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Question 1

How to use discriminant to see if equation has one repeated root

Answer 1

b² - 4ac = 0

Question 2

How to use discriminant to see if equation has no roots

Answer 2

b² - 4ac < 0

Question 3

How to use discriminant to see if equation has two distinct real roots

Answer 3

b² - 4ac > 0

Question 4

How to use set notation for inequalities

Answer 4

{x: x>3 }
n is and, u is or

Question 5

How to draw positive and negative quadratics

Answer 5

Positive is U shaped. Negative is n shaped

Question 6

How to draw positive and negative cubics

Answer 6

Positive point upwards. Negative point downwards. The graph is a sideways s shape.

Question 7

How to draw positive and negative quartics

Answer 7

The positive graphs are W shaped. The negative graphs are M shaped.

Question 8

How does
y = f(x) + a
transform a graph

Answer 8

Moves it upwards by a
(a units in the direction of the positive y- axis)

Question 9

How does
y = f(x) - a
transform a graph

Answer 9

Moves it downwards by a
(a units in the direction of the negative y- axis)

Question 10

How does
y = f(x + a)
transform a graph

Answer 10

Moves it left by a
(a units in the direction of the negative x-axis)

Question 11

How does
y = f(x - a)
transform a graph

Answer 11

Moves it right by a
(a units in the direction of the positive x-axis)

Question 12

How does
y = af(x)
transform a graph

Answer 12

stretches the graph by scale factor a in the vertical direction.

Question 13

How does
y = f(ax)
transform a graph

Answer 13

stretches the graph by scale factor 1/a in the horizontal direction.

Question 14

How does
y = -f(x)
transform a graph

Answer 14

Reflects in the x-axis

Question 15

How does
y = f(-x)
transform a graph

Answer 15

Reflects in the y-axis

Question 16

What is the equation of a circle with a centre (0,0)

Answer 16

r² = x² + y²

Question 17

What is the equation of a circle with a centre (a,b)

Answer 17

r² = (x - a)² + (y - b)²

Question 18

How to find the equation for a circle

Answer 18

complete the square

Question 19

Tangent of a circle

Answer 19

Perpendicular to radius of circle

Question 20

perpendicular bisector of a chord

Answer 20

goes through the centre of the circle

Question 21

How to find the area of a non right angled triangle

Answer 21

1/2abSinC

Question 22

Cosine rule (non right angled triangles)

Answer 22

a² = b² + c² - 2bcCosA

Question 23

Sine rule (non right angled triangles)

Answer 23

SinA/a = SinB/b

Question 24

how are sin and cos related

Answer 24

sin²x + cos²x = 1

Question 25

How to find the turning point of a function

Answer 25

use the first derivative and solve it set to zero

Question 26

How to determine if the turning point of a function is maximum of minimum

Answer 26

Insert the solution from the first derivative into the second derivative of the function.

Question 27

What will the output from the second derivative be if the turning point is a maximum?

Answer 27

it is less than zero

Question 28

What will the output from the second derivative be if the turning point is a minimum?

Answer 28

it is more than zero

Question 29

How to find area under a curve

Answer 29

integration

Question 30

logarithm power law when k = -1

Answer 30

loga(1/x) = loga(x^-1) = -loga(x)

Question 31

How to find area of a sector of a circle where r is the radius of the circle and O is the angle in radians contained by the sector

Answer 31

A = 1/2 x r² x O

Question 32

How to find the arc length of a sector of a circle where r is the radius of the circle and O is the angle in radians contained by the sector

Answer 32

L = rO