s2 (2.2) pythagoras.notebook march 04, 2016
TRANSCRIPT
S2 (2.2) Pythagoras.notebook March 04, 2016
Daily Practice 16.12.2015
Q1. Multiply out and simplify 9x ‐ 3(2x + 1)
Q2. Solve the equation 3(2x + 4) = 18
Q3. If £1 = $1.30, how much is £50 in dollars?
Q4. Factorise 20ab + 15b Q5. Find 15% of 900
Today we will be learning about Pythagoras'
Theorem.
Bring in a scientific calculator or £4 to buy one in
school.
Pythagoras' Theorem 16.12.15
A theorem is a word to describe a Mathematical idea that has been proven true.
Pythagoras was a Greek Mathematician that was born in approx. 569BC.
The Pythagorean theorem states that the sum of the squares of the two shorter sides in a right-angled triangle is equal to the square of the longest side.
Although there are many prior instances of the use of the idea by the Egyptians and Babylonians. The proof is generally accredited to Pythagoras.
Pythagoras' Theorem
ca
bIn a right-angled triangle, the longest side is called the Hypotenuse. It is always across from the right angle.
Pythagoras' Theorem - Proof
Draw a right angled triangle with sides 3cm, 4cm and a hypotenuse of 5cm .
0 1 2 3 4 5 6 7 8 9 10 11
0 1 2 3 4
0°
S2 (2.2) Pythagoras.notebook March 04, 2016
Daily Practice 17.12.15
Q1. Round 17.849 to 2 decimal places
Q2. Calculate the height of a cuboid with a volume of 300cm3 , a breadth of 20cm and a length of 3.75cm
Q3. Calculate Andy's wages if he earns £12.50 per hour and works for 6 hours.
Q4. Solve the equation 9m - 2 = 3m + 4 Q5.
Today we will be using Pythgaoras' Theorem to work out questions.
Pythagoras' Theorem - Proof
a
a
b
b
cc
a
a
b
b
c
c
Pythagoras' Theorem - Proof
Pythagoras' Theorem
ca
b
a2 + b2 = c2
Pythagoras' Theorem
Pythagoras' Theorem is used to find a missing side in a right-angled triangle.
Examples:
1. Calculate the length of p
15cm
8cm
p cm
S2 (2.2) Pythagoras.notebook March 04, 2016
Daily Practice 18.12.15
Q1. Round 18.34984 to 3 decimal places
Q2. 0.25 ÷ 500
Q3. Solve 3(2x - 1) + 4x = 27
Q4. Factorise 2x2h - xh
Q5. 28 - 33 x 4
Today we will be using Pythagoras' Theorem to find the length of a missing side in a triangle.
Pythagoras' Theorem
Examples:
2. A a pole is held up vertically by two identical pieces of rope. If the pole is 16metres tall and it is pinned onto the ground 18 metres away from the foot of the pole. How long are the pieces of rope?
16m
Daily Practice 21.12.15
Q1. Santa's elves work overtime during the Holiday Season at a rate
of time and a half. If they normally earn 60 North Pole coins per hour,
how much will they earn for 20 hours overtime?
Q2. If the temperature in the North Pole is -400C and the temperature
in Edinburgh is 90C, what is the difference in temperature?
Q3. Solve the equation 6x - 2 = 4x + 18
Daily Practice 7.1.2016
Q1. - 30 + 16
Q2. Find 15% of 7000
Q3. Multiply out and simplify 7(2x - 1) + 3x
Q4. Q5. 5.6 x 700
S2 (2.2) Pythagoras.notebook March 04, 2016
Today we will be continuing to use Pythagoras' Theorem to find the length of a missing side in a right-angled triangle.
Pythagoras' Theorem
A B
C
Calculate the length of AC
16cm
14cm
Pythagoras' Theorem
Examples:
2. A a pole is held up vertically by two identical pieces of rope. If the pole is 16metres tall and it is pinned onto the ground 18 metres away from the foot of the pole. How long are the pieces of rope?
16m
Daily Practice � � ����
Q� Find ��� of ���� Q� Solve �x � ! ��
Q� Round �� �$� to � decimal place
Q�
Q Multiply out and simplify �)x � �* � )x + *
Today we will be continuing to practise questions on
how to find the shorter side using Pythagoras
Pythagoras' Theorem - Finding a shorter side
ca
b
S2 (2.2) Pythagoras.notebook March 04, 2016
Pythagoras' Theorem - Finding a shorter side
Examples:
1. Calculate the length of p to 1 d.p.
22cm
8cm
p cm
Pythagoras' Theorem - Finding a shorter side
Examples:
2. A ramp leading onto a doorstep is 2.5m long. The height of the ramp is 0.3m. How far away is the ramp from the door.
Pythagoras' Theorem - Finding a shorter side
Pegasys
Daily Practice 11.1.2016
Q1. 92 x 4000
Q2. -11 + 13 - (-4)
Q3. 48 ÷ 5 Q4. Solve 3(2x - 1) = 21
Q5. Karl bought a bike in the sale for £340, it was originally £400. What percentage was it reduced by?
Today we will be working on mixed Pythagoras Questions.
HW online due Friday 15.1.16
Page 213 Ex. 7 Q1.
If finished, page 214, 215 odd numbered questions
Daily Practice 13.1.16
20 Questions Mental Maths
S2 (2.2) Pythagoras.notebook March 04, 2016
Today we will be completing a check-up on Pythagoras Theorem.
Homework due Friday.
S2 (2.2) Pythagoras.notebook March 04, 2016