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AQA Mathematics > AS > Flashcards

AS Flashcards

1
Q

What are the indices rules?

A
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2
Q

When should you complete the square?

A

When a quadratic equation will not factorise easily

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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

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4
Q

Complete the square of x2 + 6x + 7?

A

(x+3)2 -32 + 7

= (x+3)2 -2

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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

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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

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7
Q

What is the quadratic formula?

A
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8
Q

What is the discriminant of the quadratic formula?

A

b2 - 4ac

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9
Q

What happens when b2 - 4ac > 0 ?

A

There are two real distinct roots

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10
Q

What happens when b2 - 4ac = 0 ?

A

There is one real root (repeated)

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11
Q

What happens when b2 - 4ac

A

No real roots

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12
Q

What are the inequality symbols?

A

Same for not equal to but circle not shaded in

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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

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14
Q

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

A

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

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15
Q

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

A

Graph is transformed by (x,y+b)

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16
Q

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

A

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

(x,ay)

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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)

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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
Q

What are some values for the graph y=sinx ?

A

x = 0, y = 0

x = 90, y = 1

x = 180, y = 0

x = 270, y = -1

x = 360, y = 0

26
Q

What are some values of y=cosx?

A

x = 0, y = 1

x = 90, y = 0

x = 180, y = -1

x = 270, y = 0

x = 360, y = 1

27
Q

What is tanx equal to?

A

tanx = sinx/cosx

28
Q

What are some values of y=tanx?

A

x = 0, y = 0

x = 90, y = ∞

x = 180, y = 0

x = 270, y = ∞

x = 360, y = 0

29
Q

How do you find the values of sine after getting the principle value?

A

PV & 180 - PV

Repeat every 360

30
Q

How do you find the values of cosine after getting the principle value?

A

PV, 360 - PV

Every 360

31
Q

How do you find the values of tan after getting the principle value?

A

PV, PV +/- multiples of 180

32
Q

What is the equation that links sin2x and cos2x?

A

sin2x + cos2x = 1

33
Q

What is the √ (xy) ?

A

√ x * √ y

34
Q

What are the forms of equations of a straight line?

A

y -y1 = m(x-x1)

ax + by + c = 0

35
Q

What are the gradients of two lines for them to be perpendicular?

A

m1 * m2 = -1

m1 and m2 are the gradients of each line

36
Q

What are the gradients for two straight lines to be parallel?

A

m1 = m2

37
Q

What is the equation of a circle?

A

(x-a)2 + (y-b)2 = r2

r - radius

a = x coordinate

b = y coordinate

38
Q

What is the angle in a semicircle theorem?

A

Angle subtended across a circle’s diameter is always a right angle

39
Q

What is the theorem involving angles at the centre and circumference of the circle?

A

The angle subtended at the centre is twice that at the circumference

40
Q

What is the theorem relating angles in the same arc?

A

Angles subtended by the same arc are equal

41
Q

What is the theorem relating cyclic quadrilateral?

A

Opposite angles in cyclic quadrilaterals add up to 180º

42
Q

What is the angle between a tangent and the radius of a circle?

A

90º

43
Q

What theorem relates chords and the centre of a circle?

A

Perpendicular from the centre of a circle bisects the chord

AQA Mathematics (68 decks)

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