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Maths Higher > Unit 2 > Flashcards

Unit 2 Flashcards

1
Q

How do you find the roots of a quadratic

A

Factorise
Complete the square
Use quadratic formula

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2
Q

What is the quadratic formula

A

x = -b +- √b²-4ac

2a

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3
Q

What is the discriminant formula

A

b²-4ac

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4
Q

If b²-4ac>0…

A

The roots are real and unequal/distinct

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5
Q

If b²-4ac=0…

A

The roots are real and equal/repeated root

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6
Q

If b²-4ac<0…

A

There are no real roots

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7
Q

y=a(x+p)²+q

How to extract axis of symmetry

A

x=-p

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8
Q

y=a(x+p)²+q

How to extract turning point

A

(-p,q)

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9
Q

How to determine how many roots a parabola has

A

Use discriminant formula

b²-4ac

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10
Q

How to sketch a parabola with one or two roots

A

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

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11
Q

How to sketch a parabola with no real roots

A

Find y axis intercept with x=0

Find turning point by completing the square

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12
Q

Formula for the equation of a parabola

A

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

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13
Q

How to find the equation of a parabola

A

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

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14
Q

How to solve a quadratic inequality

A

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

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15
Q

How to find the point of contact of a tangent

A

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

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16
Q

How to find points of intersection of curves

A

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

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17
Q

Equation to determine equation of curve

A

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

18
Q

How to determine equation of curve

A

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

19
Q

How to integrate

A

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

20
Q

How to find a definite integral

A

Integrate

Sub in each limit and take them away from the other

21
Q

How to calculate the shaded area of a graph

A

Use definite integration with the two x roots

22
Q

How to find the area between curves

A

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

23
Q

Sin

A

180 - x

24
Q

Tan

A

180 + x

25
Q

Cos

A

360 - x

26
Q

Eg.

3tan(3x-20)=5

A

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

27
Q

Trig identities

A

tanx = sinx/cosx

sin²x + cos²x = 1

28
Q

How to find the equation of a circle

A

Sub in centre point and radius to equation

(x-a)² + (y-b)² = r²

29
Q

If (p-a)²+(q-b)²< r²…

A

The point lies within the circle

30
Q

If (p-a)²+(q-b)²= r²…

A

The point lies on the circumference of the circle

31
Q

If (p-a)²+(q-b)²>r²

A

The point lies outwith the circle

32
Q

How to find the centre of a circle from the equation

A

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

33
Q

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

A

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

34
Q

How to prove a line is a tangent to a circle

A

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

35
Q

How to find the equation of a tangent to a circle

A

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

36
Q

If d > r1 + r2…

A

The circles do not touch

37
Q

If d = r1 + r2…

A

The circles touch externally

38
Q

r1 - r2 < d < r1 + r2

A

The circles meet at two distinct points

39
Q

If d = r1 - r2…

A

The circles touch internally

40
Q

If d < r1 - r2…

A

The circles do not touch

Maths Higher (3 decks)

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