Trigonometry 1

Mr H in 10 years

Trigonometry 1: Applying trigonometric skills to solve equations

By the end of this topic you will be able to:
• convert Degrees to Radian measure and vice versa
• recall exact values in and calculate using radian measure
• translate graphs of trig functions
• solve trigonometric equations in degrees or radians

• including those involving the wave function or trigonometric formulae or identities, in a given interval

Homework: Trigonometry HW1

Due: Monday 20th December

ALL pupils should be able to Q1-4

MOST pupils should be able to complete Q5

SOME : Not applicable for HW1

DO NOT DO Q6

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The Circle

 

New Topic: The Circle

By the end of this topic you will:

• know that the equation of the circle centre (a,b) and radius r is (x – a)² + (y – b)² = r²

• know that x² + y² + 2gx + 2fy + c = 0 represents a circle centre (–g, –f) and
radius r = √(g² + f² – c), provided g² + f² – c > 0

• be able to determine the equation of a circle

• be able to solve problems with the intersection of a line and a circle,
and a tangent to a circle

• be able to determine whether two circles touch each other

 

Homework: Circles Set2

Due: Monday 7th December

ALL pupils should be able to complete Q1 – 4

MOST pupils should be able to complete Q7

SOME pupils should be able to complete Q6

DO NOT DO Q5

 

Circles Set2 Solutions

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Differentiation

New Topic: Differentiation, MiA Higher Ch3

By the end of this topic you will:
• be familiar with the terminology associated with differentiation
• understand the principles of differentiation
• be able to derive the gradient formula of a given function
• be able to calculate the gradient of a tangent to a curve
• be able to use differentiation to solve optimisation problems

Homework 1: Differentiation 1 Set1

Due: Friday 3:20pm – submit to Mr H’s office

ALL pupils should be able to complete Q1 & 2

MOST pupils should be able to complete Q4

SOME pupils should be able to complete Q3

 

Homework 2: Differentiation HW2

Due: Wednesday 18th November

ALL pupils should be able to complete Q1 – 4

MOST pupils should be able to complete Q5 & 6

SOME pupils should be able to complete Q7

Differentiation HW2 – Solutions

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Composite Functions

By the end of this lesson you will:

• be able to find f(g(x)) given f(x) and g(x)

Homework: Composite and Inverse Functions Set1

Due: TBC

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Completing the Square Practice

Completing the Square worksheet for Friday 11/09/15

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Translating Functions

Desmos Calculator Activity

Explore the effects of changing the vales of a, b, c and d individually.

Discuss and agree the translations:

y = f(x + a)

y = f(x) + b

y = cf(x)

y = f(dx)

 

Click the graph below to start the activity:

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What is a radian?

Click the image to view an explanation….

Polynomials

New Topic: Polynomials

By the end of this topic you will be able to:
• Factorise a cubic polynomial expression with unitary x³ coefficient
• Solve cubic polynomial equations with unitary x³ coefficient
• Factorise a cubic or quartic polynomial expression where the term of highest degree has a non-unitary coefficient
• Solve a cubic or quartic polynomial equation, where the term of highest degree has a non-unitary coefficient
• Find the coordinates of the point(s) of intersection of a straight line and a curve or of two curves

Homework: Polynomials Set1 (Q1-6 only)

Due: Thursday 17th September

Please check the solutions below and attempt the equivalent questions from the Set 2 sheet to those you struggled with first time.  These should be handed in with your next homework or earlier. Please see me for help if necessary.

Polynomials Set 1 Solutions

Polynomials Set2

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Quadratic Theory

New Topic: Quadratic Theory

By the end of this topic you will be able to:
• Given the nature of the roots of a quadratic equation, use the discriminant to find an unknown
• Finding the coordinates of the point(s) of intersection of a straight line and a curve or of two curves
• know condition for tangency; intersection of line and parabola (lines and curves)
• solve quadratic inequalities

Homework: Quadratic Theory Set1

Due: Wednesday 2nd September

Please check the solutions below and attempt the equivalent questions from the Set 2 sheet to those you struggled with first time.  These should be handed in with your next homework or earlier. Please see me for help if necessary.

Quadratic Theory Set1 Solutions

Quadratic Theory Set2

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Euler Line

Euler Line – Group Investigation

In groups of 2 or 3:

Find the equation of the Euler line of the triangle with vertices A(-2, -4), B(2, 4) and C(12, -4).

Your group submission should be in the form of a presentation in a form of your choice. Your presentation must include:
• a fully worked solution with explanation
• accurate diagram
• other relevant information you discovered during your investigation

All members of your group should be prepared to present your findings to the class.

Due: Wednesday 30th September

Euler Line Investigation Worksheet