Unit 2BMAT – Yr11 (Opt 6) Yr12 (Opt 5) Mathematics – Western Australia
Unit 2BMAT – Yr11 (Opt 6) Yr12 (Opt 5) Mathematics
| # | TOPIC | TITLE | |
|---|---|---|---|
| 1 | Study Plan | Self Assessment – Unit 2BMAT – Yr11 (Opt 6) Yr12 (Opt 5) | |
| Objective: On completion of the course formative assessment a tailored study plan is created identifying the lessons requiring revision. | |||
| 2 | Number theory – operations | Properties of real numbers using addition and multiplication | |
| Objective: On completion of the lesson the student will know and use the closure, identity, commutative, associative, identity and distributive properties for addition and multiplication. | |||
| 3 | Number theory – equations | Transformations that produce equivalent equations | |
| Objective: On completion of the lesson the student will know and use the correct terms to describe the processes in solving equations. | |||
| 4 | Percentages | Changing percentages to fractions and decimals | |
| Objective: On completion of the lesson the student will be able to change percentages to fractions and know how to change percentages to decimals. | |||
| 5 | Percentages | One quantity as a percentage of another | |
| Objective: On completion of the lesson the student will be able to find a percentage of an amount and how to express one quantity as a percentage of another. | |||
| 6 | 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. | |||
| 7 | 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. | |||
| 8 | 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. | |||
| 9 | Exponential function | The exponential function. | |
| Objective: On completion of the lesson the student will be able to graph any equation in the form y equals a to the power x, where a is any positive real number apart from 1. | |||
| 10 | Algebraic equations | Solving two step equations | |
| Objective: On completion of the lesson the student will be able to solve two step equations. | |||
| 11 | Algebraic equations | Solving equations containing binomial expressions | |
| Objective: On completion of the lesson the student will be able to move terms in binomial equations. | |||
| 12 | Algebraic equations | Equations involving grouping symbols. | |
| Objective: On completion of the lesson the student will be able to solve equations using grouping symbols | |||
| 13 | Algebraic equations | Equations involving fractions. | |
| Objective: On completion of the lesson the student will know how to solve equations using fractions. | |||
| 14 | 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. | |||
| 15 | 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. | |||
| 16 | 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. | |||
| 17 | Algebra-factorising | Simplifying easy algebraic fractions. | |
| Objective: On completion of the lesson the student will understand how to simplify algebraic fractions by factorising. | |||
| 18 | Absolute value or modulus | Solving and graphing inequalities | |
| Objective: On completion of the lesson the student will be able to solve inequalities involving one absolute value. | |||
| 19 | 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. | |||
| 20 | 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. | |||
| 21 | 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. | |||
| 22 | 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. | |||
| 23 | Logarithms-Power of 2 | Powers of 2. | |
| Objective: On completion of the lesson the student should be able to convert between logarithmic statements and index statements to the power of 2. | |||
| 24 | 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. | |||
| 25 | Volume | Finding the volume of prisms | |
| Objective: On completion of the lesson the student will be able to: use formulae to find the volume of prisms, calculate the volume of a variety of prisms, and explain the relationship between units of length and units of volume. | |||
| 26 | Volume | Volume of a cylinder and sphere. | |
| Objective: On completion of the lesson the student will be able to: calculate the volume of cylinders, spheres and hemispheres using the appropriate formulae, and use the relationship between litres and other measures of volume. | |||
| 27 | Volume | Volume of pyramids and cones. | |
| Objective: On completion of the lesson the student will be able to: use formulae to find the volume of right pyramids and cones, and calculate the volume of a variety of pyramids and cones. | |||
| 28 | Volume | Composite solids. | |
| Objective: On completion of the lesson the student will be able to: dissect composite solids into simpler shapes so that the volume can be calculated, calculate the volume of a variety of composite solids, and use formulae appropriately. | |||
| 29 | Surface area | Surface area of a cube/rectangular prism. | |
| Objective: On completion of the lesson the student will be able calculate the surface area of a number of different shapes by applying the appropriate formula. | |||
| 30 | Surface area | Surface area of a triangular/trapezoidal prism. | |
| Objective: On completion of the lesson the student will be able calculate the surface area of a number of triangular and trapezoidal shapes by applying the appropriate formula. | |||
| 31 | Surface area | Surface area of a cylinder and sphere. | |
| Objective: On completion of the lesson the student will be able calculate the surface area of different cylindrical and spherical shapes by applying the appropriate formula. | |||
