AS Flashcards

1
Q

What are the indices rules?

A
How well did you know this?
1
Not at all
2
3
4
5
Perfectly
2
Q

When should you complete the square?

A

When a quadratic equation will not factorise easily

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
3
Q

How do you complete the square? (using x2 +yx + c)

A

Write in the form (x + y/2)2 -(y/2)2 + c

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
4
Q

Complete the square of x2 + 6x + 7?

A

(x+3)2 -32 + 7

= (x+3)2 -2

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
5
Q

Complete the square of 2x2 + 8x + 7?

A

2[x2 + 4x + 7/2]

= 2[(x+2)2 -22 + 7/2)

= 2[(x+2)2 - 1/2]

= 2(x+2)2 - 1

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
6
Q

How woulkd you complete the square of -x2 + 4x + 5

A

= -1[x2 -4x -5]

Then complete as normal to get

-1(x-2)2 + 9

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
7
Q

What is the quadratic formula?

A
How well did you know this?
1
Not at all
2
3
4
5
Perfectly
8
Q

What is the discriminant of the quadratic formula?

A

b2 - 4ac

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
9
Q

What happens when b2 - 4ac > 0 ?

A

There are two real distinct roots

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
10
Q

What happens when b2 - 4ac = 0 ?

A

There is one real root (repeated)

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
11
Q

What happens when b2 - 4ac < 0 ?

A

No real roots

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
12
Q

What are the inequality symbols?

A

Same for not equal to but circle not shaded in

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
13
Q

How can you tell the line of symetry from completing the square?

A

(x + y)2 + c

Curve is left by y and up by c

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
14
Q

What is a transformation of y = f(x-a)?

A

Transformation of the graph by (x+a,y)

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
15
Q

What is the transformation of y = f(a) + b?

A

Graph is transformed by (x,y+b)

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
16
Q

What is the transformation of y = af(x)?

A

Graph is strechted by scale factor a (parallel to y-axis)

(x,ay)

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
17
Q

What is the transformation of y = f(ax)?

A

Transformation of graph by 1/a parallel to x axis

((1/a) x, y)

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
18
Q

What is the transformation of y = -f(x)

A

Reflection of graph in x-axis

(x, -y)

19
Q

What is teh transformation of y = f(-x)?

A

Reflection of graph in y-axis

(-x, y)

20
Q

What order should be done with 2f(x+1)?

A

Stretch then translate

21
Q

What is the sine rule?

A

a/sinA = b/sinB = c/sinC

sinA/a = sinB/b = sinC/c

22
Q

What is the cosine rule?

A

a2 = b2 + c2 -2bc x cosA

23
Q

What is the area of a non-right angle triangle ?

A

Area = 1/2 x base x height

Area = 1/2 x a x b x sinC

24
Q

What is the lowercase and uppercase letters in triangles?

A

Lowercase - side

Uppercase - Angle

25
What are some values for the graph y=sinx ?
x = 0, y = 0 x = 90, y = 1 x = 180, y = 0 x = 270, y = -1 x = 360, y = 0
26
What are some values of y=cosx?
x = 0, y = 1 x = 90, y = 0 x = 180, y = -1 x = 270, y = 0 x = 360, y = 1
27
What is tanx equal to?
tanx = sinx/cosx
28
What are some values of y=tanx?
x = 0, y = 0 x = 90, y = ∞ x = 180, y = 0 x = 270, y = ∞ x = 360, y = 0
29
How do you find the values of sine after getting the principle value?
PV & 180 - PV Repeat every 360
30
How do you find the values of cosine after getting the principle value?
PV, 360 - PV Every 360
31
How do you find the values of tan after getting the principle value?
PV, PV +/- multiples of 180
32
What is the equation that links sin2x and cos2x?
sin2x + cos2x = 1
33
What is the √ (xy) ?
√ x \* √ y
34
What are the forms of equations of a straight line?
y -y1 = m(x-x1) ax + by + c = 0
35
What are the gradients of two lines for them to be perpendicular?
m1 \* m2 = -1 m1 and m2 are the gradients of each line
36
What are the gradients for two straight lines to be parallel?
m1 = m2
37
What is the equation of a circle?
(x-a)2 + (y-b)2 = r2 r - radius a = x coordinate b = y coordinate
38
What is the angle in a semicircle theorem?
Angle subtended across a circle's diameter is always a right angle
39
What is the theorem involving angles at the centre and circumference of the circle?
The angle subtended at the centre is twice that at the circumference
40
What is the theorem relating angles in the same arc?
Angles subtended by the same arc are equal
41
What is the theorem relating cyclic quadrilateral?
Opposite angles in cyclic quadrilaterals add up to 180º
42
What is the angle between a tangent and the radius of a circle?
90º
43
What theorem relates chords and the centre of a circle?
Perpendicular from the centre of a circle bisects the chord