Unit 2

Question 1

How do you find the roots of a quadratic

Answer 1

Factorise
Complete the square
Use quadratic formula

Question 2

What is the quadratic formula

Answer 2

x = -b +- √b²-4ac

2a

Question 3

What is the discriminant formula

Answer 3

b²-4ac

Question 4

If b²-4ac>0…

Answer 4

The roots are real and unequal/distinct

Question 5

If b²-4ac=0…

Answer 5

The roots are real and equal/repeated root

Question 6

If b²-4ac<0…

Answer 6

There are no real roots

Question 7

y=a(x+p)²+q

How to extract axis of symmetry

Answer 7

x=-p

Question 8

y=a(x+p)²+q

How to extract turning point

Answer 8

(-p,q)

Question 9

How to determine how many roots a parabola has

Answer 9

Use discriminant formula

b²-4ac

Question 10

How to sketch a parabola with one or two roots

Answer 10

Factorise or use quadratic formula to find x axis intercepts
Use x=0 to find y axis intercepts
Find turning point, halfway in between x coordinates

Question 11

How to sketch a parabola with no real roots

Answer 11

Find y axis intercept with x=0

Find turning point by completing the square

Question 12

Formula for the equation of a parabola

Answer 12

y=k(x-a)(x-b)

Question 13

How to find the equation of a parabola

Answer 13

Sub in x coordinates to a&b in equation
Sub in y coordinates
Rearrange to find k
Write out equation

Question 14

How to solve a quadratic inequality

Answer 14

State whether concave up or down
Factorise to find where cuts the x axis
Draw graph to find where x is on parabola
State values of x

Question 15

How to find the point of contact of a tangent

Answer 15

Make equations equal
Rearrange
Factorise for x value
Sub x value into equation of line

Question 16

How to find points of intersection of curves

Answer 16

Make equations equal
Factorise for x coordinates
Sub into equation of line for y coordinates

Question 17

Equation to determine equation of curve

Answer 17

y=k(x-a)(x-b)(x-c)

Question 18

How to determine equation of curve

Answer 18

Sub roots into equation
Sub coordinates of point into equation
Rearrange to find k
Write out equation

Question 19

How to integrate

Answer 19

Plus one to indice
Divide number by indice
Write +c on end

Question 20

How to find a definite integral

Answer 20

Integrate

Sub in each limit and take them away from the other

Question 21

How to calculate the shaded area of a graph

Answer 21

Use definite integration with the two x roots

Question 22

How to find the area between curves

Answer 22

Work out points of intersection by making equations equal and factorising
Integrate upper curve - lower curve
Sub in limits

Question 23

Sin

Answer 23

180 - x

Question 24

Tan

Answer 24

180 + x

Question 25

Cos

Answer 25

360 - x

Question 26

Eg. | 3tan(3x-20)=5

Answer 26

tan (3x-20) = 5/3 3x-20 = tan-1 (5/3) =59 3x-20 = 59 or 239 or 419 or 599 or 779 or 959 3x = 79 or 259 or 439 or 619 or 799 or 979 x = 26.3 or 86.3 or 146.3 or 206.3 or 266.3 or 326.3

Question 27

Trig identities

Answer 27

tanx = sinx/cosx sin²x + cos²x = 1

Question 28

How to find the equation of a circle

Answer 28

Sub in centre point and radius to equation | (x-a)² + (y-b)² = r²

Question 29

If (p-a)²+(q-b)²< r²...

Answer 29

The point lies within the circle

Question 30

If (p-a)²+(q-b)²= r²...

Answer 30

The point lies on the circumference of the circle

Question 31

If (p-a)²+(q-b)²>r²

Answer 31

The point lies outwith the circle

Question 32

How to find the centre of a circle from the equation

Answer 32

State what 2g and 2f are equal to Rearrange State coordinates with (-g,-f)

Question 33

How to find line’s points of intersection in a circle

Answer 33

Sub equation of line into equation of circle Solve to find x coordinates Sub into equation of line for y coordinates

Question 34

How to prove a line is a tangent to a circle

Answer 34

Sub equation of line into equation of circle Solve to find x coordinates If there is only one x coordinate, the line is a tangent

Question 35

How to find the equation of a tangent to a circle

Answer 35

Find point of intersection which lies on the circle Find centre of circle Find gradient of line with centre of circle and tangent point Find perpendicular gradient Write equation

Question 36

If d > r1 + r2...

Answer 36

The circles do not touch

Question 37

If d = r1 + r2...

Answer 37

The circles touch externally

Question 38

r1 - r2 < d < r1 + r2

Answer 38

The circles meet at two distinct points

Question 39

If d = r1 - r2...

Answer 39

The circles touch internally

Question 40

If d < r1 - r2...

Answer 40

The circles do not touch