Dynamic Maths Flashcards
when you multiply two terms, what happens to the number in the powers
add the powers
when you divide two terms, what happens to the numbers in the powers
take away powers
when you take a power of a power (“nested powers”), what happens to the numbers in the powers
multiply the powers
what is the answer when something has a power of zero
1
what does it mean if the number in a power is negative
the answer is a fraction
how do you work out a negative power
move the letter to the bottom and make the power positive
what does it mean if the number in a power is a fraction
it is a root
how do you rationalise the denominator
multiply top and bottom by the surf that is on the bottom of the fraction
how do you factorise using the difference of two squares method
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
what three things are an indication that you have to use the difference of two squares method for factorising
1) only two terms
2) take away sign
3) contains square sign and/or square numbers
when completing the square, how do you get the number beide the bracket
half the coefficient of x
when completing the square, how do you get the number after the bracket
subtract the number in the bracket squared; then add the constant from the question
when do you use squares units
when you are working out an area
when do you use cubed units
when you are working out a volume
when do you use normal units (not squared or cubed)
when you are working out a distance, perimeter or arc length
what is an arc
a curve on the outside of a circle
what is a sector
a slice of the area of the inside of a circle
how do you find the area of a sector of a circle
1) (pi times radius) squared
2) divide by 360
3) multiply by the angle
how do you ging the length of an arc in a circle
a) use (pi times diameter)
b) divide by 360
c) multiply by the angle
what is the formula for the volume of a cylinder
pi times (radius squared) times height
what is the formula for the volume of a cone
one third times pi times (radius squared) times height
what is the formula for the volume of a sphere
four thirds times pi (radius cubed)
what is the formula for the volume of a pyramid
one third times area times height
what are the three steps to add or subtract fractions
a) find lowest common denominator for the denominators
b) multiply the top
c) add or subtract the top lines
d) simplify
how do you multiply two fractions
a) multiply the tops to get the new top
b) multiply the bottoms to get the new bottoms
c) simplify the fraction of needed
how do you divide two fractions
a) flip the second fraction upside down
b) multiply the fractions
c) simplify
what is the formula for the gradient between two coordinate points
y two minutes y one over x two minutes x one
what is the turning point of y equals x plus b squared plus c
(-b,c)
what is the form of an equation of a line of symmetry
x = something
how do you find an x-coordinate if you know the y-coordinate
substitute y into the original equation
how do you find a y-coordinate if you know the x-coordinate
substitute x into the original equation
what are the roots of a quadratic equation
the numbers that make the equation equal to zero
before you can solve a quadratic equation, what must you have on the right hand side
zero
what are the two ways of solving a quadratic equation
1) factorising
2) the quadratic formula
what phrase is an exam question mean is it likely that you need to use the quadratic formula
giving your answer to 2 decimal places
what is the discriminant
b squared minus four a c
if the discriminant is positive, what is the nature of the roots
real and distinct
if the discriminant is zero, what is the nature of the roots
real and equal ( or “real and repeated”)
if the discriminant is negative, what is the nature of the roots
no real roots
if the roots of a quadratic equation are real and distinct, what do we know about the discriminant
it is negative
if there are no real roots to a quadratic equation, what do we know about the discriminant
it is negatice
if the roots of a quadratic equation are real and equal, what do we know about the discriminant
it is zero
what are the steps for sketch a parabola
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
what is the equation of a straight line
y=mx+c
in the general equation of any straight line, where do you look to find the gradient
before the letter x
in the general equation of a straight line, where do you look to find the y-intercept
the letter c
what does it mean if the gradient of a straight line is negative
the line sloped downwards
what is the gradient of a horizontal line
zero
what is the gradient of a vertical line
undefined
what is the equation of a horizontal line
y=something
what is the equation of a vertical line
x=something
what are the three steps to find the equation of a straight line when you knows it’s y-intercept?
1) write down y-intercept
2) calculate gradient between two points
3) put into y = mx + c
what are two steps to find the equation of a straight line when you don’t know it’s y-intercept
1) calculate gradient between two points
2) put into y - b = m(x - a)
when solving an inequation, when do you reverse the inequality sign
when multiplying or dividing by a negative number
how do you solids a system of equations
simultaneous equations
when solving an i equation, why do you do when multiplying or dividing a negative
reverse the inequality sign
what is a tangent to a circle
a line that just touched the edge of the circle at one point
when you have a circle diagram including a tangent, what can you say about angles
the angle between the tangent and the radius is a right angle
what do you know about the angle in a semicircle
it is a right angle
what two places can you find angles in circle diagrams
1) between a tangent and radius
2) angle in a semicircle
what do the three angles in a triangle always add up to make
180 degrees
what do four angles in a quadrilateral always add up to make
360 degrees
what three places can you find equal angles in a diagram
a) in an isosceles triangle
b) in an X shape
c) in a F or Z shape (parallel lines)
what is the formula for the angles inside a regular polygon with n sides
180 minus 360 over n
how do you find the scale factor with similar shapes
length in new shape divided by length in old shapes
how do you find the scale factor for the area info two similar shapes
square the scale factor
how do you find the scale factor for the volume of two similar shapes
cube the scale factor
what are the three steps involved in a pythagoras question
1) square
2) add or take away
3) square root
what do you use to prove whether something is right-angles
use the converse of pythagoras
what are the steps to use the converse of pythagoras
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
in a sin or cos graph, what is the amplitude
the height of the graph
in a sin, cos or tan graph, what is the frequency
how often the repeats itself in 360° for sine or cos, or 180° for tan
in a sin, cos or tan graph, what is the period
how many degrees it takes for the graph to do one complete cycle before it begins to repeat
in a sin, cos or tan graph, what is the phase angle
how far the graph has been shifted to the right
for a graph of the form y=asinbx or y=acosbx, what is a?
The amplitude
for a graph of the form y=asinbx, y=acosbx or y=atanbx, what is b
the frequency
for a graph of the form y=asin(x-b), y=acos(x-b) or y=atan(x-b), what number is b
the phase angle
what are the three steps to solve an equation 0<x<360°
1) rearrange
2) use shift sin/cos/tan
3) use CAST to find the second answer
what fact do you need to know about sin squared x and cos squared x
sine squared x plus cos squared x equals 1
what fact do you need to know about how tan is linked to sin and cos
tax x equals sine x over cos x
