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Lesson Plan

Math Lesson Plan for Year 12

Math-private-tutoring

For Autumn (September, October, November)

For September

Year – 12

1 Day/Week

2 Day/Week

3 Day/Week

5 Day/Week

1st Week(Sept)

1 Equations

(1. Solve linear equations)

2 Inequalities

(1. Graph a linear inequality in one variable

2. Graph a linear inequality in the coordinate plane)

1 Equations

(1. Solve linear equations

2. Solve linear equations: word problems)

2 Inequalities

(1. Graph a linear inequality in one variable

2. Graph a linear inequality in the coordinate plane

3. Write inequalities from graphs

4. Write a linear inequality: word problems

1 Equations

(1. Solve linear equations

2. Solve linear equations: word problems

3. Solve absolute value equations)

2 Inequalities

(1. Graph a linear inequality in one variable

2. Graph a linear inequality in the coordinate plane

3. Write inequalities from graphs

4. Write a linear inequality: word problems

5. Solve linear inequalities

6. Graph solutions to linear inequalities)

1 Equations

(1. Solve linear equations

2. Solve linear equations: word problems

3. Solve absolute value equations

4. Graph solutions to absolute value equations,….etc)

2 Inequalities

(1. Graph a linear inequality in one variable

2. Graph a linear inequality in the coordinate plane

3. Write inequalities from graphs

4. Write a linear inequality: word problems

5. Solve linear inequalities

6. Graph solutions to linear inequalities

7. Solve absolute value inequalities

8. Graph solutions to absolute value inequalities,….etc)

2nd Week(Sept)

1 Functions

(1. Domain and range

2. Identify functions)

1 Functions

(1. Domain and range

2. Identify functions

3. Evaluate functions

4. Find values using function graphs)

1 Functions

(1. Domain and range

2. Identify functions

3. Evaluate functions

4. Find values using function graphs

5. Complete a table for a function graph

6. Find the gradient of a linear function)

1 Functions

(1. Domain and range

2. Identify functions

3. Evaluate functions

4. Find values using function graphs

5. Complete a table for a function graph

6. Find the gradient of a linear function

7. Gradients of parallel and perpendicular lines

8. Graph a linear function,….etc)

3rd Week(Sept)

1 Simultaneous equations

(1. Is (x, y) a solution to the simultaneous equations?
2. Solve simultaneous equations by graphing)

1 Simultaneous equations

(1. Is (x, y) a solution to the simultaneous equations?
2. Solve simultaneous equations by graphing

3. Solve simultaneous equations by graphing: word problems

4. Find the number of solutions to simultaneous equations)

1 Simultaneous equations

(1. Is (x, y) a solution to the simultaneous equations?
2. Solve simultaneous equations by graphing

3. Solve simultaneous equations by graphing: word problems

4. Find the number of solutions to simultaneous equations

5. Solve simultaneous equations using substitution

6. Solve simultaneous equations using substitution: word problems)

1 Simultaneous equations

(1. Is (x, y) a solution to the simultaneous equations?
2. Solve simultaneous equations by graphing

3. Solve simultaneous equations by graphing: word problems

4. Find the number of solutions to simultaneous equations

5. Solve simultaneous equations using substitution

6. Solve simultaneous equations using substitution: word problems

7. Solve simultaneous equations using elimination

8. Solve simultaneous equations using elimination: word problems,….etc)

4th Week(Sept)

Test

Test

Test

Test

For October

Year – 12

1 Day/Week

2 Day/Week

3 Day/Week

5 Day/Week

1st Week(Oct)

1 Factoring

(1. Factorize out a monomial)

2 Quadratic functions

(1. Characteristics of quadratic functions

2. Complete a function table: quadratic functions)

1 Factoring

(1. Factorize out a monomial

2. Factorize quadratics using algebra tiles)

2 Quadratic functions

(1. Characteristics of quadratic functions

2. Complete a function table: quadratic functions

3. Find a quadratic function

4. Graph a quadratic function)

1 Factoring

(1. Factorize out a monomial

2. Factorize quadratics using algebra tiles

3. Factorize quadratics)

2 Quadratic functions

(1. Characteristics of quadratic functions

2. Complete a function table: quadratic functions

3. Find a quadratic function

4. Graph a quadratic function

5. Match quadratic functions and graphs

6. Solve a quadratic equation using square roots)

1 Factoring

(1. Factorize out a monomial

2. Factorize quadratics using algebra tiles

3. Factorize quadratics

4. Factorize using a quadratic pattern,….etc)

2 Quadratic functions

(1. Characteristics of quadratic functions

2. Complete a function table: quadratic functions

3. Find a quadratic function

4. Graph a quadratic function

5. Match quadratic functions and graphs

6. Solve a quadratic equation using square roots

7. Solve a quadratic equation using the zero product property

8. Solve a quadratic equation by factorizing,….etc)

2nd Week(Oct)

