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Lesson Plan

Math Lesson Plan for Year 13

Math-private-tutoring

For Autumn (September, October, November)

For September

Year – 13

1 Day/Week

2 Day/Week

3 Day/Week

5 Day/Week

1st Week(Sept)

1 Functions

(1. Domain and range

2. Identify functions)

1 Functions

(1. Domain and range

2. Identify functions

3. Find the gradient of a linear function

4. Graph a linear function)

1 Functions

(1. Domain and range

2. Identify functions

3. Find the gradient of a linear function

4. Graph a linear function

5. Write the equation of a linear function

6. Linear functions over unit intervals)

1 Functions

(1. Domain and range

2. Identify functions

3. Find the gradient of a linear function

4. Graph a linear function

5. Write the equation of a linear function

6. Linear functions over unit intervals

7. Evaluate functions

8. Find values using function graphs,….etc)

2nd Week(Sept)

1 Families of functions

(1. Translations of functions,….etc)

1 Families of functions

(1. Translations of functions

2. Reflections of functions,….etc)

1 Families of functions

(1. Translations of functions

2. Reflections of functions

3. Dilations of functions,….etc)

1 Families of functions

(1. Translations of functions

2. Reflections of functions

3. Dilations of functions

4. Transformations of functions,….etc)

3rd Week(Sept)

1 Quadratic functions

(1. Characteristics of quadratic functions

2. Find the maximum or minimum value of a quadratic function)

1 Quadratic functions

(1. Characteristics of quadratic functions

2. Find the maximum or minimum value of a quadratic function

3. Graph a quadratic function

4. Match quadratic functions and graphs)

1 Quadratic functions

(1. Characteristics of quadratic functions

2. Find the maximum or minimum value of a quadratic function

3. Graph a quadratic function

4. Match quadratic functions and graphs

5. Solve a quadratic equation using square roots

6. Solve a quadratic equation by factorizing)

1 Quadratic functions

(1. Characteristics of quadratic functions

2. Find the maximum or minimum value of a quadratic function

3. Graph a quadratic function

4. Match quadratic functions and graphs

5. Solve a quadratic equation using square roots

6. Solve a quadratic equation by factorizing

7. Solve a quadratic equation by completing the square

8. Solve a quadratic equation using the quadratic formula,….etc)

4th Week(Sept)

Test

Test

Test

Test

For October

Year – 13

1 Day/Week

2 Day/Week

3 Day/Week

5 Day/Week

1st Week(Oct)

1 Polynomials

(First Half)

(1. Divide polynomials using long division

2. Write a polynomial from its roots)

1 Polynomials

(First Half)

(1. Divide polynomials using long division

2. Write a polynomial from its roots

3. Find the roots of factorised polynomials

4. Rational root theorem)

1 Polynomials

(First Half)

(1. Divide polynomials using long division

2. Write a polynomial from its roots

3. Find the roots of factorised polynomials

4. Rational root theorem

5. Complex conjugate theorem

6. Conjugate root theorems)

1 Polynomials

(First Half)

(1. Divide polynomials using long division

2. Write a polynomial from its roots

3. Find the roots of factorised polynomials

4. Rational root theorem

5. Complex conjugate theorem

6. Conjugate root theorems

7. Descartes’ Rule of Signs

8. Fundamental Theorem of Algebra)

2nd Week(Oct)

1 Polynomials

(Second Half)

(3. Find the roots of factorised polynomials

4. Rational root theorem)

1 Polynomials

(Second Half)

(5. Complex conjugate theorem

6. Conjugate root theorems

7. Descartes’ Rule of Signs

8. Fundamental Theorem of Algebra)

1 Polynomials

(Second Half)

(7. Descartes’ Rule of Signs

8. Fundamental Theorem of Algebra

9. Match polynomials and graphs

10. Factorize sums and differences of cubes

11. Solve equations with sums and differences of cubes

12. Factorize using a quadratic pattern)

1 Polynomials

(Second Half)

