapezium and Kite | |

Objective: On completion of this lesson students will be able to use the properties of the trapezium and kite for formal proofs and to find values. | |||

56 | Geometry-quadrilaterals | The quadrilateral family and coordinate methods in geometry | |

Objective: On completion of this lesson the student will know the relationships between quadrilaterals and use coordinate methods to prove some of the properties. | |||

57 | Geometry-locus | Constructions and loci – single condition | |

Objective: On completion of the lesson the student will understand the term locus and describe several using a single condition. | |||

58 | Geometry-locus | Constructions and loci – multiple conditions | |

Objective: On completion of the lesson the student will describe a locus that satisfies multiple conditions on a number plane. | |||

59 | Exam | Exam – Unit 3BMAT – Yr11 (Opt 8-9) Yr12 (Opt 7) | |

Objective: Exam |