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maths revision Flashcards

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1
Q

-adding surds
√3 + √3 =?

A

2√3

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2
Q

-adding surds
3√12 + √27

A

3√12 + √27
=3√4√3 + √9√3
=6√3 + 3√3
=9√3

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3
Q

-Expanding bracket with Surds
√5(3+√3)

A

√5(3+√3)
=3√5+√15

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4
Q

-Expanding bracket with Surds
(2√2+2) (√2-3)

A

(2√2+2) (√2-3)
=4 + -6√2 + 2√2 + -6
=-2-4√2

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5
Q

-simplifying surds
√a x b=

A

√a x b = √a x √b

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6
Q

-simplifying surds
√12

A

√12
=√4x3
=√4 x√3
=2 x√3

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7
Q

-multiplying surds
2√2 x 5√3 = ?

A

2√2 x 5√3 = 10√6

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8
Q

3√7 x 5√5 = ?

A

3√7 x 5√5 = 15√35

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9
Q

standard form
3000 = ?

A

3000 = (3 x 10³)

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10
Q

standard form
(7 x 10³)(6 x 10¹⁰)=?

A

(7 x 10³)(6 x 10¹⁰)
=(42 x 10¹³) <– this is not standard form, so…
=(4.2 x 10¹⁴)

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11
Q

standard form
(4x10³)+(2x10⁴)=?

A

(4x10³)+(2x10⁴) <— change the smaller one
=(0.4x10⁴)+(2x10⁴)
=24000

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12
Q

rules of indices
yᴬ x yᴮ =

A

yᴬ x yᴮ
=yᴬ+ᴮ

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13
Q

rules of indices
yᴬ ÷ yᴮ = ?

A

yᴬ ÷ yᴮ
= yᴬ - ᴮ

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14
Q

rules of indices
(yᴬ)ᴮ = ?

A

(yᴬ)ᴮ
= yᴬ x ᴮ

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15
Q

rules of indices
y⁰ = ?

A

y⁰
= 1

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16
Q

rules of indices
y-ᴬ = ?

A

y-ᴬ
= 1/yᴬ

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17
Q

rules of indices
(a/b)-ᴬ = ?

A

(a/b)-ᴬ
= (b/a)ᴬ

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18
Q

rules of indices
a¹/ᵇ = ?

A

a¹/ᵇ
= ᵇ√a

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19
Q

aᵇ/ᵐ =?

A

a ᵇ/ᵐ
= a⁽¹/ᵐ x ᵇ⁾

e.g.
27 ²/³
= (27 ¹/³)²
= (3)²
= 9

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20
Q

3³

A

27

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21
Q

4³

A

64

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22
Q

5³

A

125

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23
Q

6³

A

216

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24
Q

7³

A

343

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25
Q

8³

A

512

26
Q

9³

A

729

27
Q

10³

A

1000

28
Q

how do you find the prime factors of a number?

A

by making a prime factor tree

29
Q

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

A

HCF = times all the numbers in the middle section
LCM = times all the numbers in the ven-diagram

30
Q

what is a factor?

A

Factors are numbers that divide exactly into another number. For example, the factors of 8 are: 1, 2, 4, 8.

31
Q

what is a multiple?

A

A multiple is a number that a certain number can go into.

e.g. 12 is a multiple of 4

32
Q

what does a negative power do to a fraction?

A

it flips the fraction.

33
Q

how do you work out the mean?

A

you add all the numbers up and then divide it by the amount of numbers you added up.

34
Q

how do you work out the median?

A

by lining up all the numbers in ascending order and then working out the middle number.

35
Q

how do work out the mode?

A

by working out which number is the most common.

36
Q

how do you work out the range?

A

by working out the difference between the largest and smallest number.

37
Q

what is x?
2x + 9 = 15

A

2x + 9 = 15 (minus 9)
2x = 6 (divide by 2)
x = 3

38
Q

what is a?
8(a+3) = 24

A

8(a+3) = 24 (factorise)
8a + 24 = 24 (minus 24)
8a =0 (divide by 8)
a = 0

39
Q

what is x?
4x + 4 = 2x + 9

A

4x + 4 = 2x + 9 (minus 2x)
2x + 4 = 9 (minus 4)
2x = 5 ( divide by 2)
x = 2.5

40
Q

what is x?

3x-1 / x+2 = 2

A

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

41
Q

what is the nth term for this sequence?

5, 8, 11, 14

A

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)

42
Q

what is the method to work out the nth term for a quadratic sequence?

A

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 +/- _

43
Q

how do you factorise this sequence:
x² + 9x + 20

A

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

44
Q

how do you factorise this sequence:
2x² + 7x +6

A

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)

45
Q

how do you rationalise this fraction:
2/√5

A

1) times it by the denominator:
2/√5 x √5/√5 = 2/√5 / √25
2) simplify :
= 2/√5 / 5

46
Q

rationalise this fraction:
5-√6 / √6

A

5-√6 / √6

1) times by the denominator
= 5-√6 / √6 x √6 / √6
2)simplify if you can
= 5√6 - 6 / 6

47
Q

how do you rationalise this fraction?

2 / 4+√2

A

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

48
Q

what calculation do you do to work out the angle of a pie chart a set of the data should have?

A

frequency / total of frequencies x 360

49
Q

what things must a graph include?

A

heading, label, key, pencil lines, and ruler used.

50
Q

what calculation should you do to work out the angle of 1 person on a pie chart?

A

360 / total of frequencies

51
Q

what must you remember when making a stem and leaf diagram?

A

a key

52
Q

what correlation would a graph with the points going from the top left –> the bottom right have?

A

a negative correlation

53
Q

what correlation would a graph with the points going from the bottom left –> the top right have?

A

positive correlation

54
Q

how do you work out frequency density?

A

frequency / class width

55
Q

what type of data is ‘its delicious’

A

qualitative data

56
Q

what do you call data that is numbers?

A

quantitative data

57
Q

what type of data is counted?

A

discrete

58
Q

what type of data is measured?

A

continuous

59
Q

what type of data is ‘goals scored’

A

quantitative, discrete

60
Q

what type of data is the height of a tree?

A

quantitative, continuous

Maths GCSE (3 decks)

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