# MYP Grade 10 – 1 Algebra II and Trig Mathematics – International Baccalaureate

### MYP Grade 10 – 1 Algebra II and Trig Mathematics

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

1 | Self Assessment | Self Assessment – MYP Grade 10 – 1 Algebra II & Trig | |

Objective: Assessment | |||

2 | 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. | |||

3 | Coordinate Geometry-midpoint, slope | Mid-point formula | |

Objective: On completion of the lesson the student will be able to understand the mid point formula and use it practically. | |||

4 | 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. | |||

5 | 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. | |||

6 | 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. | |||

7 | 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. | |||

8 | 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. | |||

9 | 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. | |||

10 | 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. | |||

11 | Statistics | Scatter Diagrams | |

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

12 | 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. | |||

13 | 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. | |||

14 | 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. | |||

15 | 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. | |||

16 | Co-ordinate Geometry-Inequalities | Inequalities on the number plane. | |

Objective: On completion of the lesson the student will be able to derive the expression for an inequality given its graph. The student will also be able to solve some problems using inequalities. | |||

17 | Uniform motion | Average speed | |

Objective: On completion of the lesson the student will be able to convert units for speed, distance and time. | |||

18 | Uniform motion | Using subscripted variables | |

Objective: On completion of the lesson the student will use subscripted variables for calculations of speed, distance and time. | |||

19 | Uniform motion | Uniform motion with equal distances | |

Objective: On completion of the lesson the student will use subscripted variables for calculations of speed, equal distances and time. | |||

20 | Uniform motion | Uniform motion adding the distances | |

Objective: On completion of the lesson the student will use subscripted variables for calculations of speed, adding distances for total distance and time. | |||

21 | Uniform motion | Uniform motion with unequal distances | |

Objective: On completion of the lesson the student will use subscripted variables for calculations of speed, unequal distances and time. | |||

22 | Uniform motion | Uniform motion of all types | |

Objective: On completion of the lesson the student will use all types of subscripted variables for calculations to determine speed, distance and time. | |||

23 | 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 | |||

24 | 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. | |||

25 | Functions | Notation and evaluations | |

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

26 | 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. | |||

27 | 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. | |||

28 | Functions | Evaluating and graphing piecewise functions | |

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

29 | 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. | |||

30 | 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. | |||

31 | 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. | |||

32 | 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. | |||

33 | 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. | |||

34 | Vectors | 2 vector addition in 2 and 3D (stage 2) | |

Objective: On completion of the lesson the student will understand and use component forms for vector resolution. | |||

35 | 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. | |||

36 | 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. | |||

37 | Linear systems | Row-echelon form (Stage 2) | |

Objective: On completion of the lesson the student will process matrices formed from linear systems of equations using the row-echelon form. | |||

38 | Algebraic equations | Solving equations containing binomial expressions | |

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

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

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

40 | Algebraic equations | Equations involving fractions. | |

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

41 | 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. | |||

42 | 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. | |||

43 | 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. | |||

44 | Absolute value or modulus | Simplifying absolute values | |

Objective: On completion of the lesson the student will be able to simplify expressions involving absolute values or the modulus of real numbers. | |||

45 | Absolute value or modulus | Solving for the variable | |

Objective: On completion of the lesson the student will be able to solve equations involving a single absolute value. | |||

46 | 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. | |||

47 | 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. | |||

48 | 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. | |||

49 | 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. | |||

50 | 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 | |||

51 | 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. | |||

52 | Surds | Expanding surds | |

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

53 | 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. | |||

54 | 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. | |||

55 | 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. | |||

56 | 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. | |||

57 | 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. | |||

58 | 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. | |||

59 | 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. | |||

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

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

61 | 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. | |||

62 | 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. | |||

63 | 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. | |||

64 | 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. | |||

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

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

66 | 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. | |||

67 | 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. | |||

68 | 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. | |||

69 | 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. | |||

70 | 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. | |||

71 | Factorising quads | Factorising quadratic trinomials [monic] – Case 2. | |

Objective: On completion of the lesson the student will accurately identify the process if the middle term of a quadratic trinomial is negative. | |||

72 | Factorising quads | Factorising quadratic trinomials [monic] – Case 3. | |

Objective: On completion of the lesson the student will have an increased knowledge on factorising quadratic trinomials and will understand where the 2nd term is positive and the 3rd term is negative. | |||

73 | Factorising quads | Factorising quadratic trinomials [monic] – Case 4. | |

Objective: On completion of the lesson the student will understand how to factorise all of the possible types of monic quadratic trinomials and specifcally where the 2nd term and 3rd terms are negative. | |||

74 | Factorising quads | Factorisation of non-monic quadratic trinomials | |

Objective: On completion of the lesson the student will be capable of factorising any quadratic trinomial. | |||

75 | Factorising quads | Factorisation of non-monic quadratic trinomials – moon method | |

