Transcript Maths GCSE revision - Ysgol Uwchradd Tywyn

Maths GCSE revision
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Read the question
Identify key words
Think what type of maths COULD be used
Go through the stages
• ANYTHING is better than nothing
Triangles
• Area = base x vertical height
2
• BUT if there is no right angle use the
formula
(b x c x Sin A) ÷ 2
Right angled triangles
For pythag. the triangle must have a right
angle and there will be the lengths of 2
sides and it will ask about the other length.
10
8
Write down the 2 side -
10
8
Square them
100
64
Is it add or take?
100 - 64 = 36
Square root
?
6
Trig. – finding the angle
• Must be right angled triangle
• Question will be about finding an angle
given 2 sides
Write down SOHCAHTOA
Label the 2 sides
Write O ÷ H = shift SIN
10 H
6 ÷ 10 = shift Sin
36.9
6
O
??
6
TRY
3
??
Ans = 60
Trig – finding a side
• Must show a right angle
• Question will give one side and another
angle and ask about a side
Write down SOHCAHTOA
Label the known side and the wanted one
?
O
10
H
Write Sin 30 = O/H = ?/10
Rearrange 10 x Sin 30 = 5
30
Ans is 20
60
10
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Must be
larger than
10
Triangles without a right angle
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Question involves 2 sides and 2 angles
Find PAIRS
8
10
40/8 & ?/10
40
= Sine rule ?
Start with ?
Sin ? = Sin 40
8
10
10
70
50
Rearrange sin? = Sin40 x 8 = 0.51423
10
then shift Sin = ans = 30.9
? Ans = 10.9
Triangles without a right angle
• Question involves 3 sides and 1 angle
• Cosine rule
5
• Write the formula out
• Replace letters
?
40
• Know how to use your calculator
3
a² = b² + c² - (2bcCosA) use brackets
a² = 5x5 + 3x3 – (2x3x5xCos40)
TRY
= 11.02
5
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50
2
Ans = 4
then square root = 3.32
Typical question
No right angle so need ½ abSinC
• Find the area of DCB
B
3
Can I find CD or BD?
OR would it be easier to find BD and
angle DBC?
C What can I do with triangle ABD?
Sine rule won’t work but Cosine will.
5
A
70
Use Cosine rule to find BD (5.22)
30
4
D
Then I have enough information in triangle
BCD to use Sine rule to find angle DCB (60.5)
This allows me to find angle DBC (89.5)
I can then use area rule. (7.83)
Bearings
• Key words are from and to.
• From tells you where to start
• The angle between N and to is the bearing
N
N
Look to see if F
angles can help
If joining all the points
produces a triangle
then Sine/Cosine rules
are possible
Proportionality
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Directly proportional
W α T
Is it just T – read
Include k
W = kT
Use the data to find k
Write out the equation
Use the equation
• Inversely proportional
• W α 1
T
Is it just T
Include k
W = k/T
Use the data to find k
Write out the equation
Use the equation
The kinetic energy (E) of an object varies inversely with the square of
its velocity (v). If the kinetic energy is 144j when the velocity is 4m/s.
Find i) the K.E. when the velocity is 10m/s and ii) the velocity when it
has a K.E. of 360 joules.
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Key word inversely
Is it just v?
Include k
Use the data to find k
• Write out the equation
• Use it to find E
• Use it to find v
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E α 1/v
E α 1/v²
E = k/v²
144 = k/4x4
K = 144 x 16 = 2304
E = 2304/v²
E = 2304/10x10 = 23.04j
360 = 2304/v²
v² = 2304/360 = 6.4
v = √6.4 = 2.53m/s
The force (f) needed to stretch a rubber band is directly proportional to
the square root of its length (L)
If a force of 18N is needed to stretch it 9cm find
i) the force needed to stretch it 49cm
ii) the amount a 24N force will stretch it.
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Use the key words
Check if its just L
K should be 6
i) Force will be 42N
ii) Length will be 16cm
Circle theorems
• How many rules are there?
• Can you draw them?
The example contains 4
rules.
Which are they?
What is a and b
How many other angles
can you find?
Solving quadratic equations using
the formula
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Solve 5x² - 3x – 10 = 0.
Write the answer correct to 2 significant figures
Key words mean use the formula
Write out the formula
- b +or- √b² - 4ac
2a
Write out a (+5), b (-3) and c (-10), remember +/Replace the letters by the numbers
- -3 +or- √ -3x-3 – (4 x 5 x -10) ÷ 2x5
Use your calculator to do the underlined part (=209)
Then(- - 3 + √209) ÷ 2x5 and also (- -3 - √209) ÷ 2x5
1.75
and -1.15
answer is 1.8 and -1.2
Try using the formula
• Solve 2x² - x – 15 = 0
• The √ bit should work out as 121 = 11
• The answers are +3 and -2.5