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GCSE Maths > Final Exams Notes > Flashcards

Final Exams Notes Flashcards

1
Q

What does a sign change signify in iteration?

A

That there is a solution between the two values you have just put in, therefore you must try more values between those two.

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2
Q

When you use an iteration machine, when do you know when you have found the solution?

A

When you find two values that are equal when rounded to the desired number of decimal places.

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3
Q

What is the equation for a circle with centre (0,0) and radius r?

A

r^2= x^2 + y^2

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4
Q

Write out the initial bracket for completing the square

A

(x + b/2)^2 - (balancing number)

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5
Q

When a is positive what does the completing the square balancing number tell you?

A

the minimum y point.

The minimum y point is (-b/2, balancing number)

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6
Q

If the balancing number is positive, what does this tell you?

A

There are no real roots

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7
Q

What is the difference of two squares?

A

a^2-b^2 = (a + b)(a - b)

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8
Q

What is a geometric sequence?

A

One where the term to term rule is to multiply or divide by the same value.

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9
Q

How do you find the multiplier or divider in a geometric sequence?

A

Divide a term by the previous term

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10
Q

What are the equations for exponential graphs?

A 
y= k^x
y= k^-x
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11
Q

Under what conditions do exponential graphs curve up?

A

If k>1 and the power is positive

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12
Q

If x^2 > a^2

A

x > a or x < -a

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13
Q

If x^2 < a^2

A

-a < x < a

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14
Q

Explain the graph transformation: y = f (x-1)

A

Shifts to the right

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15
Q

Explain the graph transformation: y = f (x) -1

A

Shifts down

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16
Q

Explain the graph transformation: y = f (-x)

A

Reflects in the x axis

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17
Q

Explain the graph transformation: y = f (2x)

A

Squashed by stretch factor 2

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18
Q

Explain the graph transformation: y = 2f (x)

A

Height doubles

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19
Q

State the alternate segment theorem

A

The angle between a tangent and a chord is always equal to the angle made at the circumference by the two lines drawn from the ends of the chord.

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20
Q

What does “the angle subtended at” mean

A

The angle made at

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21
Q

How do you read column vectors?

A

The numerator is the horizontal movement

The denominator is the vertical movement

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22
Q

How should you write vectors?

A

Underline them

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23
Q

What does
—>
AB

mean?

A

Go from point A to point B

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24
Q

What is the consequence of multiplying a vector by a positive number?

A

Magnitude is changed

25
Q

What are the consequences of multiplying a vector by a negative number?

A

Direction and magnitude may change

26
Q

How do you add column vectors?

A

Add the tops then add the bottoms

27
Q

How do you find an unknown vector?

A

Find any route there made up of known vectors then simplify

28
Q

How do you show vectors to be on a straight line?

A

Show that the vectors are all in the same direction by showing that they are multiples of each other.

29
Q

How do you prove congruency?

A

SSS, AAS, SAS, RHS

30
Q

How do you prove similarity?

A

All the sides are proportional,
All the angles are the same,
Any two sides are proportional and the angle between them the same.

31
Q

How are scale factors calculated?

A

old length

32
Q

Explain scale factors for sides, areas and volumes

A

The sides are n times bigger
The areas are n^2 times bigger
The volumes are n^3 times bigger

33
Q

How do you calculate scale factor n^2

A

Old area

34
Q

How do you calculate scale factor n^3

A

Old volume

35
Q

What is the lower quartile?

A

The value 25% of the way through a data set

36
Q

What is the median?

A

The value 50% of the way through the data set

37
Q

What is the upper quartile?

A

The value 75% of the way through the data set

38
Q

In probability, how is “and” written?

A

n

39
Q

In probability, how is “or” written?

A

u

40
Q

How is relative frequency calculated?

A

Total no. outcomes

41
Q

How many probabilities when rolling 4 dice?

A

6 x 6 x 6 x6

42
Q

How do you add and subtract in standard form?

A

Make sure the powers are all the same

43
Q

Define equation

A

A statement that the values of two expressions are equal

44
Q

Define formula

A

A rule written with mathematical symbols

45
Q

Define identity

A

An equation that is true regardless of the values chosen

46
Q

Define term

A

A single number or variable

47
Q

Define expression

A

Numbers, symbols and operators grouped together to show the value of something.

48
Q

Define inequality

A

An equation that uses < and > rather than =

49
Q

Define factor

A

A number that multiplies with another number to produce a multiple

50
Q

What do functions mean?

A

The function f takes a value for x, multiplies it by 5 then adds 2

51
Q

Equation for a line (not y = mx +c)

A

y - y1 = m (x - x1)

52
Q

For inequalities on number lines, when do you use dotted and filled lines?

A

Solid lines means including points on the line

Dotted lines means not including points on the line

53
Q

For inequalities on graphs, when do you use open and closed dots

A

Open dots, not including the values

Closed dots, including the values

54
Q

How do you calculate the sum of the internal angles of any polygon with n sides

A

180(n-2)

55
Q

What is the sine rule?

A

a/sinA = b/sinB = c/sinC

56
Q

What is the normal cosine rule?

A

a^2 = b^2 + c^2 - 2bc cos A

57
Q

What is the cosine rule for finding angles?

A

Cos A = b^2 + c^2 - a^2
—————————–
2bc

58
Q

How do you calculate the area of a triangle?

A

0.5 ab sin c

GCSE Maths (3 decks)

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