Faculty of Science, Technology, Engineering and Mathematics
MU123 Discovering mathematics
MU123
TMA 04 2020J
Covers Units 10, 11 and 12 Cut-off date 20 April 2021
Submission instructions
You will find instructions for completing TMAs in the ‘Assessment’ area of
the MU123 website. Please read these instructions before beginning work on
this TMA.
Reviewing your tutor’s comments on your previous TMA will help you as
you work on this one.
Special instructions
Remember that you need to explain your reasoning and communicate your
ideas clearly, as described in Subsection 5.3 of Unit 1. This includes:
• explaining your mathematics in the context of the question
• the correct use of notation and units
• appropriate rounding.
Your score out of 5 for good mathematical communication (GMC) will be
recorded against Question 8. You do not have to submit any work for
Question 8.
Copyright © 2020 The Open University WEB 08610 0
22.1
, TMA 04 Cut-off date 20 April 2021
Question 1 – 18 marks
This question is based on your work on MU123 up to and including Unit 10.
(a) This part of the question concerns the quadratic equation
8x2 − x − 2 = 0.
(i) Find the discriminant of the quadratic expression 8x2 − x − 2. [2]
(ii) What does this tell you about the number of solutions of the
equation? Explain your answer briefly. [2]
(iii) What does this tell you about the graph of y = 8x2 − x − 2? [1]
(b) Figure 1 shows part of the graph of the quadratic function
y = −x2 + 2x + 35.
Figure 1
(i) Find the equation of the axis of symmetry of the parabola given by
y = −x2 + 2x + 35, explaining your method. [2]
(ii) Use your answer to part (b)(i) to find the coordinates of the vertex
of the parabola given by y = −x2 + 2x + 35. [2]
(c) This part of the question concerns the quadratic function
y = x2 − 14x + 11.
(i) Write the quadratic expression x2 − 14x + 11 in completed-square
form. [2]
page 2 of 10
MU123 Discovering mathematics
MU123
TMA 04 2020J
Covers Units 10, 11 and 12 Cut-off date 20 April 2021
Submission instructions
You will find instructions for completing TMAs in the ‘Assessment’ area of
the MU123 website. Please read these instructions before beginning work on
this TMA.
Reviewing your tutor’s comments on your previous TMA will help you as
you work on this one.
Special instructions
Remember that you need to explain your reasoning and communicate your
ideas clearly, as described in Subsection 5.3 of Unit 1. This includes:
• explaining your mathematics in the context of the question
• the correct use of notation and units
• appropriate rounding.
Your score out of 5 for good mathematical communication (GMC) will be
recorded against Question 8. You do not have to submit any work for
Question 8.
Copyright © 2020 The Open University WEB 08610 0
22.1
, TMA 04 Cut-off date 20 April 2021
Question 1 – 18 marks
This question is based on your work on MU123 up to and including Unit 10.
(a) This part of the question concerns the quadratic equation
8x2 − x − 2 = 0.
(i) Find the discriminant of the quadratic expression 8x2 − x − 2. [2]
(ii) What does this tell you about the number of solutions of the
equation? Explain your answer briefly. [2]
(iii) What does this tell you about the graph of y = 8x2 − x − 2? [1]
(b) Figure 1 shows part of the graph of the quadratic function
y = −x2 + 2x + 35.
Figure 1
(i) Find the equation of the axis of symmetry of the parabola given by
y = −x2 + 2x + 35, explaining your method. [2]
(ii) Use your answer to part (b)(i) to find the coordinates of the vertex
of the parabola given by y = −x2 + 2x + 35. [2]
(c) This part of the question concerns the quadratic function
y = x2 − 14x + 11.
(i) Write the quadratic expression x2 − 14x + 11 in completed-square
form. [2]
page 2 of 10
