# Year 10 (Leading to Level 6) Mathematics – Victoria

### VIC Year 10 (Leading to Level 6) Mathematics

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

1 | Study Plan | Study plan – Year 10 | |

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

2 | Rules for indices/exponents | Adding indices when multiplying terms with the same base | |

Objective: On completion of the lesson the student will know how to use the index law of addition of powers when multiplying terms with the same base. | |||

3 | Rules for indices/exponents | Subtracting indices when dividing terms with the same base | |

Objective: On completion of the lesson the student will know how to use the index law of subtraction of powers when dividing terms with the same base. | |||

4 | Rules for indices/exponents | Multiplying indices when raising a power to a power | |

Objective: On completion of the lesson the student will use the law of multiplication of indices when raising a power to a power. | |||

5 | Rules for indices/exponents | Multiplying indices when raising to more than one term | |

Objective: On completion of the lesson the student will be able to use the law of multiplication of indices when raising more than one term to the same power. | |||

6 | Rules for indices/exponents | Terms raised to the power of zero | |

Objective: On completion of the lesson the student will learn how to evaluate or simplify terms that are raised to the power of zero. | |||

7 | Rules for indices/exponents | Negative Indices | |

Objective: On completion of the lesson the student will know how to evaluate or simplify expressions containing negative indices. | |||

8 | Fractional indices/exponents | Fractional indices | |

Objective: On completion of the lesson the student will know how to evaluate or simplify expressions containing fractional indices. | |||

9 | Fractional indices/exponents | Complex fractions as indices | |

Objective: On completion of the lesson the student will know how to evaluate or simplify expressions containing complex fractional indices. | |||

10 | 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. | |||

11 | 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. | |||

12 | 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. | |||

13 | 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. | |||

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

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

15 | Algebraic fractions | Simplifying algebraic fractions using the index laws. | |

Objective: On completion of the lesson the student will be able to simplify most algebraic fractions using different methodologies. | |||

16 | Algebra-negative indices | Algebraic fractions resulting in negative indices. | |

Objective: On completion of the lesson the student will be able to understand how to simplify an algebraic fractional expression with a negative index, and also how to write such an expression without a negative index. | |||

17 | Factorisation | Factorisation of algebraic fractions including binomials. | |

Objective: On completion of the lesson the student should be able to simplify more complex algebraic fractions using a variety of methods. | |||

18 | Algebraic fractions-binomial | Cancelling binomial factors in algebraic fractions. | |

Objective: On completion of the lesson the student should be able to factorise binomials to simplify fractions. | |||

19 | Graphing binomials | Binomial products. | |

Objective: On completion of the lesson the student will understand the term binomial product and be capable of expanding and simplifying an expression. | |||

20 | Graphing binomials | Binomial products with negative multiplier | |

Objective: On completion of the lesson the student will understand specific terms and be prepared to expand and simplify different monic binomial products. | |||

21 | Graphing binomials | Binomial products [non-monic]. | |

Objective: On completion of the lesson, the student will have examined more complex examples with binomial products. | |||

22 | Squaring binomial | Squaring a binomial. [monic] | |

Objective: On completion of the lesson the student should understand the simple one-step process of squaring a monic binomial. | |||

23 | Squaring binomial | Squaring a binomial [non-monic]. | |

Objective: On completion of the lesson the student will apply the same rule that is used with monic binomials. | |||

24 | Factorising | Expansions leading to the difference of two squares | |

Objective: On completion of the lesson the student will understand expansions leading to differences of 2 squares. | |||

25 | Algebraic expressions-products | Products in simplification of algebraic expressions | |

Objective: On completion of the lesson the student will understand simplification of algebraic expressions in step-by-step processing. | |||

26 | Algebraic expressions-larger expansions | Algebraic Expressions – Larger expansions. | |

Objective: On completion of the lesson the student will be capable of expanding larger algebraic expressions. | |||

27 | 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. | |||

28 | 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. | |||

29 | 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. | |||

30 | 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. | |||

31 | 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 | |||

32 | 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. | |||

33 | 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. | |||

34 | 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. | |||

35 | Trigonometry-exact ratios | Trigonometric ratios of 30., 45. and 60. – exact ratios. | |

Objective: On completion of the lesson the student will be able to find the exact sine, cosine and tangent ratios for the angles 30., 45.and 60. | |||

36 | 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. | |||

37 | 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. | |||

38 | Decimals | Comparing and ordering decimals to two decimal places | |

Objective: On completion of the lesson the student will be able to compare and order decimals to two decimal places and understand decimal notation to two places. | |||