(9. Match polynomials and graphs

10. Factorize sums and differences of cubes

11. Solve equations with sums and differences of cubes

12. Factorize using a quadratic pattern

13. Solve equations using a quadratic pattern

14. Pascal’s triangle

15. Pascal’s triangle and the Binomial Theorem

16. Binomial Theorem I,….etc)

3rd Week(Oct)

1 Rational functions

(1. Rational functions: asymptotes and excluded values)

1 Rational functions

(1. Rational functions: asymptotes and excluded values)

1 Rational functions

(1. Rational functions: asymptotes and excluded values

2. Solve rational equations)

1 Rational functions

(1. Rational functions: asymptotes and excluded values

2. Solve rational equations

3. Check whether two rational functions are inverses,….etc)

4th Week(Oct)

Test

Test

Test

Test

For November

Year – 13

1 Day/Week

2 Day/Week

3 Day/Week

5 Day/Week

1st Week(Nov)

1 Exponential and logarithmic functions

(1. Domain and range of exponential and logarithmic functions

2. Convert between exponential and logarithmic form)

1 Exponential and logarithmic functions

(1. Domain and range of exponential and logarithmic functions

2. Convert between exponential and logarithmic form

3. Evaluate logarithms

4. Change of base formula)

1 Exponential and logarithmic functions

(1. Domain and range of exponential and logarithmic functions

2. Convert between exponential and logarithmic form

3. Evaluate logarithms

4. Change of base formula

5. Product property of logarithms

6. Quotient property of logarithms)

1 Exponential and logarithmic functions

(1. Domain and range of exponential and logarithmic functions

2. Convert between exponential and logarithmic form

3. Evaluate logarithms

4. Change of base formula

5. Product property of logarithms

6. Quotient property of logarithms

7. Power property of logarithms

8. Evaluate logarithms using properties,….etc)

2nd Week(Nov)

1 Radical functions

(1. Domain and range of radical functions)

1 Radical functions

(1. Domain and range of radical functions)

1 Radical functions

(1. Domain and range of radical functions)

1 Radical functions

(1. Domain and range of radical functions

2. Solve radical equations,….etc)

3rd Week(Nov)

1 Roots and rational indices

(1. Roots of integers

2. Roots of rational numbers)

1 Roots and rational indices

(1. Roots of integers

2. Roots of rational numbers

3. Find roots using a calculator

4. Evaluate rational indices)

1 Roots and rational indices

(1. Roots of integers

2. Roots of rational numbers

3. Find roots using a calculator

4. Evaluate rational indices

5. Operations with rational indices

6. Nth roots)

1 Roots and rational indices

(1. Roots of integers

2. Roots of rational numbers

3. Find roots using a calculator

4. Evaluate rational indices

5. Operations with rational indices

6. Nth roots

7. Simplify radical expressions with variables

8. Simplify expressions involving rational indices,….etc)

4th Week(Nov)

Test

Test

Test

Test

For Spring (March, April,May)

For March

Year – 13

1 Day/Week

2 Day/Week

3 Day/Week

5 Day/Week

1st Week(March)

1 Simultaneous equations

(1. Solve simultaneous equations by graphing

2. Solve simultaneous equations by graphing: word problems)

1 Simultaneous equations

(1. Solve simultaneous equations by graphing

2. Solve simultaneous equations by graphing: word problems

3. Classify simultaneous equations

4. Solve simultaneous equations using substitution)

1 Simultaneous equations

(1. Solve simultaneous equations by graphing

2. Solve simultaneous equations by graphing: word problems

3. Classify simultaneous equations

4. Solve simultaneous equations using substitution

5. Solve simultaneous equations using substitution: word problems

6. Solve simultaneous equations using elimination)

1 Simultaneous equations

(1. Solve simultaneous equations by graphing

2. Solve simultaneous equations by graphing: word problems

3. Classify simultaneous equations

4. Solve simultaneous equations using substitution

5. Solve simultaneous equations using substitution: word problems

6. Solve simultaneous equations using elimination

7. Solve simultaneous equations using elimination: word problems

8. Solve simultaneous equations in three variables using substitution,….etc)

2nd Week(March)

