Formula Not Given

Question 1

Quadratic formula

Answer 1

Minus b plus or minus the square root of b squared minus 4ac all over 2a

Question 2

The discriminant

Answer 2

B squared -4ac

Discriminant > 0 2 real roots

Discriminant = 0 1 repeated root

Discriminant < 0 0 real roots

Question 3

Modulus ( |x| )

Answer 3

|x| means the positive value of x

Question 4

a^m multiplied by a^n

Answer 4

a^m+n

Question 5

a^m divided by a^n

Answer 5

a^m-n

Question 6

a^0

Answer 6

1

Question 7

a^-m

Answer 7

1/a^m

Question 8

a^1/n

Answer 8

n root of a

Question 9

(a^m)^n

Answer 9

a^mn

Question 10

Gradient

Answer 10

Change in y over change in x

Question 11

Equation for a circle with centre (a,b) and radius r

Answer 11

(x-a)^2 + (y-b)^2 = r^2

Question 12

Log(x) + log(y)

Answer 12

Log(xy)

Question 13

Log(x^n)

Answer 13

nLog(x)

Question 14

Log(x) - log(y)

Answer 14

Log(x/y)

Question 15

Log(n root x)

Answer 15

1/nLog(x)

Question 16

Log(1)

Answer 16

0

Question 17

Sin(x)/cos(x)

Answer 17

Tan(x)

Question 18

Sin^2(x) + cos^2(x)

Answer 18

1

Question 19

Area of a triangle

Answer 19

1/2abSin(C)

Question 20

Sine rule

Answer 20

a/SinA = b/SinB = c/SinC

Flip for angles

Question 21

2 pi in degrees

Answer 21

360 degrees

Question 22

Arc length (for radians)

Answer 22

r times theta

Question 23

Area of a sector (for radians)

Answer 23

1/2 r^2 times theta

Question 24

Differentiation from first principles

Answer 24

F’(x) = lim (h->0) = f(x+h) - f(x)
——————
h

Question 25

Differential of e^kx

Answer 25

ke^kx

Question 26

Differential of ln(x)

Answer 26

1/x

Question 27

Differential of sin(kx)

Answer 27

kcos(kx)

Question 28

Differential of cos(kx)

Answer 28

-ksin(kx)

Question 29

Product rule

Answer 29

VU’+UV’

Question 30

Quotient rule

Answer 30

VU’-UV’ ———— V^2

Question 31

Chain rule

Answer 31

Multiply the bracket by the old power and the differential of the inside of the bracket and bring the power down by one.

Question 32

Integral of e^kx

Answer 32

1/k e^kx

Question 33

Integral of 1/x

Answer 33

ln|x|

Question 34

Integral of sin(kx)

Answer 34

-1/k cos(kx)

Question 35

Integral of cos(kx)

Answer 35

1/k sin(kx)

Question 36

Sec^2(x) is exactly equal to

Answer 36

1 + tan^2(x)

Question 37

Cosec^2(x) is exactly equal to

Answer 37

1 + cot^2(x)

Question 38

Sin(2x) =

Answer 38

2sin(x)cos(x)

Question 39

Cos(2x) =

Answer 39

Cos^2(x)-sin^2(x) OR 2cos^2(x) - 1 OR 1 - 2sin^2(x)

Question 40

Tan(2x) =

Answer 40

2tan(x) —————— 1- tan^2(x)

Question 41

SUVAT constant acceleration equations

Answer 41

s = ut + 1/2at^2 s = 1/2(u + v)t s = vt - 1/2at^2 v = u + at v^2 = u^2 + 2as

Question 42

Non-constant acceleration

Answer 42

a differentiates to v and v differentiates to s s integrates to v and v integrates to a

Question 43

Individual data -> mean

Answer 43

X bar = sum of all x values —————————— n

Question 44

Grouped data -> mean

Answer 44

X bar = the sum of fx ——————— n

Question 45

sin 2A ≡

Answer 45

2sin A cos A

Question 46

cos 2A ≡

Answer 46

cos^2(A) – sin^2(A) OR 2cos^2(A) – 1 OR 1 – 2sin^2A

Question 47

tan 2A ≡

Answer 47

2 tan A ---------------- 1 – tan^2(A)

Question 48

arc length (for degrees)

Answer 48

theta/360 x 2(pi)r

Question 49

area of sector (for degrees)

Answer 49

theta/360 x pi(r^2)

Question 50

area of a segment (for radians)

Answer 50

1/2r^2 ( theta - sin(theta) )

Question 51

area of a segment (for degrees)

Answer 51

1/2r^2 [ (pi/180)theta - sin(theta) ]

Question 52

length of a chord

Answer 52

(cosine rule) | a^2 = b^2 + c^2 - 2bcCos(A)

Question 53

cosine rule

Answer 53

(for sides) a^2 = b^2 + c^2 - 2bcCos(A) (for angles) cos(A) = b^2 + c^2 - a^2 ---------------------- 2bc

Question 54

small angle approximation of sin(x)

Answer 54

sin(x) = x

Question 55

small angle approximation of cos(x)

Answer 55

cos(x) = 1 - 1/2 x^2

Question 56

small angle approximation of tan(x)

Answer 56

tan(x) = x