39 | Decimals | Using decimals – shopping problems | |

Objective: On completion of the lesson the student will be able to: read and interpret problems involving money, interpret the everyday use of decimals, and perform calculations with money. | |||

40 | Decimals | Using decimals to record length | |

Objective: On completion of the lesson the student will be able to interpret the everyday use of fractions and decimals and use their knowledge of decimals to record measurements. | |||

41 | Decimals | Rounding decimals | |

Objective: On completion of the lesson the student will be able to round a number with one or two decimal places to the nearest whole number. | |||

42 | Decimals | Decimals to three decimal places | |

Objective: On completion of the lesson the student will be able to express thousandths as a decimal and interpret decimal notation for thousandths. | |||

43 | Decimals | Adding decimals with a different number of decimal places | |

Objective: On completion of the lesson the student will be able to add decimal numbers with different numbers of decimal places. | |||

44 | Decimals | Subtracting decimals with a different number of places | |

Objective: On completion of the lesson the student will be able to subtract decimals with different numbers of decimal places. | |||

45 | Decimals | Multiplication of decimals by decimals to two decimal places | |

Objective: On completion of the lesson the student will be able to multiply decimals to two digits. | |||

46 | Decimals | Dividing decimal fractions by whole numbers | |

Objective: On completion of the lesson the student will be able to divide decimal fractions by whole numbers. | |||

47 | Decimals | Dividing numbers by a decimal fraction | |

Objective: On completion of the lesson the student will be able to divide numbers by a decimal fraction. | |||

48 | Number theory – sets | Number sets and their members | |

Objective: On completion of the lesson the student will understand the notation used with sets and the subsets of the real number system. | |||

49 | 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. | |||

50 | 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. | |||

51 | Surds | Introducing surds | |

Objective: On completion of the lesson the student will be able to identify and know the properties of surds as irrational numbers and be able to distinguish them from rational numbers. | |||

52 | Surds | Some rules for the operations with surds | |

Objective: On completion of the lesson the student will know how to use the rules for division and multiplication of surds. | |||

53 | Surds | Simplifying surds | |

Objective: On completion of the lesson the student will know how to use the rules for simplifying surds using division and multiplication. | |||

54 | Surds | Creating entire surds | |

Objective: On completion of the lesson the student will be able to write numbers as entire surds and compare numbers by writing as entire surds | |||

55 | Surds | Adding and subtracting like surds | |

Objective: On completion of the lesson the student will be able to add and subtract surds and simplify expressions by collecting like surds. | |||

56 | Surds | Expanding surds | |

Objective: On completion of the lesson the student will be able to expand and then simplify binomial expressions involving surds. | |||

57 | Surds | Binomial expansions | |

Objective: On completion of the lesson the student will be able to expand and simplify the squares of binomial sums and differences involving surds. | |||

58 | Surds | Conjugate binomials with surds | |

Objective: On completion of the lesson the student will be able to expand and simplify conjugate binomial expressions involving surds. | |||

59 | Surds | Rationalising the denominator | |

Objective: On completion of the lesson the student will be able to rationalise denominators of fractions where the denominator involves surds. | |||

60 | Surds | Rationalising binomial denominators | |

Objective: On completion of the lesson the student will be able to rationalise denominators of fractions where the denominator involves binomial expressions. | |||

61 | Area | Area of a circle. | |

Objective: On completion of the lesson the student will be able calculate the area of a circle, and also calculate the radius and diameter of a circle. | |||

62 | Multiplication | Multiplication by 2 and 3 digits | |

Objective: On completion of the lesson the student will be able to solve and record 2 and 3 digit multiplication problems in extended and short form. | |||

63 | Division/repeat subtraction | Using divide, multiply and subtraction in the bring down method | |

Objective: On completion of the lesson the student will be able to use Long Division using the Divide, Multiply, Subtract and Bring Down method. | |||

64 | 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. | |||

65 | 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. | |||

66 | 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. | |||

67 | 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. | |||

68 | 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. | |||

69 | 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. | |||

70 | Matrices | Basic concepts – Matrices | |

Objective: On completion of the lesson the student will have had an introduction to matrices | |||

71 | Matrices | Addition and subtraction of matrices | |

Objective: On completion of this lesson the student will be able to recognise when addition and subtraction of matrices is possible, and perform these operations. | |||

72 | Matrices | Scalar matrix multiplication | |

Objective: On completion of this lesson the student will be able to perform scalar multiplication of a matrix. | |||