1 Trigonometry

(1. Convert between radians and degrees

2. Radians and arc length)

1 Trigonometry

(1. Convert between radians and degrees

2. Radians and arc length

3. Quadrants

4. Coterminal and reference angles)

1 Trigonometry

(1. Convert between radians and degrees

2. Radians and arc length

3. Quadrants

4. Coterminal and reference angles

5. Find trigonometric ratios using right triangles

6. Find trigonometric ratios using the unit circle)

1 Trigonometry

(1. Convert between radians and degrees

2. Radians and arc length

3. Quadrants

4. Coterminal and reference angles

5. Find trigonometric ratios using right triangles

6. Find trigonometric ratios using the unit circle

7. Find sin, cos and tan using reference angles

8. Find csc, sec and cot using reference angles,….etc)

3rd Week(March)

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)

4th Week(March)

Test

Test

Test

Test

For April

Year – 13

1 Day/Week

2 Day/Week

3 Day/Week

5 Day/Week

1st Week(April)

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)

2nd Week(April)

1 Parabolas and circles

(1. Find properties of parabolas)

1 Parabolas and circles

(1. Find properties of parabolas

2. Write equations of parabolas in vertex form)

1 Parabolas and circles

(1. Find properties of parabolas

2. Write equations of parabolas in vertex form

3. Graph parabolas)

1 Parabolas and circles

(1. Find properties of parabolas

2. Write equations of parabolas in vertex form

3. Graph parabolas

4. Find properties of circles,….etc)

3rd Week(April)

1 Two – dimensional vectors

(1. Find the magnitude of a vector

2. Find the direction angle of a vector)

1 Two – dimensional vectors

(1. Find the magnitude of a vector

2. Find the direction angle of a vector

3. Find the component form of a vector

4. Find the component form of a vector from its magnitude and direction angle)

1 Two – dimensional vectors

(1. Find the magnitude of a vector

2. Find the direction angle of a vector

3. Find the component form of a vector

4. Find the component form of a vector from its magnitude and direction angle

5. Find a unit vector

6. Add and subtract vectors)

1 Two – dimensional vectors

(1. Find the magnitude of a vector

2. Find the direction angle of a vector

3. Find the component form of a vector

4. Find the component form of a vector from its magnitude and direction angle

5. Find a unit vector

6. Add and subtract vectors

7. Multiply a vector by a scalar

8. Find the magnitude or direction of a vector scalar multiple,….etc)

4th Week(April)

Test

Test

Test

Test

For May

Year – 13

1 Day/Week

2 Day/Week

3 Day/Week

5 Day/Week

1st Week(May)

1 Three

– dimensional vectors

(1. Find the magnitude of a three-dimensional vector)

1 Three

– dimensional vectors

(1. Find the magnitude of a three-dimensional vector

2. Find the component form of a three-dimensional vector)

1 Three

– dimensional vectors

(1. Find the magnitude of a three-dimensional vector

2. Find the component form of a three-dimensional vector

3. Find a three-dimensional unit vector)

1 Three

– dimensional vectors

(1. Find the magnitude of a three-dimensional vector

2. Find the component form of a three-dimensional vector

3. Find a three-dimensional unit vector

4. Add and subtract three-dimensional vectors,….etc)

2nd Week(May)