Objective: On completion of the lesson the student know two methods for factorisation of quadratic trinomials including the cross method. | |||

76 | Quadratic equations | Introduction to quadratic equations. | |

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

77 | 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. | |||

78 | Quadratic equations | Solving quadratic equations. | |

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

79 | Quadratic equations | Completing the square | |

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

80 | 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. | |||

81 | Quadratic equations | The quadratic formula | |

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

82 | 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. | |||

83 | 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.. | |||

84 | Motion under acceleration | Motion under gravity – objects in vertical motion | |

Objective: On completion of the lesson the student will convert rates and use equations of motion that include uniform acceleration. | |||

85 | Motion under acceleration | Introducing initial velocity | |

Objective: On completion of the lesson the student will use equations of motion that include uniform acceleration and an initial velocity. | |||

86 | Algebra-polynomials | Introduction to polynomials | |

Objective: On completion of the lesson the student will understand all the terminology associated with polynomials and be able to judge if any algebraic expression is a polynomial or not. | |||

87 | Algebra-polynomials | The sum, difference and product of two polynomials. | |

Objective: On completion of the lesson the student will be able to add subtract and multiply polynomials and find the degrees of the answers. | |||

88 | Algebra-polynomials | Polynomials and long division. | |

Objective: On completion of the lesson the student will understand the long division process with polynomials. | |||

89 | Remainder theorem | The remainder theorem. | |

Objective: On completion of the lesson the student will understand how the remainder theorem works and how it can be applied. | |||

90 | Remainder theorem | More on remainder theorem | |

Objective: On completion of the lesson the student will understand the remainder theorem and how it can be applied to solve some interesting questions on finding unknown coefficients of polynomials. | |||

91 | Factor theorem | The factor theorem | |

Objective: On completion of the lesson the student will be able to use the factor theorem and determine if a term in the form of x minus a is a factor of a given polynomial. | |||

92 | Factor theorem | More on the factor theorem | |

Objective: On completion of the lesson the student will fully understand the factor theorem and how it can be applied to solve some questions on finding unknown coefficients of polynomials. | |||

93 | Factor theorem | Complete factorisations using the factor theorem | |

Objective: On completion of the lesson the student will be able to factorise polynomials of a higher degree than 2 and to find their zeros. | |||

94 | Polynomial equations | Polynomial equations | |

Objective: On completion of the lesson the student will be capable of solving polynomial equations given in different forms. | |||

95 | Graphs, polynomials | Graphs of polynomials | |

Objective: On completion of the lesson the student will understand how to graph polynomials using the zeros of polynomials, the y intercepts and the direction of the curves. | |||

96 | 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. | |||

97 | Statistics | Frequency histograms and polygons | |

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

98 | Statistics | Relative frequency | |

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

99 | 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. | |||

100 | 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. | |||

101 | 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. | |||

102 | 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 | |||

103 | Statistic-probability | Cumulative frequency | |

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

104 | 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. | |||

105 | 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. | |||

106 | 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. | |||

107 | 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. | |||

108 | 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. | |||

109 | 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. | |||

110 | 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. | |||

111 | 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 | |||

112 | 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. | |||

113 | 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. | |||

114 | 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. | |||

115 | 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. | |||

116 | 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. | |||

117 | 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. | |||

118 | 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. | |||

119 | Fractional indices/exponents | Fractional indices | |

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

120 | 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. | |||

121 | 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. | |||

122 | 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. | |||

123 | 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. | |||

124 | 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. | |||

125 | 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. | |||

126 | 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 | |||

127 | 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. | |||

128 | Logarithms-Equations and logs | Equations of type log x to the base 3 = 4. | |

Objective: On completion of the lesson the student will have an enhanced understanding of the definition of a logarithm and how to use it to find an unknown variable which in this case is the number from which the logarithm evolves. | |||

129 | Logarithms-Equations and logs | Equations of type log 32 to the base x = 5. | |

Objective: On completion of the lesson the student will have an enhanced understanding of the definition of a logarithm and how to use it to find an unknown variable which in this case is the base from which the number came. | |||

130 | Logarithms-Log laws | Laws of logarithms. | |

Objective: On completion of the lesson the student will be familiar with 5 logarithm laws. | |||

131 | Logarithms-Log laws expansion | Using the log laws to expand logarithmic expressions. | |

Objective: On completion of the lesson the student will be able to use the log laws to expand logarithmic expressions. | |||

132 | Logarithms-Log laws simplifying | Using the log laws to simplify expressions involving logarithms. | |

Objective: On completion of the lesson the student will be able to simplify logarithmic expressions using the log laws. | |||

133 | Logarithms-Log laws numbers | Using the log laws to find the logarithms of numbers. | |

Objective: On completion of the lesson the student will have an enhanced understanding of the use of the log laws and be able to do more applications with numerical examples. | |||