1 Complex numbers

(1. Introduction to complex numbers)

1 Complex numbers

(1. Introduction to complex numbers

2. Add and subtract complex numbers)

1 Complex numbers

(1. Introduction to complex numbers

2. Add and subtract complex numbers

3. Complex conjugates)

1 Complex numbers

(1. Introduction to complex numbers

2. Add and subtract complex numbers

3. Complex conjugates

4. Multiply and divide complex numbers,….etc)

3rd Week(Oct)

1 Polynomials

(1. Polynomial vocabulary

2. Add and subtract polynomials)

1 Polynomials

(1. Polynomial vocabulary

2. Add and subtract polynomials

3. Multiply polynomials

4. Divide polynomials using long division)

1 Polynomials

(1. Polynomial vocabulary

2. Add and subtract polynomials

3. Multiply polynomials

4. Divide polynomials using long division

5. Solve polynomial equations

6. Find the roots of factorised polynomials)

1 Polynomials

(1. Polynomial vocabulary

2. Add and subtract polynomials

3. Multiply polynomials

4. Divide polynomials using long division

5. Solve polynomial equations

6. Find the roots of factorised polynomials

7. Rational root theorem

8. Descartes’ Rule of Signs,….etc)

4th Week(Oct)

Test

Test

Test

Test

For November

Year – 12

1 Day/Week

2 Day/Week

3 Day/Week

5 Day/Week

1st Week(Nov)

1 Radical functions and expressions

(1. Roots of integers

2. Roots of rational numbers)

1 Radical functions and expressions

(1. Roots of integers

2. Roots of rational numbers

3. Find roots using a calculator

4. Nth roots)

1 Radical functions and expressions

(1. Roots of integers

2. Roots of rational numbers

3. Find roots using a calculator

4. Nth roots

5. Simplify radical expressions with variables I

6. Simplify radical expressions with variables II)

1 Radical functions and expressions

(1. Roots of integers

2. Roots of rational numbers

3. Find roots using a calculator

4. Nth roots

5. Simplify radical expressions with variables I

6. Simplify radical expressions with variables II

7. Multiply radical expressions

8. Divide radical expressions,….etc)

2nd Week(Nov)

1 Rational indices

(1. Evaluate rational indices)

1 Rational indices

(1. Evaluate rational indices

2. Multiplication with rational indices)

1 Rational indices

(1. Evaluate rational indices

2. Multiplication with rational indices

3. Division with rational indices)

1 Rational indices

(1. Evaluate rational indices

2. Multiplication with rational indices

3. Division with rational indices

4. Power rule,….etc)

3rd Week(Nov)

1 Rational functions and expressions

(1. Rational functions: asymptotes and excluded values)

1 Rational functions and expressions

(1. Rational functions: asymptotes and excluded values

2. Evaluate rational expressions I)

1 Rational functions and expressions

(1. Rational functions: asymptotes and excluded values

2. Evaluate rational expressions I

3. Evaluate rational expressions II)

1 Rational functions and expressions

(1. Rational functions: asymptotes and excluded values

2. Evaluate rational expressions I

3. Evaluate rational expressions II

4. Simplify rational expressions,….etc)

4th Week(Nov)

Test

Test

Test

Test

For Spring (March, April,May)

For March

Year – 12

1 Day/Week

2 Day/Week

3 Day/Week

5 Day/Week

1st Week(March)

1 Function operations

(1. Add and subtract functions

2. Multiply functions)

2 Families of functions

(1. Translations of functions)

1 Function operations

(1. Add and subtract functions

2. Multiply functions

3. Divide functions

4. Composition of linear functions: find a value)

2 Families of functions

(1. Translations of functions

2. Reflections of functions)

1 Function operations

(1. Add and subtract functions

2. Multiply functions

3. Divide functions

4. Composition of linear functions: find a value

5. Composition of linear functions: find an equation

6. Composition of linear and quadratic functions: find a value)

2 Families of functions

(1. Translations of functions

2. Reflections of functions

3. Dilations of functions)

1 Function operations

(1. Add and subtract functions

2. Multiply functions

3. Divide functions

4. Composition of linear functions: find a value

5. Composition of linear functions: find an equation

6. Composition of linear and quadratic functions: find a value

7. Composition of linear and quadratic functions: find an equation

8. Identify inverse functions,….etc)

2 Families of functions

(1. Translations of functions

2. Reflections of functions

3. Dilations of functions

4. Transformations of functions,….etc)

2nd Week(March)

