# 14.2.3 Ratio, Rates and Proportions II, PT3 Focus Practice

Question 10:
Diagram below shows the distance from Town P to Town Q and Town Q to Town R.
(a) Rahim rode his bicycle from Town P at 9.00 a.m. and took 2 hours to reach Town Q.
What is the speed, in km/h, of the bicycle?
(b) Rahim took 30 minutes rest at Town Q and continued his journey to Town R three times faster than his earlier speed.
State the time he reached Town R.

Solution:
(a)

(b)

Question 11:
Diagram below shows a trailer travelling from a factory to location P and location P to location Q. The trailer departs at 8.00 a.m.

(a) Based on the Table, calculate the total mass, in tonne, of the trailer and its load.
(b) The trailer arrived at location P at 10.00 a.m. and it stopped for 1½ hours to unload half of the concrete pipes. The trailer then continued its journey to location Q two times faster than its earlier speed. State the time, the trailer reached at location Q.

Solution:
(a)

(b)

Question 12:
Diagram below shows travel information of Jason and Mary from Town A to Town B. Jason drives a lorry while Mary drives a car.

(a) Jason started his journey from Town A at 7.00 a.m.
State the time, Jason reached at Town B.
(b) If both of them reached Town B at the same time, state the time Mary started her journey from Town A.

Solution:
(a)
Total time taken from Town A to Town B
= 3 hours + 1 hour + 2 hours
= 6 hours

Time Jason reached Town B
= 0700 + 0600
= 1300 hours → 1.00 p.m.

(b)

# 14.2.2 Ratio, Rates and Proportions II, PT3 Focus Practice

Question 6:
Mei Ling drives her car from Kuantan to Kuala Terengganu for a distance of 170 km for 2 hours. She then continues her journey to Kota Bahru and increases her speed to 100 kmh-1 for 45 minutes.
Calculate the acceleration, in kmh-2, of the car.

Solution:

Question 7:
Diagram shows the distance between K and L.

A car moves from K to L with an average speed of 80 kmh-1. After rest for 1 hour 30 minutes, the car then returns to K. The average speed of the car from L to K increases 20%. If the car reaches K at 5 p.m., calculate the time the car starts its journey from K.

Solution

The car starts its journey from K at 11:50 a.m.

Question 8:
Mr Wong is going to watch a movie at 2.30 p.m at a cinema that is 60 km away from his house. He leaves at 1.25 p.m and drives at an average speed of 70 km/h for half an hour. If he drives at an average speed of 75 km/h for the remaining journey, will he arrive before the movie starts?

Solution

Question 9:
Karen drives her car from town P to town Q at an average speed of 80 km/h for 2 hours 15 minutes. She continues her journey for a distance of 90 km from town Q to town R and takes 45 minutes.
Calculate the average speed, in km/h, for the journey from P to R.

Solution:

# 14.2.1 Ratio, Rates and Proportions II, PT3 Focus Practice

Question 1:
The distance from town A to town B is 120 km. A car leaves town A for town B at 11.00 a.m. The average speed is 80 km h-1 .
At what time does the car arrive at town B.

Solution:

Question 2:
Kenny drives his car from town P to town Q at a distance of 180 km in 3 hours.
Faisal takes 30 minutes less than Kenny for the same journey.
Calculate the average speed, in km/h, of Faisal’s car.

Solution:

Question 3:
Rafidah drives her car from town L to town M at an average speed of 90 km/h for 2 hours 40 minutes. She continues her journey for a distance of 100 km from town M to town N and takes 1 hour 20 minutes.
Calculate the average speed, in km/h, for the journey from L to M.

Solution:

Question 4:
Susan drives at an average speed of 105 km/h from town F to town G.
The journey takes 3 hours.
Susan takes 30 minutes longer for her return journey from town G to town F. Calculate the average speed, in km/h, for the return journey.

Solution:

Question 5:
Table below shows the distances travelled and the average speeds for four vehicles.

 Vehicle Distance (km) Average speed (km/h) A 230 115 B 250 100 C 170 85 D 245 70
Which vehicles took the same time to complete the journey?

Solution:

Thus, the vehicles A and C took the same time to complete the journey.

