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National 5 Maths > Dynamic Maths > Flashcards

Dynamic Maths Flashcards

1
Q

when you multiply two terms, what happens to the number in the powers

A

add the powers

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2
Q

when you divide two terms, what happens to the numbers in the powers

A

take away powers

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3
Q

when you take a power of a power (“nested powers”), what happens to the numbers in the powers

A

multiply the powers

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4
Q

what is the answer when something has a power of zero

A

1

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5
Q

what does it mean if the number in a power is negative

A

the answer is a fraction

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6
Q

how do you work out a negative power

A

move the letter to the bottom and make the power positive

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7
Q

what does it mean if the number in a power is a fraction

A

it is a root

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8
Q

how do you rationalise the denominator

A

multiply top and bottom by the surf that is on the bottom of the fraction

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9
Q

how do you factorise using the difference of two squares method

A

you have two brackets that are almost the same - except that one has a plus sign in and the other has a minus sign in

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10
Q

what three things are an indication that you have to use the difference of two squares method for factorising

A

1) only two terms
2) take away sign
3) contains square sign and/or square numbers

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11
Q

when completing the square, how do you get the number beide the bracket

A

half the coefficient of x

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12
Q

when completing the square, how do you get the number after the bracket

A

subtract the number in the bracket squared; then add the constant from the question

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13
Q

when do you use squares units

A

when you are working out an area

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14
Q

when do you use cubed units

A

when you are working out a volume

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15
Q

when do you use normal units (not squared or cubed)

A

when you are working out a distance, perimeter or arc length

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16
Q

what is an arc

A

a curve on the outside of a circle

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17
Q

what is a sector

A

a slice of the area of the inside of a circle

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18
Q

how do you find the area of a sector of a circle

A

1) (pi times radius) squared
2) divide by 360
3) multiply by the angle

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19
Q

how do you ging the length of an arc in a circle

A

a) use (pi times diameter)
b) divide by 360
c) multiply by the angle

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20
Q

what is the formula for the volume of a cylinder

A

pi times (radius squared) times height

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21
Q

what is the formula for the volume of a cone

A

one third times pi times (radius squared) times height

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22
Q

what is the formula for the volume of a sphere

A

four thirds times pi (radius cubed)

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23
Q

what is the formula for the volume of a pyramid

A

one third times area times height

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24
Q

what are the three steps to add or subtract fractions

A

a) find lowest common denominator for the denominators
b) multiply the top
c) add or subtract the top lines
d) simplify

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25
Q

how do you multiply two fractions

A

a) multiply the tops to get the new top
b) multiply the bottoms to get the new bottoms
c) simplify the fraction of needed

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26
Q

how do you divide two fractions

A

a) flip the second fraction upside down
b) multiply the fractions
c) simplify

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27
Q

what is the formula for the gradient between two coordinate points

A

y two minutes y one over x two minutes x one

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28
Q

what is the turning point of y equals x plus b squared plus c

A

(-b,c)

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29
Q

what is the form of an equation of a line of symmetry

A

x = something

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30
Q

how do you find an x-coordinate if you know the y-coordinate

A

substitute y into the original equation

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31
Q

how do you find a y-coordinate if you know the x-coordinate

A

substitute x into the original equation

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32
Q

what are the roots of a quadratic equation

A

the numbers that make the equation equal to zero

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33
Q

before you can solve a quadratic equation, what must you have on the right hand side

A

zero

34
Q

what are the two ways of solving a quadratic equation

A

1) factorising
2) the quadratic formula

35
Q

what phrase is an exam question mean is it likely that you need to use the quadratic formula

A

giving your answer to 2 decimal places

36
Q

what is the discriminant

A

b squared minus four a c

37
Q

if the discriminant is positive, what is the nature of the roots

A

real and distinct

38
Q

if the discriminant is zero, what is the nature of the roots

A

real and equal ( or “real and repeated”)

39
Q

if the discriminant is negative, what is the nature of the roots

A

no real roots

40
Q

if the roots of a quadratic equation are real and distinct, what do we know about the discriminant

A

it is negative

41
Q

if there are no real roots to a quadratic equation, what do we know about the discriminant