1 Sequences and series(First half)

(1. Find terms of a sequence

2. Find terms of a recursive sequence)

1 Sequences and series(First half)

(1. Find terms of a sequence

2. Find terms of a recursive sequence

3. Identify a sequence as explicit or recursive

4. Find a recursive formula)

1 Sequences and series(First half)

(1. Find terms of a sequence

2. Find terms of a recursive sequence

3. Identify a sequence as explicit or recursive

4. Find a recursive formula

5. Find recursive and explicit formulas

6. Convert a recursive formula to an explicit formula)

1 Sequences and series(First half)

(1. Find terms of a sequence

2. Find terms of a recursive sequence

3. Identify a sequence as explicit or recursive

4. Find a recursive formula

5. Find recursive and explicit formulas

6. Convert a recursive formula to an explicit formula

7. Convert an explicit formula to a recursive formula

8. Convert between explicit and recursive formulas)

3rd Week(May)

1 Sequences and series(Second half)

(3. Identify a sequence as explicit or recursive

4. Find a recursive formula)

1 Sequences and series(Second half)

(5. Find recursive and explicit formulas

6. Convert a recursive formula to an explicit formula

7. Convert an explicit formula to a recursive formula

8. Convert between explicit and recursive formulas)

1 Sequences and series(Second half)

(7. Convert an explicit formula to a recursive formula

8. Convert between explicit and recursive formulas

9. Introduction to sigma notation

10. identify arithmetic and geometric series

11. Find the sum of a finite arithmetic or geometric series

12. Introduction to partial sums)

1 Sequences and series(Second half)

(9. Introduction to sigma notation

10. identify arithmetic and geometric series

11. Find the sum of a finite arithmetic or geometric series

12. Introduction to partial sums

13. Partial sums of arithmetic series

14. Partial sums of geometric series,….etc)

4th Week(May)

Test

Test

Test

Test

For Summer (June,July,August)

For June

Year – 13

1 Day/Week

2 Day/Week

3 Day/Week

5 Day/Week

1st Week(June)

1 Probability

(1. Introduction to probability

2. Calculate probabilities of events)

1 Probability

(1. Introduction to probability

2. Calculate probabilities of events

3. Combinations and permutations

4. Find probabilities using combinations and permutations)

1 Probability

(1. Introduction to probability

2. Calculate probabilities of events

3. Combinations and permutations

4. Find probabilities using combinations and permutations

5. Find probabilities using two-way frequency tables

6. Identify independent events)

1 Probability

(1. Introduction to probability

2. Calculate probabilities of events

3. Combinations and permutations

4. Find probabilities using combinations and permutations

5. Find probabilities using two-way frequency tables

6. Identify independent events

7. Find conditional probabilities

8. Independence and conditional probability,…etc)

2nd Week(June)

1 Probability distributions

(First half)

(1. Identify discrete and continuous random variables

2. Write a discrete probability distribution)

1 Probability distributions

(First half)

(1. Identify discrete and continuous random variables

2. Write a discrete probability distribution

3. Graph a discrete probability distribution

4. Expected values of random variables)

1 Probability distributions

(First half)

(1. Identify discrete and continuous random variables

2. Write a discrete probability distribution

3. Graph a discrete probability distribution

4. Expected values of random variables

5. Variance of random variables

6. Standard deviation of random variables)

1 Probability distributions

(First half)

(1. Identify discrete and continuous random variables

2. Write a discrete probability distribution

3. Graph a discrete probability distribution

4. Expected values of random variables

5. Variance of random variables

6. Standard deviation of random variables

7. Write the probability distribution for a game of chance

8. Expected values for a game of chance,….etc)

3rd Week(June)

1 Probability distributions

(Second half)

(3. Graph a discrete probability distribution

4. Expected values of random variables)

1 Probability distributions

(Second half)

(5. Variance of random variables

6. Standard deviation of random variables

7. Write the probability distribution for a game of chance

8. Expected values for a game of chance)

1 Probability distributions

(Second half)

(7. Write the probability distribution for a game of chance

8. Expected values for a game of chance

9. Choose the better bet

10. Find probabilities using the binomial distribution

11. Mean, variance and standard deviation of binomial distributions

12. Find probabilities using the normal distribution I)

1 Probability distributions

(Second half)