134 | Logarithms-Equations and logs | Equations involving logarithms. | |

Objective: On completion of the lesson the student will be able to solve equations with log terms. | |||

135 | Logarithms-Logs to solve equations | Using logarithms to solve equations. | |

Objective: On completion of the lesson the student will be able to use logarithms to solve index equations with the assistance of a calculator. | |||

136 | Logarithms-Change base formula | Change of base formula | |

Objective: On completion of the lesson the student will have seen the change of base formula for logarithms and be capable of using it to change the logarithm of one base to another base. | |||

137 | Logarithms-Graph-log curve | The graph of the logarithmic curve | |

Objective: On completion of the lesson the student will be able to draw a logarithmic curve to a given base and know the general properties of log curves. | |||

138 | Logarithms-Log curves | Working with log curves. | |

Objective: On completion of the lesson the student will be able to solve problems with log curves | |||

139 | Sequences and Series-Geometric means | Geometric means. | |

Objective: On completion of the lesson the student will be able to make a geometric progression between two given terms. This could involve finding one, two, or even larger number of geometric means. | |||

140 | Sequences and Series-Sum of gp | The sum to n terms of a G.P. | |

Objective: On completion of the lesson the student will understand the formulas and how to use them to solve problems in summing terms of a Geometric Progression (G.P). | |||

141 | Sequences and Series-Sigma notation | Sigma notation | |

Objective: On completion of the G.P. lesson the student will be familiar with the sigma notation and how it operates. | |||

142 | Sequences and Series-Sum-infinity | Limiting sum or sum to infinity. | |

Objective: On completion of the lesson the student will have learnt the formula for the limiting sum of a G.P., the conditions for it to exist and how to apply it to particular problems. | |||

143 | Sequences and Series-Recurring decimal infinity | Recurring decimals and the infinite G.P. | |

Objective: On completion of the G.P. lesson the student will have understood how to convert any recurring decimal to a rational number. | |||

144 | 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. | |||

145 | Sequences and Series-Superannuation | Superannuation. | |

Objective: On completion of the lesson the student will understand the method of finding the accumulated amount of a superannuation investment using the sum formula for a G.P. | |||

146 | Sequences and Series-Time payments | Time payments. | |

Objective: On completion of the lesson the student will have examined examples carefully and be capable of setting out the long method of calculating a regular payment for a reducible interest loan. | |||

147 | Sequences and Series | Applications of arithmetic sequences | |

Objective: On completion of the lesson the student will be capable of problems involving practical situations with arithmetic series. | |||

148 | Functions | Functions combinations | |

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

149 | Functions | Composition of functions | |

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

150 | Functions | Inverse functions | |

Objective: On completion of the lesson the student will be able to find inverse functions, use the notation correctly and the horizontal line test will be used. | |||

151 | Functions | Rational functions Part 1 | |

Objective: On completion of the lesson the student will be able to work with the division of functions and to interpret this on the coordinate number plane showing vertical and horizontal asymptotes. | |||

152 | Functions | Rational functions Part 2 | |

Objective: On completion of the lesson the student will be able to use the degree of polynomials and polynomial division to assist in graphing rational functions on the coordinate number plane showing vertical, horizontal and slant asymptotes. | |||

153 | Functions | Parametric equations (Stage 2) | |

Objective: On completion of the lesson the student will be able to eliminate the parameter from a set of equations and identify appropriate restrictions on the domain and range. | |||

154 | Functions | Polynomial addition etc in combining and simplifying functions (Stage 2) | |

Objective: On completion of the lesson the student will have multiple techniques to understand and construct graphs using algebra. | |||

155 | Functions | Parametric functions (Stage 2) | |

Objective: On completion of the lesson the student will understand some standard parametric forms using trigonometric identities, appreciate the beauty of the the graphs that can be generated and an application to projectile motion. | |||

156 | 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. | |||

157 | 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. | |||

158 | 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. | |||

159 | 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. | |||

160 | Algebraic fractions | Simplifying algebraic fractions. | |

Objective: On completion of the lesson the student should be familiar with all of the factorisation methods presented to this point. | |||

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

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

162 | 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. | |||

163 | Statistic-probability | Experimental probability | |

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

164 | 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. | |||

165 | 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. | |||

166 | 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. | |||

167 | 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. | |||

168 | Statistic-probability | Binomial Theorem – Pascal’s Triangle | |

Objective: On completion of this lesson the student will use Pascal’s triangle and the binomial theorem to write the expansion of binomial expressions raised to integer powers. | |||

169 | Statistic-probability | Binomial probabilities using the Binomial Theorem | |

Objective: On completion of the lesson the student will be able to solve certain types of probability questions using the binomial theorem | |||

170 | Statistic-probability | Counting techniques and ordered selections – permutations | |

