equations

Question 1

compound growth and decay

Answer 1

N = N0 x (multiplier)^n

Amount after = initial amount x (percentage change multiplier)^number of days/hours/years

Question 2

area of trapezium

Answer 2

1/2 (a+b)hv

Question 3

quadratic equation (solution to ax²+bx+c=0

Answer 3

x= -b ±√(b²-4ac)
—————–
2a

Question 4

Pythagoras’ theorem (right-angled triangle)

Answer 4

a² + b² = c²

Question 5

trigonometry ratios (right-angled triangle)

Answer 5

SOH, CAH, TOA

Question 6

compound measures

Answer 6

distance=speed x time
mass=volume x density
force=pressure x area

Question 7

sine rule (any triangle)

Answer 7

a over sinA = b over sinB = c over sinC
or
sinA over a = sinB over b = sinC over c

Question 8

cosine rule (any triangle)

Answer 8

a² = b² + c² - 2bc cos A.

Question 9

area of triangle (any triangle)

Answer 9

1/2 ab sin C

Question 10

first rule on circle geometry

Answer 10

tangent and radius meet at 90 °

Question 11

second rule of circle geometry

Answer 11

two radii from an isosceles triangle

Question 12

third rule of circle geometry

Answer 12

perpendicular bisector of chord passes through centre of circle

Question 13

fourth rule of circle geometry

Answer 13

angle at centre of circle is twice angle at circumference

Question 14

fifth rule of circle geometry

Answer 14

angle in semicircle is 90 °

Question 15

sixth rule of circle geometry

Answer 15

angles in same segment are equal

Question 16

seventh rule of circle geometry

Answer 16

opposite angles in a cyclic quadrilateral add up to 180 °

Question 17

eighth rule of circle geometry

Answer 17

tangents from same point are same length

Question 18

ninth rule of circle geometry

Answer 18

alternate segment theorem, angle between tangent and chord always equal to angle in opposite segment

Question 19

how to work out LCM

Answer 19

-list all prime factors that appear in either number
-if factor appears more than once
in one of numbers, list it that many times
-multiply these together

Question 20

how to work out HCF

Answer 20

• list all prime factors that appear in both numbers

- multiply all numbers

Question 21

what is difference of two squares (D.O.T.S) (factorising)

Answer 21

a²- b² = (a+b)(a-b)

Question 22

rules for surds

Answer 22

1. √a x √b = √a x b
2. √a/√b = √a/b
3. √a + √b = √a + √b
4. (a+√b)²=(a+√b)(a+√b)= a²+2a√b +b
5. (a+√b)(a-√b)= a²-b
6. a/√b=a√b/b

Question 23

first method for drawing straight-line graphs; table of 3 values

Answer 23

• draw up table with 3 suitable values of x
• find y-values by putting each x-values into equation
• plot points + draw line

Question 24

second method of drawing straight-line graph; =mx+c

Answer 24

• put equation in form y=mx+c
• put dot on y-axis at value of c
• using m,go across and up or down certain number of units. make another dot and repeat until can draw line

Question 25

third method of drawing straight line graph; x=0, y=0

Answer 25

- set x=0 in equation, and find y where it crosses y axis - then set y=0 and find x where it crosses x-axis - mark on 2 points and join with line

Question 26

how to find midpoint on a graph

Answer 26

add x-coordinates and divide by 2 then do same for y-coordinates

Question 27

y is proportional to x

Answer 27

y=kx

Question 28

y is inversely proportional to x

Answer 28

y=k/x

Question 29

how to find position of the median

Answer 29

(n+1)/2 (n=total frequency)

Question 30

how to work out lower quartile Q1

Answer 30

(n+1)/4 (n=number of values)

Question 31

median Q2

Answer 31

(n+1)/2 (n=number of values)

Question 32

upper quartile Q3

Answer 32

3(n+1)/4 (n=number of values)

Question 33

interquartile range

Answer 33

difference between upper quartile and lower quartile

Question 34

median on cumulative frequency graph

Answer 34

go halfway up side, across curve, down and read off bottom scale

Question 35

lower quartile on cumulative frequency graph

Answer 35

go 1/4 up, across to line , down read value

Question 36

upper quartile on cumulative frequency graph

Answer 36

go 3/4 up, across to line , down to value

Question 37

frequency density

Answer 37

frequency / class width

Question 38

frequency

Answer 38

frequency density x class width = area of bar

Question 39

the AND RULE

Answer 39

``` gives P(both events happening P(A) x P(B) ```

Question 40

the OR RULE

Answer 40

gives P(at least one event happens ) P(A) + P(B) - P(A and B) or if events cannot happen together, mutually exclusive P(AorB)=P(A) + P(B)