### MYP Grade 10 – 2 Algebra II and Trig Hons Mathematics

# TOPIC TITLE
1 Self Assessment Self Assessment – MYP Grade 10 – 2 Algebra II & Trig Hons
Objective: Assessment
2 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.
3 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.
4 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.
5 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.
6 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.
7 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.
8 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.
9 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.
10 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.
11 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.
12 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.
13 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.
14 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.
15 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.
16 Fractions Subtracting fractions from whole numbers
Objective: On completion of the lesson the student will be able to: use a diagram to subtract fractions from a whole number, develop mental strategies for subtracting fractions from whole numbers, and recognise and use the written form for subtracting fractions from
17 Fractions Adding and subtracting fractions with the same denominator
Objective: On completion of the lesson the student will be able to add and subtract fractions with the same denominator.
18 Fractions Adding and subtracting fractions with different denominators
Objective: On completion of the lesson the student will be able to add and subtract fractions where one denominator is a multiple of the other.
19 Fractions Multiplying fractions by whole numbers
Objective: On completion of the lesson the student will be able to multiply simple fractions by whole numbers.
20 Fractions Fractions of whole numbers
Objective: On completion of the lesson the student will be able to calculate unit fractions of a collection.
21 Fractions Multiplying fractions
Objective: On completion of the lesson the student will be able to multiply fractions and reduce the answer to its lowest form.
22 Fractions Multiplying mixed numbers (mixed numerals)
Objective: On completion of the lesson the student will be able to multiply mixed numbers (mixed numerals) and reduce the answer to its lowest form.
23 Fractions Finding reciprocals of fractions and mixed numbers (mixed numerals)
Objective: On completion of the lesson the student will be able to find the reciprocals of fractions and mixed numbers (mixed numerals).
24 Fractions Dividing fractions
Objective: On completion of the lesson the student will be able to divide fractions.
25 Fractions Dividing mixed numbers (mixed numerals)
Objective: On completion of the lesson the student will be able to divide mixed numbers (mixed numerals).
26 Rules properties Using Order of Operation procedures (BIDMAS) with Fractions
Objective: On completion of the lesson the student will know how to apply the order of operations rules to simplify expressions with integers and fractions.
27 Percentages Calculating Percentages and Fractions of Quantities
Objective: To find percentages and fractions of quantities and solve problems with percentages
28 Percentages Introduction to percentages, including relating common fractions to percentages
Objective: On completion of the lesson the student will be able to recognise that the symbol % means ‘per cent’ and relate common fractions to a percentage.
29 Percentages Changing fractions and decimals to percentages using tenths and hundredths
Objective: On completion of the lesson the student will be able to change simple fractions to percentages and decimals to percentages by using place value conversion.
30 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.
31 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.
32 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.
33 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.
34 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.
35 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
36 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.
37 Surds Expanding surds
Objective: On completion of the lesson the student will be able to expand and then simplify binomial expressions involving surds.
38 Algebraic equations Solving equations containing addition and subtraction
Objective: On completion of the lesson the student will understand how solve simple equations involving addition and subtraction by moving everything but the pronumeral onto one side of the equation, leaving the pronumeral by itself on the other side.
39 Algebraic equations Solving equations containing multiplication and division
Objective: On completion of the lesson the student will be able to solve simple equations involving all operations.
40 Algebraic equations Solving two step equations
Objective: On completion of the lesson the student will be able to solve two step equations.
41 Algebraic equations Solving equations containing binomial expressions
Objective: On completion of the lesson the student will be able to move terms in binomial equations.
42 Algebraic equations Equations involving grouping symbols.
Objective: On completion of the lesson the student will be able to solve equations using grouping symbols
43 Algebraic equations Equations involving fractions.
Objective: On completion of the lesson the student will know how to solve equations using fractions.
44 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.
45 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.
46 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.
47 Algebra-factorising Simplifying easy algebraic fractions.
Objective: On completion of the lesson the student will understand how to simplify algebraic fractions by factorising.
48 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.
49 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.
