#### Parabola. 1.
The accompanying sketch shows the graph
of the distance that a stone falls.
The formula used to calculate the distance,
2
is given by s = 5t
1.1
Calculate the co-ordinates of the
unmarked points on the graph and then
complete the table below:
Time, t   (s)           0     0,6       c      d
Distance, s  (m)    a      b       5      7,2
Time, t   (s)              e         2,4      g       3
Distance, s  (m)   12,8       f      33,8     h
1.2
1.2.1
The time taken to
1.2.1.1
fall 10 m.
1.2.1.2
fall 40 m.
1.2.2
The distance that the stone falls in
1.2.2.1
2 seconds.
1.2.2.2
2,4 seconds.
1.3
from the graph and then calculate the answer by using the formula.
1.4
What is the shape of the graph?
1.5
Is distance fallen and time taken, directly proportional to each other? Explain. 2.    The accompanying sketch shows the graphs of the
movement of two identical stones.
One stone is allowed to fall and the other stone is
thrown downwards.
2.1    Which stone will move the greatest distance
in 1 second? Explain.
2.2    Which graph, ff or th, shows the movemnet of
the stone that is allowed to fall?
2.3    How long does it take each stone to move 10 m?
2.4    How far does each stone move in 1,8 seconds?
Which letter on the graph gives each answer?
2.5    Which stone will first fall 40 m and how long does
it take to fall 40 m?
2.6    Is the distance directly proportional to the time
taken for the fall? Explain.

3.    The table below shows values for the area of a circle. Take pi = 3 to simplify the calculations.

Diameter        1     2         c         d       3,6       f
Area                a     b      4,32    6,75      e      12

3.1    Calculate the value of each letter in the table.
3.2    Is the diameter directly proportional to the area? Explain.
3.3    What will be the shape of the graph of the diameter, on the x-axis, against area, on the y-axis? Explain.
3.4    Draw the graph of diameter, on the x-axis, against area, on the y-axis.
Use values from 0 to 4 for the diameter.
3.5    Does the form of the graph confirm your answer in 3.2?
3.6    Read the anwsers to the follwing questions from the graph and mark the point where you
took the reading with the letter in brackets :
3.6.1    The ares if the diametr is 4 m. (A)
3.6.2    The diameter if the area is 2,43 square metres. (B)
3.6.3    The area if the diametr is 3,2 cm. (C)
3.6.4    The diameter if the area is 4,32 square cm. (Q)
3.6.5    The area if the diameter is 1,5 m. (P)
3.7    Use the formula and calculate the values. Compare them to the readings from the graph. 4.
The accompanying sketch shows the graph
of a brick that is thrown upwards to a
worker standing on a scaffold.
The height, h (in metre), that the brick
reaches after t seconds, is
2
given by h = 8t - 5t
4.1
4.1.1
the height of the brick after 0,1 seconds.
4.1.2
the time that the brick takes to
reach a height of 2 m.
4.1.3
the maximum height that the
brick reaches.
4.2
Use the formula to calculate the
4.3
The worker on the scaffold misses the
brick and it falls to the ground.
Sketch on the given system of axes the graph that represents the movement to the ground.
4.4
4.4.1
time taken to reach the ground.
4.4.2
total time that the brick moved.
4.4.3
times at which the brick was 3 m above the ground.
4.4.4
total time that the sbrick was 3 m or higher.
4.4.5
times at which the brick was 0,75 m above the ground. 5.
The accompanying sketch shows the graph
2
of y = x    - 9 = 0
5.1.1
Write down the co-ordinates of points C and D.
5.2.1
From the graph read the following values
and also write down the letter of the point
on the graph:
2
5.2.1.1
the roots of the equation x    - 9 = 0
2
5.2.1.2
the roots of the equation x    - 4 = 0
5.3
Write down the length of each of the following lines:
5.3.1
AO
5.3.2
OM
5.3.3
AB
5.3.4
PQ
5.3.5
MN
5.3.6
NQ
5.4
Write down the equation of the line passing through points P, N and Q. 6.
The accompanying sketch shows the grah
2
of y = x    - 4
6.1
Read the points of interscetion of f
with the x-axis from the graph.
6.2
Write down the roots of the equation
2
x    - 4 = 0 .
6.3
Solve the equation by calculating
2
the roots: x    - 4 = 0.
6.4
For which value(s) of x is
2
2
6.4.1
x    - 4 = 0
6.4.2
x    - 4 > 0
2
6.4.3
x    - 4 < 0
6.5
Write down the equation of the graph of g.
6.6
For which value(s) of x is
6.6.1
g = 0
6.6.2
g > 0
6.6.3
g < 0 7.
The accompanying sketch shows the graph
2
of y = x    + 2
7.1
Calculate the co-ordinates of points
A, B, C and Q.
V, T and S are points on the Y-axis so that
VC, PTQ and BS are parallel to the X-axis.
7.2
Write down the lengths of BS, PT and PQ.
7.3
Write down the equation of the line PTS.
7.4
Write down the co-ordinates of the points
V, T and S.
7.5
Write down the length of AS, TS and VA.
7.6
Calculate the length of PS and QA.
7.7
Read from the graph the solution of the
2
equation:    x    + 2 = 0 8.
The accompanying sketch shows the graph
2
of y = 25 - x
8.1
Calculate the co-ordinates of points A, B
and C.
8.2
D is the point (4,1 ; 8,19). Write down
the co-ordinates of L and the length
of LD.
8.3
MO = 17. Calculate the co-ordinates of G
and the length of MG.
8.4
EN = 6,5 and N is the point (0 ; -17,25).
Write down the co-ordinates of
E and F and also the length of EF.
8.5
Write down the length of CO, ML, CN
and MN.
8.6
Calculate the length of AN and LG.
2
8.7
Read from the graph the roots of 25 - x   = 0 .
8.8
Use the graph to solve the following equations. Write down the roots and also the names
of the points where you took the readings:
2
2
2
8.8.1
25 - x    = 0
8.8.2
25 - x    = -17,25
8.8.3
42,25 - x    = 0
8.9
For which value(s) of x is
2
2
2
8.9.1
25 - x    >   0
8.9.2
25 - x    >   -17,25
8.9.3
25 - x    <   8,19