Objective: On completion of this lesson the student will be competent in using some new counting techniques used for solving probability. | |||

171 | Statistic-probability | Unordered selections – combinations | |

Objective: On completion of the lesson the student will be able to use the formula, n c r both with and without a calculator and be able to use it to solve probability problems where unordered selections happen. | |||

172 | 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 | |||

173 | 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. | |||

174 | 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. | |||

175 | 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. | |||

176 | 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. | |||

177 | 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. | |||

178 | 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. | |||

179 | 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. | |||

180 | 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. | |||

181 | 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. | |||

182 | 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. | |||

183 | 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. | |||

184 | Trigonometry-cosine rule | The cosine rule to find an unknown side. [Case 1 SAS]. | |

Objective: On completion of the lesson the student will be able to use the cosine rule to find the length of an unknown side of a triangle knowing 2 sides and the included angle. | |||

185 | Trigonometry-cosine rule | The cosine rule to find an unknown angle. [Case 2 SSS]. | |

Objective: On completion of the lesson the student will be able to find the size of an unknown angle of a triangle using the cosine rule given the lengths of the 3 sides. | |||

186 | Trigonometry-sine rule | The sine rule to find an unknown side. Case 1. | |

Objective: On completion of the lesson the student will be able to use the Sine rule to find the length of a particular side when the student is given the sizes of 2 of the angles and one of the sides. | |||

187 | Trigonometry-sine rule | The sine rule to find an unknown angle. Case 2. | |

Objective: On completion of the lesson the student will be able to use the sine rule to find an unknown angle when given 2 sides and a non-included angle. | |||

188 | Trigonometry-areas | The area formula | |

Objective: On completion of the lesson the student will be able to use the sine formula for finding the area of a triangle given 2 sides and the included angle. | |||

189 | Trig-reciprocal ratios | Reciprocal ratios. | |

Objective: On completion of the lesson the student will be able to identify and use the reciprocal trigonometric ratios of sine, cosine and tan, that is, the cosecant, secant and cotangent ratios. | |||

190 | Trig complementary angles | Complementary angle results. | |

Objective: On completion of the lesson the student will understand how to establish the complementary angle results for the sine and cosine ratios and then how to use these results to solve trig equations. | |||

191 | Trig identities | Trigonometric identities | |

Objective: On completion of the lesson the student will be able to simplify trigonometrical expressions and solve trigonometry equations using the knowledge of trig identities. | |||

192 | Trig larger angles | Angles of any magnitude | |

Objective: On completion of the lesson the student will be able to find the trigonometric values of angles of any magnitude by assigning angles to the four quadrants of the circle. | |||

193 | Trig larger angles | Trigonometric ratios of 0°, 90°, 180°, 270° and 360° | |

Objective: On completion of the lesson the student will learn how to find the Trigonometric Ratios of 0, 90, 180, 270 and 360 degrees. | |||

194 | Graph sine | Graphing the trigonometric ratios – I Sine curve. | |

Objective: On completion of the lesson the student will recognise and draw the sine curve exploring changes in amplitude and period. | |||

195 | Graph cosine | Graphing the trigonometric ratios – II Cosine curve. | |

Objective: On completion of the lesson the student will know how to recognise and draw the cosine curve exploring changes in amplitude and period. | |||

196 | Graphs tan curve | Graphing the trigonometric ratios – III Tangent curve. | |

Objective: On completion of the lesson the student will know how to recognise and draw the tan curve. | |||

197 | Graph reciprocals | Graphing the trigonometric ratios – IV Reciprocal ratios. | |

Objective: On completion of the lesson the student will know how to recognise and draw the curves of the reciprocal ratios: cosec, sec and cot. | |||

198 | Trig larger angles | Using one ratio to find another. | |

Objective: On completion of the lesson the student will find other trig ratios given one trig ratio and to work with angles of any magnitude. | |||

199 | Trig equations | Solving trigonometric equations – Type I. | |

Objective: On completion of the lesson the student will solve simple trig equations with restricted domains. | |||

200 | Trig equations | Solving trigonometric equations – Type II. | |

Objective: On completion of the lesson the student will solve trig equations with multiples of theta and restricted domains. | |||

201 | Trig equations | Solving trigonometric equations – Type III. | |

Objective: On completion of the lesson the student will solve trig equations with two trig ratios and restricted domains. | |||

202 | Polar coordinates | Plotting polar coordinates and converting polar to rectangular | |

Objective: On completion of the lesson the student will understand the polar coordinate system and relate this to the rectangular coordinate system. | |||

203 | Polar coordinates | Converting rectangular coordinates to polar form | |

Objective: On completion of the lesson the student will understand the polar coordinate system and report these from rectangular coordinates. | |||

204 | Exam | Exam – MYP Grade 10 – 1 Algebra II & Trig | |

Objective: Exam |