GCSE Higher Tier revision Flashcards
Round 135 to 1sf
100
The 1 column is the first significant figure, so round that as normal
How do you find the area of a triangle?
base times height divided by 2
If boys and girls are in the ration 3:7, what fraction of them are boys?
3
10
Which is better value, 9 pens for £1.75, 20 pens for £3.95 or 50 pens for £9.75?
9 pens.
9 pens - each pen is £0.194
20 pens - each pen is £0.1975
50 pens - each pen is £0.195
If a sequence is:
3, 7, 11, 15
Which of the following numbers are in the sequence?
(hint - find the nth term)
29 41 31
31.
The nth terms is 4n - 1
If 4n - 1 = 31, n = 8 so the 8th number in the sequence is 31
For 29 and 41, n is a decimal.
Which of these will give you a “U” shaped graph?
y = 3x + 1
y = x3 - 5
y = x2 + 2x
y = x2 + 2x
This is a quadratic graph. y = 3x + 1 is a straight line and y = x3 - 5 is a cubic (“S” shape)
Which is further, 17 miles or 27km?
17 miles.
Convert both to the same unit, use 1 mile = 1.6 km
17 x 1.6 = 27.2km
or
27 divided by 1.6 = 16.85 miles
A sequence begins with 4, 7, 10, 13, …
Is 500 in the sequence?
No
Find the nth term (3n + 1)
Put 500 = 3n + 1 then solve.
3n + 1 = 500
3n = 499
n = 166.6… so as n is not a whole number, it isn’t in the sequence.
In a 4 sided shape, the angles add up to what?
360
What do angles around a point add up to?
360
If you get 31 out of 40 on a test, what is your percetage score?
72.5%
Get the denominator to 100. (or do 31/40 *100 on a calculator)
Because
31 = 155 = 72.5
40 = 200 = 100
3a4b5 x 5a3b-1 simplifies to:
15a7b4
Remember, mulitply numbers, add powers.
If a circle has radius ot 5cm, what is its circumference?
31.4cm.
Circumference = pi x diameter.
As the radius = 5cm, the diameter = 10cm
So circumference = pi x 10 = 31.4 cm
Which is quicker - 14 metres per second or 30 miles per hour?
You must show WHY!
14 metres per second
14 metres per second
= 840 metres per minute (x 60)
= 50400 metres per hour (x 60 again)
= 50.4 km per hour (divide by 1000)
= 31.5 mph (divide by 1.6)
You could also do these in the oppostie order to 30 instead! (x1.6, x1000, divde by 60, divide by 60)
If a polygon is regular, what does this mean?
All the sides and angle are equal
How do you find an exterior angle?
Extend a side of the shape, from the extension, draw the angle to the next side. This is the exterior angle.
What do the exterior angles of a polygon add up to?
3600
If the interior angle of a regular polygon is 1080, what is the exterior angle?
72
Interior + exterior angle = 180
If a regular shape has 20 sides, calculate the size of one exterior angle.
180
360 divided by 20 = 18
Solve:
3(2x + 5) = 4(3x - 1)
x = 9.5
4(3x - 1) = 5(2x + 3)
12x - 4 = 10x + 15
2x - 4 = 15
2x = 19
x = 9.5
What is 3.75 x 106 as a normal number
3750000
What is 6.713 x 10-4
0.0006713
What is (2 x 105)x (8.1 x 106). Give your answer in standard form.
1.62 x 1012
Multiply the numbers: 2 x 8.1 = 16.2
Add the powers: 1011
- 2 x 1011 (as 16.2 is not between 1 and 10, this is not in standard form)
- 62 x 1012
Change 3180000 to standard form.
3.18 x 106
Convert 0.00014 to standard form
1.4 x 10-4
A t-shirt costs £15 in a 10% off sale. How much was it before the sale?
£16.67
If you said £16.50 you’re thinking of the wrong way.
If it is now reduced by 10%, it is 90% of it’s original price.
To find the find the original: 15 divided by 0.9 (90% as a decimal)
This gives £16.67
AThe navy has 23000 people in 2015. This is a increase of 8% from 3 years ago. How many people were in the navy in 2012?
21296
8% increase means it is now 108% (1.08 as a decimal)
23000 divided by 1.08 = 21296
Factorising the following expression:
x2 - 36
(x + 6)(x - 6)
This is known as a difference of two squares as both x2 and 36 are square numbers.
Factorise the following expression:
4x2 - 49y2
(2x - 7y)(2x + 7y)
Both 4x2 and 49y2 are both square numbers so you can use the difference of two squares.
Make h the subject of
3y - ph = 2h + py
h = 3y- py
2 + p
Because (you might need to scrool down)
3y - ph = 2h + py
(move ph)
3y = 2h + py +ph
(move py)
3y - py = 2h + ph
Factorise the right
3y - py = h(2 + p)
Divide by 2 + p
