Dynamic Maths

Question 1

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

Answer 1

add the powers

Question 2

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

Answer 2

take away powers

Question 3

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

Answer 3

multiply the powers

Question 4

what is the answer when something has a power of zero

Answer 4

1

Question 5

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

Answer 5

the answer is a fraction

Question 6

how do you work out a negative power

Answer 6

move the letter to the bottom and make the power positive

Question 7

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

Answer 7

it is a root

Question 8

how do you rationalise the denominator

Answer 8

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

Question 9

how do you factorise using the difference of two squares method

Answer 9

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

Question 10

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

Answer 10

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

Question 11

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

Answer 11

half the coefficient of x

Question 12

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

Answer 12

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

Question 13

when do you use squares units

Answer 13

when you are working out an area

Question 14

when do you use cubed units

Answer 14

when you are working out a volume

Question 15

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

Answer 15

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

Question 16

what is an arc

Answer 16

a curve on the outside of a circle

Question 17

what is a sector

Answer 17

a slice of the area of the inside of a circle

Question 18

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

Answer 18

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

Question 19

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

Answer 19

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

Question 20

what is the formula for the volume of a cylinder

Answer 20

pi times (radius squared) times height

Question 21

what is the formula for the volume of a cone

Answer 21

one third times pi times (radius squared) times height

Question 22

what is the formula for the volume of a sphere

Answer 22

four thirds times pi (radius cubed)

Question 23

what is the formula for the volume of a pyramid

Answer 23

one third times area times height

Question 24

what are the three steps to add or subtract fractions

Answer 24

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

Question 25

how do you multiply two fractions

Answer 25

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

Question 26

how do you divide two fractions

Answer 26

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

Question 27

what is the formula for the gradient between two coordinate points

Answer 27

y two minutes y one over x two minutes x one

Question 28

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

Answer 28

(-b,c)

Question 29

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

Answer 29

x = something

Question 30

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

Answer 30

substitute y into the original equation

Question 31

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

Answer 31

substitute x into the original equation

Question 32

what are the roots of a quadratic equation

Answer 32

the numbers that make the equation equal to zero

Question 33

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

Answer 33

zero

Question 34

what are the two ways of solving a quadratic equation

Answer 34

1) factorising 2) the quadratic formula

Question 35

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

Answer 35

giving your answer to 2 decimal places

Question 36

what is the discriminant

Answer 36

b squared minus four a c

Question 37

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

Answer 37

real and distinct

Question 38

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

Answer 38

real and equal ( or “real and repeated”)

Question 39

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

Answer 39

no real roots

Question 40

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

Answer 40

it is negative

Question 41

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

Answer 41

it is negatice

Question 42

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

Answer 42

it is zero

Question 43

what are the steps for sketch a parabola

Answer 43

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

Question 44

what is the equation of a straight line

Answer 44

y=mx+c

Question 45

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

Answer 45

before the letter x

Question 46

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

Answer 46

the letter c

Question 47

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

Answer 47

the line sloped downwards

Question 48

what is the gradient of a horizontal line

Answer 48

zero

Question 49

what is the gradient of a vertical line

Answer 49

undefined

Question 50

what is the equation of a horizontal line

Answer 50

y=something

Question 51

what is the equation of a vertical line

Answer 51

x=something

Question 52

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

Answer 52

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

Question 53

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

Answer 53

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

Question 54

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

Answer 54

when multiplying or dividing by a negative number

Question 55

how do you solids a system of equations

Answer 55

simultaneous equations

Question 56

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

Answer 56

reverse the inequality sign

Question 57

what is a tangent to a circle

Answer 57

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

Question 58

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

Answer 58

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

Question 59

what do you know about the angle in a semicircle

Answer 59

it is a right angle

Question 60

what two places can you find angles in circle diagrams

Answer 60

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

Question 61

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

Answer 61

180 degrees

Question 62

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

Answer 62

360 degrees

Question 63

what three places can you find equal angles in a diagram

Answer 63

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

Question 64

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

Answer 64

180 minus 360 over n

Question 65

how do you find the scale factor with similar shapes

Answer 65

length in new shape divided by length in old shapes

Question 66

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

Answer 66

square the scale factor

Question 67

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

Answer 67

cube the scale factor

Question 68

what are the three steps involved in a pythagoras question

Answer 68

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

Question 69

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

Answer 69

use the converse of pythagoras

Question 70

what are the steps to use the converse of pythagoras

Answer 70

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

Question 71

in a sin or cos graph, what is the amplitude

Answer 71

the height of the graph

Question 72

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

Answer 72

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

Question 73

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

Answer 73

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

Question 74

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

Answer 74

how far the graph has been shifted to the right

Question 75

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

Answer 75

The amplitude

Question 76

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

Answer 76

the frequency

Question 77

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

Answer 77

the phase angle

Question 78

what are the three steps to solve an equation 0

Answer 78

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

Question 79

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

Answer 79

sine squared x plus cos squared x equals 1

Question 80

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

Answer 80

tax x equals sine x over cos x