Question 1:
Diagram 1 shows the stem-and-leaf plot for time taken by a group of students in a survey.
(a) State the number of students who took part in the survey. [1 mark]
(b) Determine the mode of distribution. [1 mark]
(c) Write one inference based on distribution of the time. [1 mark]
Solution:
(a)
Time of answering the Survey for each student
1st student = 15 minutes
2nd student = 18 minutes
3rd student = 32 minutes
.
.
.
.
.
12th student = 54 minutes
Number of students = 12
(b) Mode of distribution = 46
(c) Inference : Maximum time of answering the survey is 54 minutes
Diagram 1 shows the stem-and-leaf plot for time taken by a group of students in a survey.
(a) State the number of students who took part in the survey. [1 mark]
(b) Determine the mode of distribution. [1 mark]
(c) Write one inference based on distribution of the time. [1 mark]
Solution:
(a)
Time of answering the Survey for each student
1st student = 15 minutes
2nd student = 18 minutes
3rd student = 32 minutes
.
.
.
.
.
12th student = 54 minutes
Number of students = 12
(b) Mode of distribution = 46
(c) Inference : Maximum time of answering the survey is 54 minutes
Question 2:
(a) In the answer space, complete Table 1 for the equation y = 2x2 – 3 for -3 ⩽ x ⩽ 3. [1 mark]
(b) Hence, draw the graph of y = 2x2 – 3 for -3 ⩽ x ⩽ 3. [2 marks]
Solution:
(a)
$$ \begin{aligned} & y=2 x^2-3 \\ & \text { When } x=-2.5 \\ & y=2(-2.5)^2-3 \\ & y=9.5 \end{aligned} $$
$$ \begin{aligned} & \text { When } x=-1.5 \\ & y=2(-1.5)^2-3 \\ & y=1.5 \end{aligned} $$
$$ \begin{aligned} & \text { When } x=1 \\ & y=2(1)^2-3 \\ & y=-1 \end{aligned} $$
$$ \begin{aligned} & \text { When } x=1 \\ & y=2(2)^2-3 \\ & y=5 \end{aligned} $$
(b)
(a) In the answer space, complete Table 1 for the equation y = 2x2 – 3 for -3 ⩽ x ⩽ 3. [1 mark]
(b) Hence, draw the graph of y = 2x2 – 3 for -3 ⩽ x ⩽ 3. [2 marks]
Solution:
(a)
$$ \begin{aligned} & y=2 x^2-3 \\ & \text { When } x=-2.5 \\ & y=2(-2.5)^2-3 \\ & y=9.5 \end{aligned} $$
$$ \begin{aligned} & \text { When } x=-1.5 \\ & y=2(-1.5)^2-3 \\ & y=1.5 \end{aligned} $$
$$ \begin{aligned} & \text { When } x=1 \\ & y=2(1)^2-3 \\ & y=-1 \end{aligned} $$
$$ \begin{aligned} & \text { When } x=1 \\ & y=2(2)^2-3 \\ & y=5 \end{aligned} $$
(b)