1 Logarithms

(1. Convert between exponential and logarithmic form: rational bases

2. Evaluate logarithms)

1 Logarithms

(1. Convert between exponential and logarithmic form: rational bases

2. Evaluate logarithms

3. Change of base formula

4. Identify properties of logarithms)

1 Logarithms

(1. Convert between exponential and logarithmic form: rational bases

2. Evaluate logarithms

3. Change of base formula

4. Identify properties of logarithms

5. Product property of logarithms

6. Quotient property of logarithms)

1 Logarithms

(1. Convert between exponential and logarithmic form: rational bases

2. Evaluate logarithms

3. Change of base formula

4. Identify properties of logarithms

5. Product property of logarithms

6. Quotient property of logarithms

7. Power property of logarithms

8. Properties of logarithms: mixed review,….etc)

3rd Week(March)

1 Exponential and logarithmic functions

(1. Domain and range of exponential and logarithmic functions

2. Evaluate exponential functions)

1 Exponential and logarithmic functions

(1. Domain and range of exponential and logarithmic functions

2. Evaluate exponential functions

3. Match exponential functions and graphs

4. Solve exponential equations by rewriting the base)

1 Exponential and logarithmic functions

(1. Domain and range of exponential and logarithmic functions

2. Evaluate exponential functions

3. Match exponential functions and graphs

4. Solve exponential equations by rewriting the base

5. Solve exponential equations using common logarithms

6. Solve logarithmic equations I)

1 Exponential and logarithmic functions

(1. Domain and range of exponential and logarithmic functions

2. Evaluate exponential functions

3. Match exponential functions and graphs

4. Solve exponential equations by rewriting the base

5. Solve exponential equations using common logarithms

6. Solve logarithmic equations I

7. Solve logarithmic equations II

8. Identify linear and exponential functions,….etc)

4th Week(March)

Test

Test

Test

Test

For April

Year – 12

1 Day/Week

2 Day/Week

3 Day/Week

5 Day/Week

1st Week(April)

1 Parabolas

(1. Identify the direction a parabola opens

2. Find the vertex of a parabola)

1 Parabolas

(1. Identify the direction a parabola opens

2. Find the vertex of a parabola

3. Find the focus or directrix of a parabola

4. Find the axis of symmetry of a parabola)

1 Parabolas

(1. Identify the direction a parabola opens

2. Find the vertex of a parabola

3. Find the focus or directrix of a parabola

4. Find the axis of symmetry of a parabola

5. Write equations of parabolas in vertex form from graphs

6. Write equations of parabolas in vertex form using properties)

1 Parabolas

(1. Identify the direction a parabola opens

2. Find the vertex of a parabola

3. Find the focus or directrix of a parabola

4. Find the axis of symmetry of a parabola

5. Write equations of parabolas in vertex form from graphs

6. Write equations of parabolas in vertex form using properties

7. Convert equations of parabolas from general to vertex form

8. Find properties of a parabola from equations in general form,…etc)

2nd Week(April)

1 Angle measures

(1. Convert between radians and degrees)

1 Angle measures

(1. Convert between radians and degrees

2. Radians and arc length)

1 Angle measures

(1. Convert between radians and degrees

2. Radians and arc length

3. Quadrants)

1 Angle measures

(1. Convert between radians and degrees

2. Radians and arc length

3. Quadrants

4. Graphs of angles,…etc)

3rd Week(April)

1 Trigonometry

(1. Pythagoras’ Theorem and its converse

2. Special right triangles)

1 Trigonometry

(1. Pythagoras’ Theorem and its converse

2. Special right triangles

3. Trigonometric ratios: sin, cos and tan

4. Trigonometric ratios: csc, sec and cot)

1 Trigonometry

(1. Pythagoras’ Theorem and its converse

2. Special right triangles

3. Trigonometric ratios: sin, cos and tan

4. Trigonometric ratios: csc, sec and cot

5. Trigonometric ratios in similar right triangles

6. Find trigonometric ratios using the unit circle)

1 Trigonometry

(1. Pythagoras’ Theorem and its converse

2. Special right triangles

3. Trigonometric ratios: sin, cos and tan

4. Trigonometric ratios: csc, sec and cot

5. Trigonometric ratios in similar right triangles

6. Find trigonometric ratios using the unit circle

7. Sin, cos and tan of special angles

8. Csc, sec and cot of special angles,….etc)

4th Week(April)

