Core Modus

Question 1

f(x) is continuous at x=a if?

Answer 1

f(a) exists

lim(x>a) f(x) exists

lim(x>a) f(x) = f(a)

Question 2

x intercept is where?

Answer 2

y=0

and vice versa

means make y=0 in equation from standard form

Question 3

equation of a given line?

Answer 3

y-y₁ = m(x-x₁)

where x₁ & y₁ is a point on the line

Question 4

when given two points

(x₁, y₁) (x₂, y₂)

Answer 4

rise over run to find gradient

m = y2-y1/x2-x1

Question 5

perpendicular lines

Answer 5

meet at right angles

m₁*m₂ = -1 always

Question 6

parallel lines

Answer 6

always have the same gradient

Question 7

to get m (gradient) you must

Answer 7

convert to gradient intercept form

Question 8

quadratic function

form?

Answer 8

y = ax²+bx+c

Question 9

line of symmetry formula

Answer 9

x = -b/2a

from ax²+bx+c

Question 10

find Turning Point

Answer 10

substitute the line of symmetry into x of

y = ax²+bx+c

if Line of Symmetry x = -1 and evaluating gives y = -4

then Turning Point is (-1, -4)

Question 11

cubic function polynomial form

Answer 11

f(x) = ax³+bx²+cx+d

Question 12

quartic function polynomial form

Answer 12

f(x) = ax⁴+bx³+cx²+dx+e

Question 13

3/5 / 5

Answer 13

3/5 / 5

3/25

Question 14

3/5 * 5

Answer 14

3/5 * 5

3

Question 15

-x/3

also looks like

Answer 15

• 1/3 x

Question 16

y = -3x+4

make y negative

Answer 16

-y = 3x-4

inverting all values keeps the balance

Question 17

find inverse function

template?

Answer 17

• sub y for f(x)
• make x subject
• switch x and y
• write f^-1(x) instead of y

Question 18

ln(4)-3/2 =

Answer 18

ln(4)-3/2 =

1/2(ln(4)-3)

Question 19

inverse function of y = e^x

Answer 19

inverse function of y = e^x

y = lnx

Question 20

find Period

Answer 20

2π/B

where B is the coefficient of x

example: y = cos2x

B = 2

Question 21

definition of the Derivative

Answer 21

dy/dx

= lim(h>0) f(x+h)-f(x)/h

rise/run

Question 22

d/dx C

Answer 22

= 0

the derivative of any constant even when negative are equal to 0.

No rise, only run.

Question 23

dy/dx of y = 3x

Answer 23

dy/dx of y = 3x

dy/dx

= d/dx 3x

= 3

Always equal to the coefficient/ gradient

Question 24

table of derivatives

Answer 24

c ^{_{<em>(a constant)</em>}} 0

axⁿ nax^n-1

sinx ^{_{<em>(x in radians)</em>}} cosx

cosx ^{_{(x in radians)}} -sinx

e^{ax _{(a is constant)}} ae^ax

lnx or log_ex 1/x or x^-1

Question 25

dy/dx _16/x_

Answer 25

**dy/dx _16/x_** = 16x^-1 = (-1)16x^-2 = -16x^-2 = -16/x²

Question 26

dy/dx 5√x

Answer 26

**dy/dx 5√x** = 5x^1/2 = _1/2_(5)x^{- 1/2} = _5/2_x^{- 1/2} = _5/2√x_

Question 27

dy/dx 7e^4x

Answer 27

**dy/dx 7e^4x** = 7 d/dx e^4x = 7 \* 4e^4x = 28e^4x

Question 28

dy/dx 2lnx

Answer 28

**dy/dx 2lnx** = d/dx 2lnx = 2 d/dx lnx = 2 \* 1/x = 2/1 \* 1/x = 2/x

Question 29

dy/dx 3cosx

Answer 29

**dy/dx 3cosx** = 3 d/dx cosx = -3sinx

Question 30

dy/dx -√2 sinx

Answer 30

**dy/dx -√2 sinx** = -√2 d/dx sinx = -√2 cosx

Question 31

(6+x)(2-x) x = ?

Answer 31

**(6+x)(2-x)** x = -6 or 2 similar to horizontal shift

Question 32

y = -x² parabola shape?

Answer 32

negative frowney face

Question 33

graph of a function vs its derivative -y = 12-4x-x²

Answer 33

**function** - y = 12-4x-x² x-int @ y = 0 - 0 = 12-4x-x2 = (6+x)(2-x) = -6 or 2 **derivative** dy/dx = -4 -2x x-int @ dy/dx = 0 0 = -4 -2x 4 = -2x 4/-2 = x = -2

Question 34

turning points occur when

Answer 34

dy/dx = 0