11 December, S2 - 10/M1*

Book review
Exercise 1
Solve the following simultaneous equations:

• 2x + y = 7
• 3x - y = 8

• 2x + 3y = 6
• 4x - 6y = - 4

Exercise 2

Plot the following graphs on the same axis:
y = x^2
y = x^3
y = x^2 + 3x - 1

Exercise 3
Factorise and solve the following and explain your method:
x^2 + 8x + 15
x^2 + 3x + 2
x^2 + 5x + 4

Exercise 4
Find the expression for these sequences and explains how you found them:
2, 5, 10, 17, 26...
7, 16, 29, 46, 67, 92, 121...

Exercise 5
Solve the following simultaneous equations:
x^2 + y^2 = 25
y = x -1 

x^2 + y^2 = 16

y = 2x + 2

Lesson
Title: Trigonometry

Learning Objectives 

Grade B
To to be able to explain which is the correct trigonometric rule to use and use it to calculate the lengths of sides & angles in right-angled triangles.
How do you know which of the three rules to use?
Grade A
To be able to use the sine and cosine rules to calculate missing angles or sides in non right-angles triangles.
When is it possible to use either of these rules?

Resources 

Grade B

Ten Ticks  - 7-8, 5, page 29+

MEP 10 - 4.4

CIMT Interactive
Trigonometric Functions
Calculating Sides
Calculating Angles

Grade A

Introduce the Sine Rule (noting it can be turned around).

Start by finding the length of a side.

Ten Ticks - 9-10, 2, page 7 (part A).

On students are happy with this move on to examples of finding a missing angles.

Ten Ticks - 9-10, 2, page 7 (part B).

Move on to the Cosine Rule (different ways around).

Ten Ticks - 9-10, 2, page 8

Move to a mix of questions

Ten Ticks - 9-10, 2, pages 9-10

Further real life examples and proofs.

MEP 4 pages 27-34

Homework:

Learning Objective for next lesson:

Grade A

To be able to use the sine and cosine rules to calculate missing angles or sides in non right-angles triangles

When is it possible to use either of these rules?

To be able to calculate the area of a triangle using the formula: Area = ½ ab sin C.

What information do we need to do this calculation?