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GCSE Maths EDEXCEL > ze big one > Flashcards

ze big one Flashcards

1
Q

What is the product rule ?

A

Finding the amount of possible outcomes via multiplication.

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2
Q

A spinner that has 18 sections is spun, and a six-sided die is rolled. How many possible outcomes are there ?

A

108

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3
Q

How do you find the LCM ?

A
  • Find the prime factors of each number and place in a venn diagram
  • multiply everything in the venn diagram
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4
Q

How do you find the HCF ?

A
  • Find the prime factors of each number and place in a venn diagram
  • multiply everything in the middle section
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5
Q

Write 0.473473473… (recurring) as a fraction.

A

r = 0.473
10r = 4.734
100r = 47.347
1000r = 473.473

1000r - r = 999r
473.473 - 0.473 = 473
999r = 473
r = 473/999

[473/999]

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6
Q

Express 0.233333… (only the 3 recurring) as a fraction

A

r = 0.233333…
10r = 2.3333…
100r = 23.3333…
100r - 10r = 90r
23.333… - 2.333… = 21
90r = 21
r = 21/90 -> [7/30]

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7
Q

Estimate the cost of astroturf that is £14.30 +18% for every square metre, for a garden that is 7.7m x 13.2m.

A

step 1: estimate area of garden
- 7.7 -> 8
- 13.2 -> 13
- 8 x 13 = 104

step 2: estimate pricing:
- £14.30 -> £14
- 18% -> 20%
- 14 x 20% = £16.80 per sqm

step 3: round current estimated values
- 104sqm -> 100sqm
- £16.80 per sqm -> £17 per sqm

step 4: multiply to get final answer
- 17 x 100 = £1700 for the whole garden

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8
Q

How do you estimate the square root of 95 ?

A
  • find square numbers before and after the number
  • 81 and 100
  • square root is therefore between 9 and 10
  • 95 is closer to 100 than 81, so the square root is likely closer to 10 than 9
  • estimated value = 9.6, 9.7, 9.8
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9
Q

Work out:
3 x 10^6 x 4.5 x 10^-4

A

step 1:
3 x 4.5 = 13.5

step 2:
10^6 x 10^-4 = 10^2

step 3:
- 13.5 x 10^2 IS NOT standard form
- 13.5 -> 1.35
10^2 -> 10^3

final answer = 1.35 x 10^3

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10
Q

Work out:
3 x 10^3 / 600 000

A

step 1:
600 000 -> 6 x 10^5

step 2:
3/6 = 0.5

step 3:
10^3 / 10^5 = 10^-2

step 4:
- 0.5 x 10^-2 IS NOT standard form
- 0.5 -> 5
- 10^-2 -> 10^-3

final answer = 5 x 10^-3

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11
Q

What must be the same before adding or subtracting in standard form ?

A

the power of 10

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12
Q

Calculate:
7.4 x 10^8 + 9.5 x 10^9

A

step 1: make powers of 10 the same
- 9.5 x 10^9 + 7.4 x 10^8
- 10^8 -> 10^9 = x10
- 7.4 -> 0.74
- 9.5 x 10^9 + 0.74 x 10^9

step 2: carry out the calculation
- 9.5 + 0.74 = 10.24
- 10.24 x 10^9

step 3: make final answer in standard form
- 10.24 -> 1.024
- 10^9 -> 10^10

final answer = 1.024 x 10^10

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13
Q

Simplify:
4a + 2a^2 + 5ab - 4 - 3a + 7

A
  • 4a - 3a = a
  • -4 + 7 = 3

final answer: 2a^2 + 5ab + a + 3

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14
Q

What is the value of (p x p x p)^0 ?

A

1

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15
Q

Simplify p^5 / p

A

p^4

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16
Q

Simplify 8b^11 / 2b^5

A

step 1: numbers
- 8/2 = 4

step 2: indices
- 11 - 5 = 6

final answer = 4b^6

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17
Q

Work out:
(3p^-2)^3

A

step 1: numbers
3^3 = 27

step 2: indices
p^-2x3 = p^-6

final answer = 27p^-6

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18
Q

Work out:
(x^-2/x^4)^3

A

step 1: simplify inside the bracket
x^-2/x^4 = x^-6

step 2: raise (multiply) the internal and external powers
-6 x 3 = -18

final answer = x^-18

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19
Q

Evaluate 4^-3

A
  • 4^-3
  • 1/4^3
  • 1/64
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20
Q

Evaluate 2^-5

A
  • 2^-5
  • 1/2^5
  • 1/32
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21
Q

Work out (3/2)^-3

A
  • (3/2)^-3
  • (2/3)^3
  • 2^3/3^3
  • 8/27
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22
Q

