Richard test 4(FIXED)

x
y

-2
9

-1
3

0
-1

1
-3

2
-3

3
-1

4
3

5
9

6
17

c) i)
the lowest point: (1/2;-9/4)
•

To define the lowest point:

y = ax 2 + bx + c

For every
If a>0 we have the lowest point
a<0 we have the highest point.

(
That point is

•

−b
−b
; f ( ))
2a
2a

In this case, we have

ii) solution:

−b 3
= = 1.5

2a 2

and

f (1.5) = 1.52 − 1.5 × 3 − 1 = −9 / 4

3 ± 13
2

We use the formulate: solutions for the

ax 2 + bx + c = 0


x1,2 =
We have 2 values of x:

−b ± b2 − 4ac 3 ± 9 + 4 3 ± 13
=
=
2a
2
2

d) y=mx+c ( formulate of straight line)
the origin has the coordinate (0;0) so that c=0 because when x=0 we have y=c=0 as the value of origin
and because the gradient is 2 so that we have the straight line : y=2x

e) to find down the coordinates intersects the graph we solve this equation:

x2 − 3x −1 = 2 x
⇔ x 2 − 3x − 2 x − 1 = 0
⇔ x2 − 5x − 1 = 0
⇔x=

5 ± 29
2

When we have the value of x, we obtain the value of y by y=2x=

5 ± 29


T=
a)

−23 + 2
= −3
7

x+2
=
4
⇔ 324 = x + 2
⇔ x = 324 − 2 = 322

81 =

b)
c)

x = Tn − 2


Angle ABD=180-DBC=140-40


ADB=180-ABD-BAD=20
iii) isosceles triangle


The range
The lowest value and the highest value within the data surveyed
For the 1st test: 20-85
The second test: 15-80
The mean: 56.45
Mode and Median are all correct.
Pos itive Co rrel atio n


Po si ti ve cor re l ati on o ccu r s w he n an in cr e ase in on e var i able
i ncre ase s th e valu e in an o th er .

T he li ne cor r e spon din g to th e scatte r pl o t i s an incr e asi n g l ine .

Neg ative Correl atio n

N e gati ve cor r el ati on o ccu r s w he n an in cr e ase in on e var i able
de cr e ase s th e valu e o f an o th e r .

T he li ne cor r e spon din g to th e scatte r pl o t i s a de cr e asi n g li ne .

No Co rrel atio n


N o cor r el ati on o ccur s w he n th er e i s no li ne ar de pe n de n cy
be tw e en the var i able s.

Perfect Co rrel atio n

Pe r fe ct co r re l atio n o ccu r s wh en the re is a fu nci on al de pe n de n cy
be tw e en the var i able s.

In th i s case all th e poi n ts ar e in a str ai gh t li ne .

Stro ng Co rrelatio n


A cor r el ati on i s str on ger th e clo se r the po in ts ar e l ocate d to o ne
ano th er o n th e li ne .

We ak Correl atio n

A cor r el ati on i s we ake r the far th er apar t the po in ts are l o cate d
to one ano the r o n th e li ne .

THE SULT:
Almost >80%.