50 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.
51 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.
52 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.
53 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.
54 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.
55 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.
56 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.
57 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.
58 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.
Objective: On completion of the lesson the student will understand the factorisation of quadratic trinomial equations with all terms positive.
Objective: On completion of the lesson the student will accurately identify the process if the middle term of a quadratic trinomial is negative.
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.
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.
Objective: On completion of the lesson the student will be capable of factorising any quadratic trinomial.
Objective: On completion of the lesson the student know two methods for factorisation of quadratic trinomials including the cross method.
65 Sum/diff 2 cubes Sum and difference of two cubes.
Objective: On completion of the lesson the student will be cognisant of the sum and difference of 2 cubes and be capable of factorising them.
66 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.
Objective: On completion of the lesson the student will understand simple quadratic equations.
Objective: On completion of the lesson the student will be able to find both roots of a quadratic equation by factorising.
Objective: On completion of the lesson the student will have gained more confidence in working with quadratic equations.
70 Quadratic equations Completing the square
Objective: On completion of the lesson the student will understand the process of completing the square.
Objective: On completion of the lesson the student will understand the reasoning behind completing the square.
Objective: On completion of the lesson the student will be familiar with the quadratic formula.
Objective: On completion of the lesson the student will be able to express a problem as a quadratic equation and then solve it.
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..
75 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.
76 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.
77 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.
78 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.
79 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.
80 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.
81 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.
82 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.
83 Fractional indices/exponents Fractional indices
Objective: On completion of the lesson the student will know how to evaluate or simplify expressions containing fractional indices.
84 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.
85 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.
86 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.
87 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.
88 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
89 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.
90 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.
91 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
92 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.
93 Functions Notation and evaluations
Objective: On completion of the lesson the student will be understand different notations for functions.
94 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.
95 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.
96 Functions Evaluating and graphing piecewise functions
Objective: On completion of the lesson the student will be able to evaluate and graph piecewise functions.
97 Functions Functions combinations
Objective: On completion of the lesson the student will be able to perform operations with functions while working with their domains.
98 Functions Composition of functions
Objective: On completion of the lesson the student will understand composition of functions or a function of a function.
99 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.
100 Circle Geometry Theorem – Equal arcs on circles of equal radii subtend equal angles at the centre. Theorem – Equal angles at the centre of a circle on equal arcs.
Objective: On completion of the lesson the student will be able to prove that ‘Equal arcs on circles of equal radii, subtend equal angles at the centre’, and that ‘Equal angles at the centre of a circle stand on equal arcs.’ They should then be able to use these pro
101 Circle Geometry Theorem – The perpendicular from the centre of a circle to a chord bisects the chord. Theorem – The line from the centre of a circle to the mid-point of the chord is perpendicular to the chord.
Objective: On completion of the lesson the student will be able to prove that ‘The perpendicular from the centre of a circle to a chord bisects the chord.’ and its converse theorem ‘The line from the centre of a circle to the mid-point of the chord is perpendicular’
102 Circle Geometry Theorem – Equal chords in equal circles are equidistant from the centres. Theorem – Chords in a circle which are equidistant from the centre are equal.
Objective: On completion of the lesson the student will be able to prove that equal chords in equal circles are equidistant from the centre.
103 Circle Geometry Theorem – The angle at the centre of a circle is double the angle at the circumference standing on the same arc.
Objective: On completion of the lesson the student will be able to prove that the angle at the centre of a circle is double the angle at the circumference standing on the same arc.
104 Circle Geometry Theorem – Angles in the same segment of a circle are equal.
Objective: On completion of the lesson the student will be able to prove that the angles in the same segment are equal.
105 Circle Geometry Theorem – The angle of a semi-circle is a right angle.
Objective: On completion of the lesson the student will be able to prove that ‘The angle of a semi-circle is a right-angle.’
106 Circle Geometry Theorem – The opposite angles of a cyclic quadrilateral are supplementary.
Objective: On completion of the lesson the student will be able to prove that the opposite angles of a cyclic quadrilateral are supplementary.
