Download HIGHER Maths GCSE Unit 2 Key Facts

HIGHER Maths GCSE Unit 2
– Things to Remember
Multiples of a number are the numbers in its multiplication
table
e.g. multiples of 7 are 7, 14, 21, 28, 35 ........
Factors of a number are the numbers that divide into it without
any remainder e.g. factors of 12 are 1 and 12, 2 and 6, 3 and 4
A prime number has only two factors, one and the number
itself
e.g. the first few prime numbers are 2, 3, 5, 7, 11, 13......
A square number is the result you get when multiplying a
number by itself. The first few square numbers are 1, 4, 9, 16, 25...
A square root is the opposite or inverse of a square number
e.g. the square root of 16 is 4 (√16 = 4), the square root of 49 is 7, etc..
A cube number is the result you get when multiplying a
number by itself and then by itself again
The first few cube numbers are 1, 8, 27, 64, 125 ....
A cube root is the opposite or inverse of a cube number
e.g. the cube root of 8 is 2 (3√8 = 2), the cube root of 27 is 3, etc.....
BIDMAS
– the order in which calculations are done
Brackets
Indices (or powers)
Division
Multiplication
Addition
Subtraction
e.g. 4 + 6 x 5 = 4 + 30 = 34
Fractions, Decimals and Percentages:
F → D → P
÷
x 100
e.g.
2 = 2 ÷ 5 = 0.4, and 0.4 x 100 = 40%
5
5 of 24 = 24 ÷ 8 x 5 = 3 x 5 = 15
8

30% of 64 = 3 lots of 10% of 60 = 3 x 6.4 = 19.2

8 as a percentage of 20 = 8_ = _40 = 40%
20
100
Reverse Percentages
After an increase of 20%, the new amount is 120% of the original
amount
After a decrease of 10%, the new amount is 90% of the original
amount
Ratio
To split £160 in the ratio 3 : 5, you need to split it into 3 + 5 = 8
parts……..
£160 ÷ 8 = £20
And then find what 3 parts and 5 parts are………
3 x £20 = £60
5 x £20 = £100
Standard Form Numbers
3 x 107 = 30 000 000
460 000 = 4.6 x 105
2.4 x 10-5 = 0.000024
0.000000081 = 8.1 x 10-8
nth term of a sequence
the sequence 3, 11, 19, 27…….
has a common difference of 8, so the nth term must include 8n
but the sequence for 8n is 8, 16, 24, 32…..
So the sequence 3, 11, 19, 27……. must be 8n – 5
Expanding and Factorising
To expand a bracket, multiply all the terms inside the bracket
e.g. 3(x + 7) = 3x + 21
x(x – 4) = x2 – 4x
Factorising is the opposite of expanding
e.g. 6x – 15 = 3(2x – 5)
x2 + 8x = x(x + 8)
To expand a double bracket, use the FOIL method
e.g. (x +3)(x + 7) = x2 + 7x + 3x + 21
= x2 + 10x + 21
To factorise a quadratic expression such as x2 + 11x + 24,
you need two numbers that multiply to give 24 and add to give 11, i.e. 3
and 8, so:
x2 + 11x + 24 = (x +3)(x + 8)
Solving Equations and Re-arranging Formulae
 Remember to always do the same to all terms on both sides
of the equal sign
 Try to eliminate negatives, brackets and fractions first
The equation of a straight line graph
y = mx + c
m is the gradient
of the graph
c is the y-intercept
(where the line
crosses the y axis)
Laws of Indices
ax x a y = a x + y
e.g. 35 x 37 = 312
ax ÷ a y = a x – y
e.g. x8 ÷ x3 = x5
a-x = 1
ax
e.g. 3-2 = 1
32
a½ = √a
a⅔ = (3√a)2
e.g. 6½ = √6
e.g. 8⅔ = (3√8)2 = 22 = 4
Surds
√a x √b = √(ab)
e.g. √3 x √5 = √15
√a ÷ √b = √(a/b)
e.g. √18 ÷ √3 = √6
Now try these questions to test your knowledge………..
1. Simplify 3a5b2 x 4a3b4
2. Simplify 24x6y2
3x2b8
3. Simplify x4 ÷ x7
⅔
4. Evaluate 27
5. After an increase of 20% a TV now costs £288. What was its original price?
6. If a = 3, b = -7 and c = 11, find the value of 3b2 – 4ac
3a - c
7. Factorise x2 - 3x – 28
8. Factorise 4x2 – 25
9. Solve y + 5 + y – 1 = 10
6
2
10. Rearrange the formula g = am - t to make a the subject
P
11. Rearrange the formula kx + h = m(x + t) to make x the
subject
12. Work out the equation of the line, parallel to the line 3x + y = 2,
which goes through the point (2, 1)
13. Expand √5(√2 + √3)
14. Expand (√3 + 2)(√3 - 5)
15. Rationalise the denominator of 2
√3
16. Prove that for any five consecutive numbers the difference
between the square of the middle number and the product of
the largest and smallest is always 4.