Grade 12 - More exercises : answers.
Straight line graphs.
1.1
Car A
moves at a constant speed .
1.2
At point P
car A stops and is in rest (does not move) for 1 hour, from t = 2 to t = 3.
1.3
Speed
of car A = 75 km/h.
1.4
Car B
travels at the higher speed because the gradient of the graph for car B is greater than
the gradient of the graph for car A.
distance
150 km
1.5
Average
speed of car A = ————— = ————
= 50 km/h
time
3 h
1.6
Average
speed of car B = 100 km/h.
1.7
Yes, from
t = 5 to t = 6 both cars travel 100 km in 1 hour, their speed is 100 km/h.
1.8
Yes. Both
cars travel 400 km in 6 ours. Their average speed = 66,667 km/h.
2.1
If
x = – 2, y = –1 and if x = 8, y = 19.
The points
(–2 ; –1) and (8 ; 19) are points on the line f.
We can
now say that if x = –2 then y f = –1 and if x = 8
then y f = 19.
2.2
If
y = 4 , x = 0,5 and if y = –5, x = –4.
2.3
If
x = –2, y = 19 and if x = 8, y = 14.
2.4
If
y = 13, x = 10 and if y = 17, x = 2.
2.5
P is
the point (6 ; 15)
2.6
If x = –2
then y f = 2x + 3 = –1 and y g = 18 – 0,5x = 19. Therefore, if x = –2
(a) false: 2x + 3 ≠ 18 – 0,5x because –1 ≠ 19 ;
–1 < 19
(b) true; 2x + 3 < 18 – 0,5x because –1 < 19
(c) false; 2x + 3 < 18 – 0,5x because –1 < 19
2.7
(a) false: f ≠ g because –1 ≠ 19 ; –1 < 19
(b) true; f < g because –1 < 19
(c) false; f < g because –1 < 19
2.8
(a) f < g if x < 6
(a) f = g if x = 6
(a) f > g if x > 6
2.9
MN = 20
2.10
If
x = –2 then f – g = 20 [Note: distance is ALWAYS POSITIVE].
2.11
If
x = 8 then f – g = 19 – 14 = 5 : if x = 0,5 then f – g = – 13,75
If
x = –4,5 then f – g = – 26,25
2.12
f = 0 if
x = – 1,5 ; f < 0 if x < – 1,5 ;
f > 0 if x > – 1,5
2.13
f.g < 0 if
x < – 1,5 ; f.g = 0 if x = –1,5 and f.g > 0 if
x > – 1,5
3.1
There is no
income from the sale of 0 items.
3.2
There may
be costs involved in the production process, e.g. hiring staff, buildings, machinery, etc.
3.3
A profit
is made if the income is greater than the expenses or costs.
Using the
graph we want that part of the graph where the graph of the income has a greater
y value than
the graph of the costs, we say that the graph of the income must be greater or
lie "above"
the graph of the costs. Therefore, a profit is made if f > g.
A profit is
thus made if the number of items sold is greater than the number of items at the
point of
intersection of f and g.
3.4
Income = R6
Δ y 6
3
3.5
m = ——— = ——
= —— = 1,5
Δ x 4
2
3.6
y = 1,5x
3.7
At point P f = g, i.e. the graphs have the same y value for a certain x value, i.e.
at P y f = y g
f is defined by y = 1,5x and g by y = 0,875x + 5
Therefore, at P : 1,5x = 0,875x + 5
0,625x = 5
x = 8
Put x = 8 into y = 1,5x : y = 1,5 × 8 = 12
P is the point (8 ; 12)
3.8.1
No. It
is the break even point. The income is equal to the costs. No profit is made and
and no loss is made.
3.8.2
No. A
loss is made because the income is smaller than the costs. The graph of the costs lies
"above"
the graph of the income.
3.8.3
Yes, a
profit is made because the income exceeds the costs, the graph of the income lies
"above" the graph of the costs.
3.9
Profit
from 4 items : –R2,50 (a loss of R2,50) and profit from 10 items: R1,25
3.10
12 or more items.