maths

Question 1

factor theorem

Answer 1

if f(x) is a polynomial and f(a)=0, then (x-a) is a factor of f(x)

Question 2

modulus

Answer 2

size of a number

Question 3

distance between two points

Answer 3

square root of (x2-x1)^2 + (y2-y1)^2

Question 4

midpoint of a line

Answer 4

([x1+x2]/2 , [y1+y2]/2)

Question 5

condition for circles to touch

Answer 5

d=r1+r2

Question 6

condition for circles to intersect

Answer 6

d

Question 7

conditions for circles to not intersect or touch

Answer 7

d>r1+r2

Question 8

conditions for a circle to be inside another circle

Answer 8

d=r1-r2

Question 9

conditions to be a circle (not ellipse)

Answer 9

coefficients of x^2 and y^2 are the same

xs and ys don’t multiply together (no xy)

Question 10

when is a function of f(x) increasing

Answer 10

when f’(x) > 0

Question 11

when is a function of f(x) decreasing

Answer 11

when f’(x) <0

Question 12

when is a stationary point on a curve a minimum

Answer 12

when d^2y/dx^2>0

Question 13

when is a stationary point on a curve a maximum

Answer 13

when d^2y/dx^2 < 0

Question 14

a^x=b ——>

Answer 14

x=log a (b)

Question 15

log a (b)^n ——>

Answer 15

nlog a (b)

Question 16

log A + log B ——>

Answer 16

log AB

Question 17

log A - log B ——>

Answer 17

log (A/B)

Question 18

formula for nth term of an arithmetic sequence

Answer 18

u n = a +(n-1)d

Question 19

sum of first n terms of an arithmetic series (d)

Answer 19

Sn = n/2 (2a + (n-1)d)

Question 20

sum of first n terms of an arithmetic series (l)

Answer 20

Sn = n/2 (a + l)

Question 21

formula for nth term of geometric sequence

Answer 21

un = ar^ (n-1)

r is common ratio

Question 22

formulas for nth term of geometric series

Answer 22

Sn = a(1-r^n)/1-r use when r<1

Sn= a(r^n-1)/r-1 use when r>1

Question 23

sum to infinity equation

when is it only true

Answer 23

S infinity = a/1-r

only true when -1

Question 24

arc length equation

Answer 24

l=rx

x is angle in radians

Question 25

area of sector

Answer 25

A=1/2 r^2 x

x is angle in radians

Question 26

area of segment

Answer 26

A= 1/2 r^2 (x-sinx )

x is angle in radians

Question 27

sin2A

Answer 27

2sinAcosA

Question 28

cos2A

Answer 28

cos^2A - sin^2A

or

2cos^2A-1

or

1-2sin^2A

Question 29

tan2A

Answer 29

2tanA/1-tan^2A

Question 30

chain rule

Answer 30

dy/dx = dy/du x du/dx

Question 31

product rule

Answer 31

dy/dx= uv’+vu’

Question 32

quotient rule

Answer 32

dy/dx= (vu’-uv’)/v^2

Question 33

what’s a point of inflection

Answer 33

a point at which f’’(x) changes sign

Question 34

when is a function f(x) concave

Answer 34

if f’’(x) is less than or equal to 0 for every value in that interval

Question 35

when is a function f(x) convex

Answer 35

if f’’(x) is greater than or equal to 0

Question 36

how do you find a point of inflection

Answer 36

show that f’’(x)=0 at that point and that it has different signs on either side of that point

Question 37

when does a quadratic have two real roots

Answer 37

when b^2 -4ac >0

Question 38

when does a quadratic have one real root

Answer 38

when b^2-4ac=0

Question 39

when does a quadratic have no real roots

Answer 39

when b^2-4ac<0

Question 40

rational number

Answer 40

a number that can be expressed as a/b with a and b both being non-zero integers