Evaluate 9^3/2

A
  • 9^3/2
  • sqrt 9 = 3
  • 3^3 = 27
23
Q

Evaluate 16^1/2

A
  • 16^1/2
  • sqrt 16 = 4
  • 4^1 = 4
24
Q

Evaluate 16^(-3)/2

A
  • 16^(-3)/2
  • 1/16^3/2
  • sqrt 1/16 = 1/4
  • 1/4^3 = 1/64
25
Q

Evaluate (125/8)^(-4)/3

A
  • (125/8)^(-4)/3
  • ## (8/125)^4/3
  • 8^4/3
  • cube rt 8 = 2
  • ## 2^4 = 16
  • 125^4/3
  • cube rt 125 = 5
  • ## 5^4 = 625final answer = 16/625
26
Q

Evaluate (9/16)^(-3)/2

A
  • (9/16)^(-3)/2
  • ## (16/9)^3/2
  • 16^3/2
  • sqrt 16 = 4
  • ## 4^3 = 64
  • 9^3/2
  • sqrt 9 = 3
  • ## 3^3 = 27final answer = 64/27
27
Q

Evaluate (81/100)^3/2

A
  • 81^3/2
  • sqrt 81 = 9
  • ## 9^3 = 729
  • sqrt 100 = 10
  • ## 10^3 = 1000final answer = 729/1000
28
Q

Expand and simplify:
2x + 3(x - 5) -9

A
  • 3(x - 5)
  • 3x - 15
  • 2x +3x - 15 - 9
  • 5x - 26
29
Q

What is 3 - (-4) ?

A

7

30
Q

What is 8 - 9 - (-7) ?

A
  • 8 - 9 = -1
  • -1 - (-7) -> -1 + 7 = 6

final answer = 6

31
Q

Expand and simplify:
(2x + 3)(x + 3a - 2)

A
  • (2x + 3)(x + 3a - 2)
  • 2x * x = 2x^2
  • 2x * 3a = 6ax
  • ## 2x * - 2 = - 4x
  • 3 * x = 3x
  • 3 * 3a = 9a
  • ## 3 * -2 = -62x^2 + 6ax - 4x + 3x + 9a - 6
    2x^2 + 6ax - x + 9a - 6
32
Q

Expand and simplify:
(x + 3)(2x - 1)(x - 2)

A

step 1: ignore one bracket and multiply the other two
- ignore (x - 2)
- (x + 3)(2x - 1)
- x * 2x = 2x^2
- x * - 1 = -x
—-
- 3 * 2x = 6x
- 3 * - 1 = - 3
—-
- 2x^2 - x + 6x - 3
- 2x^2 + 5x - 3

step 2: multiply this expanded bracket with the formerly ignored bracket
- (2x^2 + 5x - 3)(x - 2)
—-
- 2x^2 * x = 2x^3
- 2x^2 * - 2 = -4x^2
—-
- 5x * x = 5x^2
- 5x * - 2 = -10x
—-
- -3 *x = -3x
- -3 * - 2 = 6

step 3: collect like terms again
2x^3 - 4x^2 + 5x^2 - 10x - 3x + 6
2x^3 + x^2 - 13x + 6

33
Q

Factorise:
9ab + 15b^2

A
  • 9ab + 15b^2
  • 3b is common, so goes on outside

final answer = 3b(3a + 5b)

34
Q

Factorise:
15xy + 10x + 20(x^2)y

A
  • 15xy + 10x + 20(x^2)y
  • 5x is common, so goes on outside

final answer = 5x(3y + 2 + 4xy)

35
Q

Factorise 49 - p^2

A
  • difference of two squares
  • (7 - p)(7 + p)
  • 7 * 7 = 49
  • 7 * p = 7p
  • -p * 7 = -7p
  • -p * p = -p^2
  • 49 + 7p - 7p - p^2
  • 7p - 7p cancel out, so leaves with 49 - p^2

final answer = (7 - p)(7 + p)

36
Q

Factorise 36 - 4x^2

A
  • difference of two squares

final answer = (6 - 2x)(6 + 2x)

37
Q

What is sqrt3 x sqrt7 ?

A

sqrt21

38
Q

What is sqrt80 / sqrt4 ?

A

sqrt20

39
Q

Simplify √60

A
  • √t60 = √5 x √12
  • √12 = √4 x √3
  • √60 = √5 x √4 x √3
  • √4 = 2
  • √5 x √3 = √15

√60 simplified = 2√15

40
Q

Simplify:
√125 - 2√45 + (√5 + 2)^2

A

√125 - 2√45 + (√5 + 2)^2

step 1: brackets
- (√5 + 2)^2
- (√5 + 2)(√5 + 2)
- √5 * √5 = 5
- √5 * 2 = 2√5
- 2 * √5 = 2√5
- 2 * 2 = 4
- 5 + 2√5 + 2√5 + 4
- 9 + 4√5