| 32 | Surface area | Surface area of pyramids | |
| Objective: On completion of the lesson the student will be able to find the surface areas of pyramids. | |||
| 33 | Surface area | Surface area of cones | |
| Objective: On completion of the lesson the student will be able to find the surface areas of cones by finding the area or the base ‘p r . ‘and the area of the curved surface ‘ p r l’. The student will also be able to find the slant height ‘l’ given the perpendicul | |||
| 34 | Surface area | Surface area of composite solids | |
| Objective: On completion of the lesson the student will be able to find the surface areas of Composite solids. | |||
| 35 | Trigonometry-ratios | Trigonometric ratios. | |
| Objective: On completion of the lesson the student will be able to identify the hypotenuse, adjacent and opposite sides for a given angle in a right angle triangle. The student will be able to label the side lengths in relation to a given angle e.g. the side c is op | |||
| 36 | Trigonometry-ratios | Using the calculator. | |
| Objective: On completion of the lesson the student will be able to use the calculator to find values for the sine, cosine and tangent ratios of acute angles. | |||
| 37 | Trigonometry-ratios | Using the trigonometric ratios to find unknown length. [Case 1 Sine]. | |
| Objective: On completion of the lesson the student will be able to use the sine ratio to calculate lengths and distances. | |||
| 38 | Trigonometry-ratios | Using the trigonometric ratios to find unknown length. [Case 2 Cosine]. | |
| Objective: On completion of the lesson the student will be able to use the cosine ratio to find the length of the adjacent side of a right angle triangle. | |||
| 39 | Trigonometry-ratios | Using the trigonometric ratios to find unknown length. [Case 3 Tangent Ratio]. | |
| Objective: On completion of the lesson the student will be able to use the tangent ratio to calculate the length of the opposite side in a right angle triangle. | |||
| 40 | Trigonometry-ratios | Unknown in the denominator. [Case 4]. | |
| Objective: On completion of the lesson the student will understand how to use the trig ratios to calculate lengths and distances when the denominator is unknown. | |||
| 41 | Trigonometry-compass | Bearings – the compass. | |
| Objective: On completion of the lesson the student will be able to identify compass bearings, compass bearings with acute angles and 3 figure bearings from true north. | |||
| 42 | Trigonometry-elevation | Angles of elevation and depression. | |
| Objective: On completion of the lesson the student will be able to identify angles of depression and angles of elevation, and the relationship between them. | |||
| 43 | Trigonometry-practical | Trigonometric ratios in practical situations. | |
| Objective: On completion of the lesson the student will be able to use trigonometric ratios to solve problems involving compass bearings and angles of depression and elevation. | |||
| 44 | Trigonometry-ratios | Using the calculator to find an angle given a trigonometric ratio. | |
| Objective: On completion of the lesson the student will be capable of using a calculator to find the value of an unknown angle when given a trigonometric ratio. | |||
| 45 | Trigonometry- ratios | Using the trigonometric ratios to find an angle in a right-angled triangle. | |
| Objective: On completion of the lesson the student will be able to find the value of an unknown angle in a right angle triangle given the lengths of 2 of the sides. | |||
| 46 | 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. | |||
| 47 | 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. | |||
| 48 | 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. | |||
| 49 | 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. | |||
| 50 | 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. | |||
| 51 | 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. | |||
| 52 | 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. | |||
| 53 | 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. | |||
| 54 | Co-ordinate Geometry-Two point formula | Two point formula: equation of a line which joins a pair of points. | |
| Objective: On completion of the lesson the student will be able to calculate the equation of a line given any two named points on the line. | |||
| 55 | Statistic-probability | Probability of Simple Events | |
| Objective: On completion of the lesson the student will be able to understand the probability of simple events. | |||
| 56 | 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. | |||
| 57 | Statistic-probability | Experimental probability | |
| Objective: On completion of this lesson the student will be able to find the probabilities in an experimental trial. | |||
| 58 | 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. | |||
| 59 | 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. | |||
| 60 | 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. | |||
| 61 | 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. | |||
| 62 | Statistics | Scatter Diagrams | |
| Objective: On completion of the lesson the student will be able to construct scatter plots and draw conclusions from these. | |||
| 63 | Exam | Exam – Unit 2BMAT – Yr11 (Opt 6) Yr12 (Opt 5) | |
| Objective: Exam | |||
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