Post on 07-Apr-2018
8/6/2019 Gradient & Area Under the Graf
1/25
5 marks
8/6/2019 Gradient & Area Under the Graf
2/25
BIL TOPIC FORM 03 04 05 06 07
Section A (52%) : Answer ALL questions (question 1 until 11)
1 REGION OF INEQUALITIES V 3 3 1
2 SET IV 1 1
3 SIMULTANEOUS EQUATIONS III 2 5 2 4 2
4 QUADRATIC EXPRESSION & EQUATIONS IV 1 7 1 3 3
5 LINES & PLANES IN 3-DIMENSIONS IV 4 3 4 2 4
6 THE STRAIGHT LINE IV 5 6 5 10 5
7 SOLID GEOMETRY - PERIMETER & AREA III 7 9 7 8 6
8 MATHEMATICAL REASONING IV 8 4 8 6 7
9 PROBABILITY II V 9 10 9 7 8
10 INVERSE MATRIX V 11 8 11 11 9
11 GRADIENT & AREA UNDER A GRAPH V 10 11 10 9 10
12 SOLID GEOMETRY (VOLUME) III 6 2 6 5 11
Section B (48%) : Answer FOUR questions from this section.
12 GRAPHS OF FUNCTIONS V 12 12 12 13 12
13 PLAN & ELEVATION V 15 15 15 15 13
14 EARTH AS A SPHERE V 16 16 16 16 14
15 TRANSFORMATION III V 13 13 13 12 15
16 STATISTICS IV 14 14 14 14 16
8/6/2019 Gradient & Area Under the Graf
3/25
Speed
Time
m = rate of change of speed= speed/time
= acceleration / deceleration
Constant/Uniform speed
acceleration
deceleration
8/6/2019 Gradient & Area Under the Graf
4/25
State the length of time, in s, that the particle moveswith uniform speed.
Speed (ms-1)
21
9
O 5 12 t
(t,21)
(t,0)1
Time (s)
7512 !
8/6/2019 Gradient & Area Under the Graf
5/25
takentime
speedinitialspeedfinal
speedofchangeofRate
-!
+ve acceleration
ve - deceleration
RateOfChangeOfSpeed
4
5 120
speed
Find the rateofchangeofspeedin
thefirst 5 seconds
Final speed = 4
Initial speed = 0
Rateofchangeofspeed
= = @ 0.8
5
04
5
04
5
04
5
04
5
4
8/6/2019 Gradient & Area Under the Graf
6/25
(a) State the length of time, in s, that the particlemoves with uniform speed.
(b) Calculate the rate of change of speed, in
ms
-1
, in the first 5 seconds.
Speed (ms-1)
21
9
O 5 12 t
(t,21)
(t,0)1
Time (s)
8/6/2019 Gradient & Area Under the Graf
7/25
Speed
Time
Area =
distance
travelled
Area under the graph is the distance
bb
2
1Area = ab
a(b+c)
b
Area = ab2
1
Area =
a a a
c
8/6/2019 Gradient & Area Under the Graf
8/25
A B
5
04 10 Time
speed
(i)Distanceduring thefirst 4 seconds
= area A
= x 4x 5 = 102
1
(ii)Distanceduring thelast 4 seconds= area B
= 6 x 5
= 30
(iii)Totaldistanceduring10 seconds
= area A + area B
= 10 + 30
= 40
8/6/2019 Gradient & Area Under the Graf
9/25
FindTheValueOfV(Speed)
4 10
v
2
0
speed
time
Distance travelled in the first 4 seconds
is 20 m
(2 + v) x4
= 202(2 + v) = 20
2 + v = 20/2
= 10
v = 10 2
= 8
2
1
8/6/2019 Gradient & Area Under the Graf
10/25
FindTheValueOfT(Time)
0 3 5 T
8
6
2
time
speed
TotaldistanceinT s is 45m.
Area A = (2 + 6)(3)/2 = 12
Area B = 2 X 6 = 12
Area C = (6 + 8)(T 5)/2
Totaldistance = 45
12 + 12 +7(T 5) = 45
24 +7(T 5) = 45
7(T 5) = 45 24
(T 5) = 21/7
(T - 5) = 3T = 3 + 5
= 8
8/6/2019 Gradient & Area Under the Graf
11/25
Calculate the value oft, if the total distance
travelled fortseconds is 148 metres.
Total distance= area under the graph
Speed (ms-1)
21
9
O 5 12 t
(t,21)
(t,0)1
18
18010
122192
197591
2
1148
!
!
v!
t
t
t
Stress on the correct values when substituting
8/6/2019 Gradient & Area Under the Graf
12/25
timeTotal
cetandisTotal=speedAverage
A B C
0 3 6 10
8
4
time
TotalDistance
= Area A + Area B + Area C
= (4)(3)/2 + (3)(4) + (4+8)(4)/2= 6 + 12 + 24
= 42
TotalTime = 10
AverageSpeed = 42/10
= 4.2
8/6/2019 Gradient & Area Under the Graf
13/25
Distance
Time
m = Rate of change of distance
= distance/ time
= speed
Object stops
Speed
Distance(km)
3
12
0
Distancefrom O toA = 12 0 = 12
Speedfrom O toA = Distance/Time
= 12/3
= 4 km/h
8/6/2019 Gradient & Area Under the Graf
14/25
AverageSpeed
Distance(km)
Time(minutes)
30 90
20
0
A
B
Totaldistancefrom O toB = 20
Total timefrom O toB
= 90 minutes
@Average speed(km/h)
=
= 13.33
60/90
20
8/6/2019 Gradient & Area Under the Graf
15/25
REMEMBER :1. Lengthoftimeis total time taken
2.AREA
of
trapeziu
m
3. Distance-timegraph , gradient = speed
equivalent to the rateofchangeof
distance
4. Speed-timegraph , gradient =
accelerationequivalent to the rateof
changeofspeed
GRADIENT AND AREA UNDER A GRAPH
8/6/2019 Gradient & Area Under the Graf
16/25
8/6/2019 Gradient & Area Under the Graf
17/25
8/6/2019 Gradient & Area Under the Graf
18/25
8/6/2019 Gradient & Area Under the Graf
19/25
8/6/2019 Gradient & Area Under the Graf
20/25
8/6/2019 Gradient & Area Under the Graf
21/25
8/6/2019 Gradient & Area Under the Graf
22/25
8/6/2019 Gradient & Area Under the Graf
23/25
8/6/2019 Gradient & Area Under the Graf
24/25
8/6/2019 Gradient & Area Under the Graf
25/25