73 | Matrices | Multiplication of one matrix by another matrix | |

Objective: On completion of the lesson the student will be able to state whether matrix by matrix multiplication is possible, predict the order of the answer matrix, and then perform matrix by matrix multiplication. | |||

74 | Matrices | Translation in the number plane | |

Objective: On completion of the lesson the student will be able to place ordered pairs into a matrix, then perform translation by addition using a transformation matrix, then extract ordered pairs from an answer matrix. | |||

75 | Matrices | Translation by matrix multiplication | |

Objective: On completion of the lesson the student will be able to convert ordered pairs to elements of a matrix, multiply matrices together, where possible, and interpret the answer matrix on a number plane. | |||

76 | Transformations | Special transformations – reflections, rotations and enlargements. | |

Objective: On completion of the lesson the student will be able to perform transformations: to rotate, reflect and change the size of various shapes and or points where applicable. | |||

77 | Vectors | Vectors | |

Objective: On completion of the lesson the student will be able to represent a vector in matrix and diagrammatic form, as well as add two vectors using matrices and/or a diagram. | |||

78 | 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. | |||

79 | 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. | |||

80 | 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. | |||

81 | Surface area | Surface area of pyramids | |

Objective: On completion of the lesson the student will be able to find the surface areas of pyramids. | |||

82 | 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 | |||

83 | 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. | |||

84 | 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. | |||

85 | Statistics | Frequency histograms and polygons | |

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

86 | Statistics | Relative frequency | |

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

87 | 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. | |||

88 | 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. | |||

89 | 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 | |||

90 | Statistic-probability | Cumulative frequency | |

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

91 | 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. | |||

92 | 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. | |||

93 | 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. | |||

94 | Statistics – Spread | Measures of spread | |

Objective: On completion of the lesson the student will be able to find the standard deviation, using a data set or a frequency distribution table and calculator. | |||

95 | Statistics – Standard deviation | Standard deviation applications | |

Objective: On completion of the lesson the student will be able to use standard deviation as a measure of deviation from a mean. | |||

96 | Statistics – Standard deviation | Normal distribution | |

Objective: On completion of the lesson the student will be able to use the standard deviation of a normal distribution to find the percentage of scores within ranges. | |||

97 | 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 | |||

98 | 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. | |||

99 | Statistics | Scatter Diagrams | |

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

100 | 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. | |||

101 | 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. | |||

102 | 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. | |||

103 | Functions | Notation and evaluations | |

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

104 | 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. | |||

105 | 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. | |||

106 | Functions | Evaluating and graphing piecewise functions | |

Objective: On completion of the lesson the student will be able to evaluate and graph piecewise functions. | |||

107 | Functions | Functions combinations | |

Objective: On completion of the lesson the student will be able to perform operations with functions while working with their domains. | |||

108 | Functions | Composition of functions | |

Objective: On completion of the lesson the student will understand composition of functions or a function of a function. | |||

109 | Logic | Inductive and deductive reasoning | |

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

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

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

111 | 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. | |||

112 | 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. | |||

113 | Graphing-polynomials | Graphing complex polynomials: quadratics with no real roots | |

Objective: On completion of the lesson the student will be able to determine whether a quadratic has real or complex roots and then graph it. | |||

114 | Graphing-polynomials | General equation of a circle: determine and graph the equation | |

Objective: On completion of the lesson the student will be able to solve these types of problems. Working with circles will also help the student in the topic of circle geometry, which tests the student’s skills in logic and reasoning. | |||

115 | Graphing-cubic curves | Graphing cubic curves | |

Objective: On completion of this lesson the student will be able to graph a cubic given its equation or derive the equation of a cubic given its graph or other relevant information. | |||

116 | Absolute value equations | Absolute value equations | |

Objective: On completion of this lesson the student will be able to relate to graphs involving the absolute value function. The student will be capable of graphing the function given its equation and be able to solve for the intersection of an absolute value functio | |||

117 | Rect.hyperbola | The rectangular hyperbola. | |

Objective: On completion of the lesson the student will be able to analyse and graph a rectangular hyperbola and describe its important features. | |||

118 | 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. | |||

119 | Log functions | Logarithmic functions. | |

Objective: On completion of this lesson the student will be able to define basic logarithmic functions and describe the relationship between logarithms and exponents including graph logarithmic functions. The student will understand the relationship between logarit | |||

120 | Exam | Exam – Year 10 – Level 6 | |

Objective: Exam |