107 Circle Geometry Theorem – The exterior angle at a vertex of a cyclic quadrilateral equals the interior opposite angle.
Objective: On completion of the lesson the student will be able to prove that the exterior angle at a vertex of a cyclic quadrilateral equals the interior opposite.
108 Circle Geometry Theorem – The tangent to a circle is perpendicular to the radius drawn to it at the point of contact.
Objective: On completion of the lesson the student will be able to prove that the tangent and the radius of a circle are perpendicular at the point of contact.
109 Circle Geometry Theorem – Tangents to a circle from an external point are equal.
Objective: On completion of the lesson the student will be able to prove that tangents to a circle from an external point are equal.
110 Circle Geometry Theorem – The angle between a tangent and a chord through the point of contact is equal to the angle in the alternate segment.
Objective: On completion of the lesson the student will be able to prove that the angle between a tangent and a chord through the point of contact is equal to the angle in the alternate segment.
111 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.
112 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.
113 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.
114 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.
115 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.
116 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.
117 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.
118 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.
119 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.
120 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.
121 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.
122 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.
123 Trig equations Solving trigonometric equations – Type I.
Objective: On completion of the lesson the student will solve simple trig equations with restricted domains.
124 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.
125 Statistics Frequency histograms and polygons
Objective: On completion of the lesson the student will be able to construct and interpret frequency histograms and polygons.
126 Statistics Relative frequency
Objective: On completion of the lesson the student will be able to collect, display and make judgements about data.
127 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.
128 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.
129 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.
130 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
131 Statistic-probability Cumulative frequency
Objective: On completion of the lesson the student will be able to construct cumulative frequency columns, histograms and polygons.
132 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.
133 Statistic-probability Probability of Simple Events
Objective: On completion of the lesson the student will be able to understand the probability of simple events.
134 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.
135 Statistic-probability Experimental probability
Objective: On completion of this lesson the student will be able to find the probabilities in an experimental trial.
136 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.
137 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.
138 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.
139 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.
140 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.
141 Sequences and Series General sequences.
Objective: On completion of the lesson the student will be able to work out a formula from a given number pattern and then be able to find particular terms of that sequence using the formula.
142 Sequences and Series Finding Tn given Sn.
Objective: On completion of the lesson the student will understand the concept that the sum of n terms of a series minus the sum of n minus one terms will yield the nth term.
143 Arithmetic Progression The arithmetic progression
Objective: On completion of the lesson the student will be able to test if a given sequence is an Arithmetic Progression or not and be capable of finding a formula for the nth term, find any term in the A.P. and to solve problems involving these concepts.
144 Arithmetic Progression Finding the position of a term in an A.P.
Objective: On completion of the lesson the student will be able to solve many problems involving finding terms of an Arithmetic Progression.
145 Arithmetic Progression Given two terms of A.P., find the sequence.
Objective: On completion of the lesson the student will be able to find any term of an Arithmetic Progression when given two terms
146 Arithmetic Progression Arithmetic means
Objective: On completion of the lesson the student will be able to make an arithmetic progression between two given terms. This could involve finding one, two, or even larger number of arithmetic means.
147 Arithmetic Progression The sum to n terms of an A.P.
Objective: On completion of the lesson the student will understand the formulas for the sum of an Arithmetic Progression and how to use them in solving problems.
148 Geometric Progression The geometric progression.
Objective: On completion of the lesson the student will be able to test if a given sequence is a Geometric Progression or not and be capable of finding a formula for the nth term, find any term in the G.P. and to solve problems involving these concepts.
149 Geometric Progression Finding the position of a term in a G.P.
Objective: On completion of the lesson the student will understand how to find terms in a geometric progression and how to apply it different types of problems.
150 Geometric Progression Given two terms of G.P., find the sequence.
Objective: On completion of this lesson the student will be able to solve all problems involving finding the common ratio of a Geometric Progression.
151 Exam Exam – MYP Grade 10 – 2 Algebra II & Trig Hons
Objective: Exam