maths revision Flashcards
-adding surds
√3 + √3 =?
2√3
-adding surds
3√12 + √27
3√12 + √27
=3√4√3 + √9√3
=6√3 + 3√3
=9√3
-Expanding bracket with Surds
√5(3+√3)
√5(3+√3)
=3√5+√15
-Expanding bracket with Surds
(2√2+2) (√2-3)
(2√2+2) (√2-3)
=4 + -6√2 + 2√2 + -6
=-2-4√2
-simplifying surds
√a x b=
√a x b = √a x √b
-simplifying surds
√12
√12
=√4x3
=√4 x√3
=2 x√3
-multiplying surds
2√2 x 5√3 = ?
2√2 x 5√3 = 10√6
3√7 x 5√5 = ?
3√7 x 5√5 = 15√35
standard form
3000 = ?
3000 = (3 x 10³)
standard form
(7 x 10³)(6 x 10¹⁰)=?
(7 x 10³)(6 x 10¹⁰)
=(42 x 10¹³) <– this is not standard form, so…
=(4.2 x 10¹⁴)
standard form
(4x10³)+(2x10⁴)=?
(4x10³)+(2x10⁴) <— change the smaller one
=(0.4x10⁴)+(2x10⁴)
=24000
rules of indices
yᴬ x yᴮ =
yᴬ x yᴮ
=yᴬ+ᴮ
rules of indices
yᴬ ÷ yᴮ = ?
yᴬ ÷ yᴮ
= yᴬ - ᴮ
rules of indices
(yᴬ)ᴮ = ?
(yᴬ)ᴮ
= yᴬ x ᴮ
rules of indices
y⁰ = ?
y⁰
= 1
rules of indices
y-ᴬ = ?
y-ᴬ
= 1/yᴬ
rules of indices
(a/b)-ᴬ = ?
(a/b)-ᴬ
= (b/a)ᴬ
rules of indices
a¹/ᵇ = ?
a¹/ᵇ
= ᵇ√a
aᵇ/ᵐ =?
a ᵇ/ᵐ
= a⁽¹/ᵐ x ᵇ⁾
e.g.
27 ²/³
= (27 ¹/³)²
= (3)²
= 9
3³
27
4³
64
5³
125
6³
216
7³
343
8³
512
9³
729
10³
1000
how do you find the prime factors of a number?
by making a prime factor tree
once you have put the numbers from a prime factor tree in a ven-diagram
-how do you work out the HCF
-how do you work out the LCM
HCF = times all the numbers in the middle section
LCM = times all the numbers in the ven-diagram
what is a factor?
Factors are numbers that divide exactly into another number. For example, the factors of 8 are: 1, 2, 4, 8.
what is a multiple?
A multiple is a number that a certain number can go into.
e.g. 12 is a multiple of 4
what does a negative power do to a fraction?
it flips the fraction.
how do you work out the mean?
you add all the numbers up and then divide it by the amount of numbers you added up.
how do you work out the median?
by lining up all the numbers in ascending order and then working out the middle number.
how do work out the mode?
by working out which number is the most common.
how do you work out the range?
by working out the difference between the largest and smallest number.
what is x?
2x + 9 = 15
2x + 9 = 15 (minus 9)
2x = 6 (divide by 2)
x = 3
what is a?
8(a+3) = 24
8(a+3) = 24 (factorise)
8a + 24 = 24 (minus 24)
8a =0 (divide by 8)
a = 0
what is x?
4x + 4 = 2x + 9
4x + 4 = 2x + 9 (minus 2x)
2x + 4 = 9 (minus 4)
2x = 5 ( divide by 2)
x = 2.5
what is x?
3x-1 / x+2 = 2
3x-1 / x+2 = 2 (times by (x - 2))
3x - 1 = 2(x + 2) (expand brackets)
3x - 1 = 2x + 4 ( minus 2x)
x - 1 = 4 ( plus 1 )
x = 5
what is the nth term for this sequence?
5, 8, 11, 14
5, 8, 11, 14
(3 goes there as the numbers increase by 3)
∨
nth term = 3n + 2
∧
(the 2 goes there as the 0th term is 2)
what is the method to work out the nth term for a quadratic sequence?
1) work out the difference of the difference between the terms
2)divide that number by 2 and put that in front of n²
3)make a table and work out the remainder when subtracting the quadratic from the original sequence numbers
4)work out the nth term for that sequence
5)put it together like this:
_n² +/- _n +/- _
how do you factorise this sequence:
x² + 9x + 20
x² + 9x + 20
1)list the pairs with a product of 20(the last number)=
* 1 and 20
* 2 and 10
* 4 and 5
2) find a pair with a sum of +9 (second number)
= 4 and 5
3) put it in brackets like this
= (x + 4)(x + 5
how do you factorise this sequence:
2x² + 7x +6
2x² + 7x +6
^ ^ ^
A B C
1) A(2) x C(6) = 12 (needs to be the product)
B = 7 (needs to be the sum)
2) find number pair
= 3 and 4
3)split middle term
= 2x² + 3x + 4x + 6
4) split the sequence into 2 sections
= [2x² + 3x] [4x + 6]
5) factorise the pairs
= x(2x + 3) + 2(2x + 3)
6) collect terms:
= (x + 2)(2x + 3)
how do you rationalise this fraction:
2/√5
1) times it by the denominator:
2/√5 x √5/√5 = 2/√5 / √25
2) simplify :
= 2/√5 / 5
rationalise this fraction:
5-√6 / √6
5-√6 / √6
1) times by the denominator
= 5-√6 / √6 x √6 / √6
2)simplify if you can
= 5√6 - 6 / 6
how do you rationalise this fraction?
2 / 4+√2
2 / 4+√2
1) times by the denominator but using the reverse operation:
= 2 / 4+√2 x (4-√2) / (4-√2)
2)first work out the numerator:
= 2 x (4 - √2)
= 8 + 2√2
3)work out the denominator with F.O.I.L
F = 4 x 4 = 16
O = 4 x √2 = 4√2
I = -√2 x 4 = - 4√2
L = √2 x - √2 = -√4 = -2
16 + 4√2 - 4√2 - 2 = 14
4) simplify the fraction
= 8+2√2 / 14
= 4+√2 / 7
what calculation do you do to work out the angle of a pie chart a set of the data should have?
frequency / total of frequencies x 360
what things must a graph include?
heading, label, key, pencil lines, and ruler used.
what calculation should you do to work out the angle of 1 person on a pie chart?
360 / total of frequencies
what must you remember when making a stem and leaf diagram?
a key
what correlation would a graph with the points going from the top left –> the bottom right have?
a negative correlation
what correlation would a graph with the points going from the bottom left –> the top right have?
positive correlation
how do you work out frequency density?
frequency / class width
what type of data is ‘its delicious’
qualitative data
what do you call data that is numbers?
quantitative data
what type of data is counted?
discrete
what type of data is measured?
continuous
what type of data is ‘goals scored’
quantitative, discrete
what type of data is the height of a tree?
quantitative, continuous
How do you find a fraction of a number (9/20 of 360)
You multiply bottom then times by top.( 360 / 20) x 9 = 162
How do you convert from fraction to decimal and from decimal to percentage?
Fraction—— divide —> decimal (7/20 is 7 divided by 20)
Decimal —— x by 100 —> percentage