√125 - 2√45 + 9 + 4√5

step 2: simplify √125
- √125 = √25 x √5
- √25 = 5
- √125 = 5√5

step 3: simplify 2√45
- 2√45 = 2 x √9 x √5
- √9 = 3
- 2√45 = 2 x 3 x √5
- 2 x 3 = 6
- 6 x √5 = 6√5

5√5 - 6√5 + 9 + 4√5

step 4: collect like terms
3√5 + 9

final answer = 3√5 + 9

41
Q

Simplify:
√48 + 2√75 + (√3)^2

A

step 1: brackets
- (√3)^2
- (√3)(√3)
- √3 * √3 = 3

step 2: simplify √48
- √48 = √6 x √8
- √8 = √4 x √2
- √4 = 2
- √48 = √6 x √2 x 2
- √6 x √2 = √12
- √12 = √3 x √4
- √4 = 2
- √48 = √3 x 2 x 2
- 2 x 2 = 4
- √48 = 4√3

step 3: simplify 2√75
- 2√75 = 2 x √3 x √25
- √25 = 5
- 2√75 = 2 x 5 x √3
- 2 x 5 = 10
2√75 = 10√3

step 4: collect like terms
- 10√3 + 4√3 + 3
- 14√3 + 3

final answer = 3 + 14√3

42
Q

Simplify:
(7 + √5)/(√5 - 1)
Give your answer in the form of a + b√5

A

step 1: rationalise the denominator
- (7 + √5)/(√5 - 1) x (√5 + 1)/(√5 + 1)
—-
- (7 + √5)(√5 + 1)
- 7 * √5 = 7√5
- 7 * 1 = 7
- √5 * √5 = 5
- √5 * 1 = √5
- (7√5 + 7 + 5 + √5)
- (8√5 + 12)
—-
- (√5 - 1)(√5 + 1)
- √5 * √5 = 5
- √5 * 1 = √5
- -1 * √5 = -√5
- -1 * 1 = -1
- (5 + √5 - √5 - 1)
- (4)
—-
new fraction = (8√5 + 12)/4

step 2: simplify fraction
- 12/4 = 3
- 8√5/4 = 2√5

final answer = 3 + 2√5

43
Q

Solve 4 + b = 19

A

4 + b = 19
b = 15

44
Q

Solve 3 = (14 - x)/4

A

3 = (14 - x)/4
12 = 14 - x
x + 12 = 14
x = 2

45
Q

Solve 2x + 3 = 5x - 12

A

2x + 3 = 5x - 12
2x + 15 = 5x
15 = 3x
5 = x

46
Q

Solve 4a - 5 = 7 + 6a

A

4a - 5 = 7 + 6a
4a = 12 + 6a
-2a = 12
2a = -12
a = -6

47
Q

Rearrange 6a = 3 + b/2 to make b the subject

A

6a = 3 + b/2
6a - 3 = b/2
2(6a - 3) = b
12a - 6 = b

48
Q

Make x the subject:
5(x - 3) = 4y(1 - 3x)

A

5(x - 3) = 4y(1 - 3x)
5x - 15 = 4y - 12xy
5x + 12xy - 15 = 4y
5x + 12xy = 4y + 15
x(5 + 12y) = 4y + 15
x = (4y + 15)/(5 + 12y)

49
Q

Solve x^2 + 10x + 16 = 0

A

step 1: find two factors of 16 that add to 10
2 x 8 = 10

step 2: factorise using these factors and double brackets
(x + 2)(x + 8) = 0

step 3: invert the values in the brackets to find the two values for x
x = -2
x = -8

50
Q

Solve 2x^2 + 9x + 10 = 0

A

step 1: multiply the coefficient of x^2 and the integer at the end of the equation
2 x 10 = 20

step 2: find two factors of 20 that add to 9
4 x 5 = 20

step 3: factorise using these values
(2x + 4)(x + 5) = 0

step 4: invert values in brackets to get values of x (solve where necessary)
x = -5
2x = -4 -> x = -2

51
Q

Solve 3x^2 + 10x - 8 = 0

A

step 1: multiply the coefficient and normal number
3 x -8 = -24

step 2: find factors of -24 that add to 10
-2 x 12 = -24

step 3: factorise with these values
(3x + 12)(x - 2) = 0

step 4: invert bracket values to find the value of x (solve where necessary)
x = 2
3x = -12 -> x = -4

52
Q

Solve 3x^2 + 7x - 13 = 0 using the quadratic formula

A

quadratic formula = x = (-b +- √b^2 - 4ac)/2a

b = 3
a = 7
c = -13
- input values into calculator
- x = 1.22 (2 d.p)
- x = -3.55 (2 d.p)

53
Q

What is the quadratic formula ?

A

x = (-b +- √b^2 - 4ac)/2a

GCSE Maths EDEXCEL (10 decks)

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