Test

Test

Test

Test

For May

Year – 12

1 Day/Week

2 Day/Week

3 Day/Week

5 Day/Week

1st Week(May)

1 Trigonometric functions

(1. Find properties of sine functions

2. Write equations of sine functions from graphs)

1 Trigonometric functions

(1. Find properties of sine functions

2. Write equations of sine functions from graphs

3. Write equations of sine functions using properties

4. Graph sine functions)

1 Trigonometric functions

(1. Find properties of sine functions

2. Write equations of sine functions from graphs

3. Write equations of sine functions using properties

4. Graph sine functions

5. Find properties of cosine functions

6. Write equations of cosine functions from graphs)

1 Trigonometric functions

(1. Find properties of sine functions

2. Write equations of sine functions from graphs

3. Write equations of sine functions using properties

4. Graph sine functions

5. Find properties of cosine functions

6. Write equations of cosine functions from graphs

7. Write equations of cosine functions using properties

8. Graph cosine functions,….etc)

2nd Week(May)

1 Trigonometric identities

(1. Complementary angle identities)

1 Trigonometric identities

(1. Complementary angle identities

2. Symmetry and periodicity of trigonometric functions)

1 Trigonometric identities

(1. Complementary angle identities

2. Symmetry and periodicity of trigonometric functions

3. Trigonometric identities I)

1 Trigonometric identities

(1. Complementary angle identities

2. Symmetry and periodicity of trigonometric functions

3. Trigonometric identities I

4. Trigonometric identities II,….etc)

3rd Week(May)

1 Circles

(1. Central angles)

1 Circles

(1. Central angles

2. Arcs and chords)

1 Circles

(1. Central angles

2. Arcs and chords

3. Tangent lines)

1 Circles

(1. Central angles

2. Arcs and chords

3. Tangent lines

4. Inscribed angles,…etc)

4th Week(May)

Test

Test

Test

Test

For Summer (June,July,August)

For June

Year – 12

1 Day/Week

2 Day/Week

3 Day/Week

5 Day/Week

1st Week(June)

1 Circles in the coordinate plane

(1. Find the center of a circle)

 

2 Sequences and series  

(1. Classify formulas and sequences

2. Find terms of an arithmetic sequence)

1 Circles in the coordinate plane

(1. Find the center of a circle

2. Find the radius or diameter of a circle)

 

2 Sequences and series  

(1. Classify formulas and sequences

2. Find terms of an arithmetic sequence

3. Find terms of a geometric sequence

4. Find terms of a recursive sequence)

1 Circles in the coordinate plane

(1. Find the center of a circle

2. Find the radius or diameter of a circle

3. Write equations of circles in standard form from graphs)

 

2 Sequences and series  

(1. Classify formulas and sequences

2. Find terms of an arithmetic sequence

3. Find terms of a geometric sequence

4. Find terms of a recursive sequence

5. Evaluate formulas for sequences

6. Write a formula for an arithmetic sequence)

1 Circles in the coordinate plane

(1. Find the center of a circle

2. Find the radius or diameter of a circle

3. Write equations of circles in standard form from graphs

4. Write equations of circles in standard form using properties,….etc)

 

2 Sequences and series  

(1. Classify formulas and sequences

2. Find terms of an arithmetic sequence

3. Find terms of a geometric sequence

4. Find terms of a recursive sequence

5. Evaluate formulas for sequences

6. Write a formula for an arithmetic sequence

7. Write a formula for a geometric sequence

8. Write a formula for a recursive sequence,….etc)

2nd Week(June)

1 Probability

(1. Introduction to probability

2. Theoretical and experimental probability)

1 Probability

(1. Introduction to probability

2. Theoretical and experimental probability

3. Compound events: find the number of outcomes

4. Factorials)

1 Probability

(1. Introduction to probability

2. Theoretical and experimental probability

3. Compound events: find the number of outcomes

4. Factorials

5. Calculate probabilities of events

6. Counting principle)

1 Probability

(1. Introduction to probability

2. Theoretical and experimental probability

3. Compound events: find the number of outcomes

4. Factorials

5. Calculate probabilities of events

6. Counting principle

7. Permutations

8. Permutation and combination notation,….etc)

3rd Week(June)

1 Statistics

(1. Mean, median, mode and range)

1 Statistics

(1. Mean, median, mode and range

2. Quartiles)

1 Statistics

(1. Mean, median, mode and range

2. Quartiles

3. Identify biased samples)

1 Statistics

(1. Mean, median, mode and range

2. Quartiles

3. Identify biased samples

4. Mean absolute deviation,….etc)

4th Week(June) Test Test Test Test
For July

Year – 12

1 Day/Week

2 Day/Week

3 Day/Week

5 Day/Week

1st Week(July)