# 13.2.3 Graphs of Functions, PT3 Focus Practice

Question 7:
Use graph paper to answer this question.
Table below shows the values of two variables, x and y, of a function.

The x-axis and the y-axis are provided on the graph paper on the answer space.
(a) By using a scale of 2 cm to 5 units, complete and label the y-axis.
(b) Based on the table above, plot the points on the graph paper.
(c) Hence, draw the graph of the function.

Solution:

Question 8:
Use graph paper to answer this question.
Table below shows the values of two variables, x and y, of a function.

The x-axis and the y-axis are provided on the graph paper on the answer space.
(a) By using a scale of 2 cm to 2 units, complete and label the y-axis.
(b) Based on the table above, plot the points on the graph paper.
(c) Hence, draw the graph of the function.

Solution:

# 13.2.2 Graphs of Functions, PT3 Focus Practice

 
 
13.2.2 Graphs of Functions, PT3 Focus Practice
 
 
Question 4:
 
Use graph paper to answer this question.
 
Table below shows the values of two variables, x and y, of a function.
 

 
 
   x     –3     –2     –1     0     1     2     3     y     –19     –3     1     –1     –3     1     17  
 
 
The x-axis and the y-axis are provided on the graph paper on the answer space.
 
(a)  By using a scale of 2 cm to 5 units, complete and label the y-axis.
 
(b) Based on the table above, plot the points on the graph paper.
 
(c)  Hence, draw the graph of the function.
 
 

 Answer:

 
 
Solution:

 

 
 
 
 
 
 
 
 
Question 5:
 
Use graph paper to answer this question.
 
Table below shows the values of two variables, x and y, of a function.
 

 
 
   x     –4     –3     –2     –1     0     1     2     y     31     17     7     1     –1     1     7  
 
 
The x-axis and the y-axis are provided on the graph paper on the answer space.
 
(a)  By using a scale of 2 cm to 5 units, complete and label the y-axis.
 
(b)   Based on the table above, plot the points on the graph paper.
 
(c)  Hence, draw the graph of the function.
 

 

 
 
 
Solution:

 

 
 
 
 

Question 6:
(a) Complete table below in the answer space for the equation L = x2 + 5x by writing the value of L when x = 2.
(b) Use graph paper to answer this part of the question. You may use a flexible curve rule.
By using a scale of 2 cm to 1 unit on the x-axis and 2 cm to 5 units on the y-axis, draw the graph of L = x2 + 5x for 0 ≤ x ≤ 4.

Solution:
(a)
When x = 2
L = 22 + 5(2)
= 4 + 10
= 14

(b)

# 13.2.1 Graphs of Functions, PT3 Focus Practice

13.2.1 Graphs of Functions, PT3 Focus Practice

Question 1:

In the figure shown, when x = 4, the value of y is

Solution:

is the point on the graph where x = 4.
Hence, when x = 4, y = 5.

Question 2:
Diagram shows the graph of a function on a Cartesian plane.

The equation that represents the function is

Solution:
Use points (0, 6) and (-3, 0) to determine the function.

 Function Value of y when x = 0 x = –3 y = x + 3 3 0 y = x – 3 –3 –6 y = 2x + 6 6 0 (correct) y = 2x – 6 –6 –12

Question 3:
Table below shows the values of variables x and y of a function.

 x –2 0 1 y –6 2 3
Which of the following functions is satisfied by the ordered pair?
A = 7x + 2
B = x3 + 2
C = x + x2 – 2
D = x2 + 2

Solution:
Only y = x3 + 2 is satisfied by all the ordered pairs.
(i) –6 = (–2)3 + 2
(ii)   2 = 03 + 2
(iii)  3 = 13 + 2

# 13.1 Graphs of Functions

13.1 Graphs of Functions

13.1.1 Functions
1.   Function is a relationship that expresses a variable (dependent) in terms of another variable (independent).

2.   is a function of x if and only if every value of x corresponds to only one value of y.

13.1.2  Graphs of Functions
1.   A graph of function is a representation of the function as one or more lines on a coordinate plane.
Example:

2.
When drawing graphs of functions, it is best to observe these few points:
· choose suitable scales for both axes.
· use at least three points to draw a straight line to ensure accuracy.
· use at least five points to draw a curve to ensure accuracy.