Brainscape's Knowledge GenomeTM

Browse over 1 million classes created by top students, professors, publishers, and experts.


See full index

AS Maths > C1 > Flashcards

C1 Flashcards

0
Q

Function f(x)=ax^2 +bx+c
a<0?
-

A

Maximum turning point

Sad face ^

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

Function f(x)=ax^2 +bx+c
a>0?
+

A

Minimum turning point U

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

Vertex

A

Turning point

A line of symmetry can be drawn

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

Vertex= (1,3)

Line of symmetry?

A

X=1

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

Discriminant

A

b^2 - 4ac

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

How to factories a complicated

ax^2 + bx + c

A
  • make equation so that a is +
  • a X c
  • find two factors of ac that when added= b (call these zx and yx)
  • (ax^2 +zx)+(yx+c)
  • simplify
  • delete one of the like brackets make a second bracket from what you removed
  • now add - negatives so you get original equation when multiplied
How well did you know this?
1
Not at all
2
3
4
5
Perfectly
6
Q

Completing the square

Of x^2 + bx

A

(X+b/2)^2 -(b/2)^2

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

Completing the square

Of x^2 + bx +c

A

(X+b/2)^2 -(b/2)^2 +c

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

Completing the square
3x^2 + 2x +1
Same if a is a -

A 
3(x^2 +2/3x) +1
3((x+1/3)^2 -(1/3)^2 ) +1
3((x+1/3)^2 -(1/9))+1
3(x+1/3)^2 - 1/3 +1
3(x+1/3)^2 +2/3
How well did you know this?
1
Not at all
2
3
4
5
Perfectly
10
Q

Least value of the square

Vertex

A

Make square =0
Put in “when = x”
Whatever it makes is the least value
(X,lv)

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

Vertex

2(x + 1)^2 -3

A

(-1,-3)

-b,c

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

what does the C value of the completed square form show Maximum/minimum of a parabola

A

it is the Maximum/minimum of a parabola

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

When solving an equation by completing the square what must you not forget

A

There are two answers
One is +sqr rt
Other is -sqr rt

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

Quadratic formula

A

(-b+- /b^2 -4ac) /2a

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

b^2 -4ac <0

Real roots?

A

None

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

b^2 -4ac =0

A

1

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

b^2 -4ac >0

A

2

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

Equation has one real root solve to find an imbedded letter

A

One real root so =0
b^2 -4ac
Solve to find letter

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

When you square root what does it give

A

A + and a -

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
19
Q

The degree of a polynomial

A

The highest power of x

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
20
Q

Roots of f(x)=(2x-1)(x-2)(3x+1)

A

1/2 2 -1/3

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
21
Q

Cubic functions a>0

A

Progresses from low left to high right

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
22
Q

Cubic functions a<0

A

Progresses from high left to low right

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
23
Q

How to draw a cubic graph

A

Find the 3 values of x

Find if a is a + or - (a<>0)so you know which direction it travels

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
24
Q

Circle equation

A

X^2 + y^2 =r^2

(X-a)^2 + (y-b)^2 =r^2

25
Q

Effect of changing a

(X-a)^2

A

From side to side
If it is -2 then it will touch x axis at 2
If it is 3 then it will touch x axis at -3

26
Q

Effect of changing a

X^2 + c

A

Up and down (it is the y intercept)

27
Q

translation (1/3) is applied to y=x^2

Outcome

A

Y=(x-1)^2 +3

28
Q

Sketch the circle (x-2)^2 + (y+1)^2 =4

A

Translate by (2/-1)

29
Q

What is the translation of a graph

A

The same as its vertex

30
Q

Lines are perpendicular if

A

Both gradients multiplied =-1

m1 x m2 = -1

31
Q

Lines are parallel

A

If gradients are the same

m1 = m2

32
Q

The perpendicular line to line with gradient m

A

-1/m

33
Q

Midpoint of a line

A

(X1+X2/2 ,y1+y2/2)

34
Q

Distance between two points

A

AB =sqrt((x2-x1)^2 + (y2-y1)^2)

35
Q

Gradient of a line

A

AB = y2-y1/x2-x1

36
Q

Y=3x-2

Gradient and y intercept?

A

Gradient 3

Y intercept (0,-2)

37
Q

Equation of a line using gradient formula

A

y-y1=m(x-x1)

38
Q

Fining the point of intersection

A

Simultaneous equations

Find x and y

40
Q

Put into form ax+by+c=0

A

Rearrange
Multiply by fraction denominators
Write as y=mx+c
Divide by coefficient of y

41
Q

a perpendicular line has a

A

minus reciprocal gradient m becomes -1/m

42
Q

parallel lines have

A

the same gradient

43
Q

equation of a circle

A

(x-a)^2 + (y-b)^2 =r^2

44
Q

equation of a circle center (0,0)

A

x^2 + y^2 =r^2

45
Q

find the radius and center of circle

(x+3)^2 + (y-4)^2 -25

A

radius =5

center (-3, 4)

46
Q

After completing the square to find the equation of a circle what is the number outside of the brackets

A

r^2 (and not just r)

47
Q

How do you know if an angle in a circle is a right angle

A

If it is subtended at the circumference of a circle by a diameter.
An angle in a semicircle is a right angle

48
Q

What is a tangent to a circle

A

a line on the outside, touches the circle edge once (has one root)

49
Q

What is a normal to a circle

A

Line crossing through the Circle, is the normal to a tangent so splits the circle in half

50
Q

at a stationary point what is dy/dx

A

0

51
Q

the discriminant

A

b^2 -4ac

52
Q

b^2-4ac >0

A

two real roots

53
Q

b^2 -4ac <0

A

no real roots

54
Q

b^2-4ac =0

A

one real root

55
Q

the gradient of a line can be found

A

by differentiation

56
Q

the differentiated form is also called

A

the derivative

57
Q

the increasing function

A

dy/dx >0

58
Q

the decreasing function

A

dy/dx<0

59
Q

what do you do if you get 0 for d^2/dx^2 when you need to find if it is decreasing or increasing

A

put in -1, 0, 1 into dy/dx
you can tell what shape the graph is making
min is U max is A

60
Q

another word for the gradient

A

rate of change

AS Maths (3 decks)

Brainscape helps you reach your goals faster, through stronger study habits.
© 2024 Bold Learning Solutions. Terms and Conditions