A

it is negatice

42
Q

if the roots of a quadratic equation are real and equal, what do we know about the discriminant

A

it is zero

43
Q

what are the steps for sketch a parabola

A

a) factorise to find the roots
b) substitute x=0 to find the y-intercept
c) complete the square to find the turning point
d) identify whether it is happy or unhappy

44
Q

what is the equation of a straight line

A

y=mx+c

45
Q

in the general equation of any straight line, where do you look to find the gradient

A

before the letter x

46
Q

in the general equation of a straight line, where do you look to find the y-intercept

A

the letter c

47
Q

what does it mean if the gradient of a straight line is negative

A

the line sloped downwards

48
Q

what is the gradient of a horizontal line

A

zero

49
Q

what is the gradient of a vertical line

A

undefined

50
Q

what is the equation of a horizontal line

A

y=something

51
Q

what is the equation of a vertical line

A

x=something

52
Q

what are the three steps to find the equation of a straight line when you knows it’s y-intercept?

A

1) write down y-intercept
2) calculate gradient between two points
3) put into y = mx + c

53
Q

what are two steps to find the equation of a straight line when you don’t know it’s y-intercept

A

1) calculate gradient between two points
2) put into y - b = m(x - a)

54
Q

when solving an inequation, when do you reverse the inequality sign

A

when multiplying or dividing by a negative number

55
Q

how do you solids a system of equations

A

simultaneous equations

56
Q

when solving an i equation, why do you do when multiplying or dividing a negative

A

reverse the inequality sign

57
Q

what is a tangent to a circle

A

a line that just touched the edge of the circle at one point

58
Q

when you have a circle diagram including a tangent, what can you say about angles

A

the angle between the tangent and the radius is a right angle

59
Q

what do you know about the angle in a semicircle

A

it is a right angle

60
Q

what two places can you find angles in circle diagrams

A

1) between a tangent and radius
2) angle in a semicircle

61
Q

what do the three angles in a triangle always add up to make

A

180 degrees

62
Q

what do four angles in a quadrilateral always add up to make

A

360 degrees

63
Q

what three places can you find equal angles in a diagram

A

a) in an isosceles triangle
b) in an X shape
c) in a F or Z shape (parallel lines)

64
Q

what is the formula for the angles inside a regular polygon with n sides

A

180 minus 360 over n

65
Q

how do you find the scale factor with similar shapes

A

length in new shape divided by length in old shapes

66
Q

how do you find the scale factor for the area info two similar shapes

A

square the scale factor

67
Q

how do you find the scale factor for the volume of two similar shapes

A

cube the scale factor

68
Q

what are the three steps involved in a pythagoras question

A

1) square
2) add or take away
3) square root

69
Q

what do you use to prove whether something is right-angles

A

use the converse of pythagoras

70
Q

what are the steps to use the converse of pythagoras

A

1) square the longest length
2) square and add the two shorter lengths
3) if the answers are equal it’s right-angled
if not equal, it’s not right-angled

71
Q

in a sin or cos graph, what is the amplitude

A

the height of the graph

72
Q

in a sin, cos or tan graph, what is the frequency

A

how often the repeats itself in 360° for sine or cos, or 180° for tan

73
Q

in a sin, cos or tan graph, what is the period

A

how many degrees it takes for the graph to do one complete cycle before it begins to repeat

74
Q

in a sin, cos or tan graph, what is the phase angle

A

how far the graph has been shifted to the right

75
Q

for a graph of the form y=asinbx or y=acosbx, what is a?

A

The amplitude

76
Q

for a graph of the form y=asinbx, y=acosbx or y=atanbx, what is b

A

the frequency

77
Q

for a graph of the form y=asin(x-b), y=acos(x-b) or y=atan(x-b), what number is b

A

the phase angle

78
Q

what are the three steps to solve an equation 0<x<360°

A

1) rearrange
2) use shift sin/cos/tan
3) use CAST to find the second answer

79
Q

what fact do you need to know about sin squared x and cos squared x

A

sine squared x plus cos squared x equals 1

80
Q

what fact do you need to know about how tan is linked to sin and cos

A

tax x equals sine x over cos x

National 5 Maths (1 decks)

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