(9. Choose the better bet

10. Find probabilities using the binomial distribution

11. Mean, variance and standard deviation of binomial distributions

12. Find probabilities using the normal distribution I

13. Find probabilities using the normal distribution II

14. Find z-values

15. Find values of normal variables

16. Distributions of sample means,….etc)

4th Week(June)

Test

Test

Test

Test

For July

Year – 13

1 Day/Week

2 Day/Week

3 Day/Week

5 Day/Week

1st Week(July)

1 Statistics

(1. Identify biased samples

2. Variance and standard deviation)

1 Statistics

(1. Identify biased samples

2. Variance and standard deviation

3. Identify an outlier

4. Identify an outlier and describe the effect of removing it)

1 Statistics

(1. Identify biased samples

2. Variance and standard deviation

3. Identify an outlier

4. Identify an outlier and describe the effect of removing it

5. Outliers in scatter plots

6. Match correlation coefficients to scatter plots)

1 Statistics

(1. Identify biased samples

2. Variance and standard deviation

3. Identify an outlier

4. Identify an outlier and describe the effect of removing it

5. Outliers in scatter plots

6. Match correlation coefficients to scatter plots

7. Calculate correlation coefficients

8. Find the equation of a regression line,….etc)

2nd Week(July)

1 Introduction to derivatives

(1. Average rate of change I)

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)

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,….etc)

3rd Week(July)

1 Derivative rules

(1. Sum and difference rules)

1 Derivative rules

(1. Sum and difference rules

2. Product rule)

1 Derivative rules

(1. Sum and difference rules

2. Product rule

3. Quotient rule)

1 Derivative rules

(1. Sum and difference rules

2. Product rule

3. Quotient rule

4. Power rule I,…etc)

4th Week(July)

Test

Test

Test

Test

For August

Year – 13

1 Day/Week

2 Day/Week

3 Day/Week

5 Day/Week

1st Week(August)

1 Calculate derivatives

(1. Find derivatives of polynomials

2. Find derivatives of rational functions)

1 Calculate derivatives

(1. Find derivatives of polynomials

2. Find derivatives of rational functions

3. Find derivatives of trigonometric functions I

4. Find derivatives of trigonometric functions II)

1 Calculate derivatives

(1. Find derivatives of polynomials

2. Find derivatives of rational functions

3. Find derivatives of trigonometric functions I

4. Find derivatives of trigonometric functions II

5. Find derivatives of exponential functions

6. Find derivatives of logarithmic functions)

1 Calculate derivatives

(1. Find derivatives of polynomials

2. Find derivatives of rational functions

3. Find derivatives of trigonometric functions I

4. Find derivatives of trigonometric functions II

5. Find derivatives of exponential functions

6. Find derivatives of logarithmic functions

7. Find derivatives of inverse trigonometric functions

8. Find derivatives of radical functions,….etc)

2nd Week(August)

1 Derivative strategies

(1. Find derivatives using implicit differentiation)

1 Derivative strategies

(1. Find derivatives using implicit differentiation)

1 Derivative strategies

(1. Find derivatives using implicit differentiation

2. Find tangent lines using implicit differentiation)

1 Derivative strategies

(1. Find derivatives using implicit differentiation

2. Find tangent lines using implicit differentiation

3. Find derivatives using logarithmic differentiation,….etc)

3rd Week(August)

1 Calculate higher derivatives

(1. Find higher derivatives of polynomials)

1 Calculate higher derivatives

(1. Find higher derivatives of polynomials

2. Find higher derivatives of rational and radical functions)

1 Calculate higher derivatives

(1. Find higher derivatives of polynomials

2. Find higher derivatives of rational and radical functions

3. Find second derivatives of trigonometric, exponential and logarithmic functions)

1 Calculate higher derivatives

(1. Find higher derivatives of polynomials

2. Find higher derivatives of rational and radical functions

3. Find second derivatives of trigonometric, exponential and logarithmic functions

4. Find higher derivatives using patterns,….etc)

4th Week(August)

Test

Test

Test

Test

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