1 Data and graphs

(1. Interpret bar graphs for continuous data)

1 Data and graphs

(1. Interpret bar graphs for continuous data

2. Create bar graphs for continuous data)

1 Data and graphs

(1. Interpret bar graphs for continuous data

2. Create bar graphs for continuous data

3. Interpret stem-and-leaf plots)

1 Data and graphs

(1. Interpret bar graphs for continuous data

2. Create bar graphs for continuous data

3. Interpret stem-and-leaf plots

4. Interpret box-and-whisker plots,….etc)

2nd Week(July)

1 Introduction to limits

(1. Find limits using graphs)

1 Introduction to limits

(1. Find limits using graphs)

1 Introduction to limits

(1. Find limits using graphs

2. Find one-sided limits using graphs)

1 Introduction to limits

(1. Find limits using graphs

2. Find one-sided limits using graphs

3. Determine if a limit exists,….etc)

3rd Week(July)

1 Calculate limits

(1. Find limits using addition, subtraction and multiplication laws

2. Find limits using the division law)

1 Calculate limits

(1. Find limits using addition, subtraction and multiplication laws

2. Find limits using the division law

3. Find limits using power and root laws

4. Find limits using limit laws)

1 Calculate limits

(1. Find limits using addition, subtraction and multiplication laws

2. Find limits using the division law

3. Find limits using power and root laws

4. Find limits using limit laws

5. Find limits of polynomials and rational functions

6. Find limits involving factorisation and rationalization)

1 Calculate limits

(1. Find limits using addition, subtraction and multiplication laws

2. Find limits using the division law

3. Find limits using power and root laws

4. Find limits using limit laws

5. Find limits of polynomials and rational functions

6. Find limits involving factorisation and rationalization

7. Find limits involving absolute value functions

8. Find limits involving trigonometric functions,….etc)

4th Week(July)

Test

Test

Test

Test

For August

Year – 12

1 Day/Week

2 Day/Week

3 Day/Week

5 Day/Week

1st Week(August)

1 Limits and rational functions

(1. Find limits at vertical asymptotes using graphs)

1 Limits and rational functions

(1. Find limits at vertical asymptotes using graphs

2. Determine end behavior using graphs)

1 Limits and rational functions

(1. Find limits at vertical asymptotes using graphs

2. Determine end behavior using graphs

3. Determine end behavior of polynomial and rational functions)

1 Limits and rational functions

(1. Find limits at vertical asymptotes using graphs

2. Determine end behavior using graphs

3. Determine end behavior of polynomial and rational functions

4. Find the limit at a vertical asymptote of a rational function I,….etc)

2nd Week(August)

1 Continuity

(1. Identify graphs of continuous functions

2. Determine continuity using graphs)

1 Continuity

(1. Identify graphs of continuous functions

2. Determine continuity using graphs

3. Determine one-sided continuity using graphs

4. Find and analyze points of discontinuity using graphs)

1 Continuity

(1. Identify graphs of continuous functions

2. Determine continuity using graphs

3. Determine one-sided continuity using graphs

4. Find and analyze points of discontinuity using graphs

5. Determine continuity on an interval using graphs

6. Determine the continuity of a piecewise function at a point)

1 Continuity

(1. Identify graphs of continuous functions

2. Determine continuity using graphs

3. Determine one-sided continuity using graphs

4. Find and analyze points of discontinuity using graphs

5. Determine continuity on an interval using graphs

6. Determine the continuity of a piecewise function at a point

7. Make a piecewise function continuous

8. Intermediate Value Theorem,….etc)

3rd Week(August)

1 Introduction to derivatives

(1. Average rate of change I

2. Average rate of change II)

1 Introduction to derivatives

(1. Average rate of change I

2. Average rate of change II

3. Find instantaneous rates of change

4. Velocity as a rate of change)

1 Introduction to derivatives

(1. Average rate of change I

2. Average rate of change II

3. Find instantaneous rates of change

4. Velocity as a rate of change

5. Find values of derivatives using limits

6. Find the gradient of a tangent line using limits)

1 Introduction to derivatives

(1. Average rate of change I

2. Average rate of change II

3. Find instantaneous rates of change

4. Velocity as a rate of change

5. Find values of derivatives using limits

6. Find the gradient of a tangent line using limits

7. Find equations of tangent lines using limits

8. Power rule I,….etc)

4th Week(August)

Test

Test

1 Test

1 Test

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