PLC Papers
Created For:
pic question assessment every 3 days by using the mark scheme to conficently attain 8 out of 10 marks over time
Quadratic equations (completing the square) 1
Grade 8
Objective: Solve quadratic equations by completing the square.
Question 1.
Rewrite � 2 − 8� + 5 in the form (� + �)2 − �
………………………
(Total 1 mark)
Question 2.
Solve � 2 + 2� − 3 = 0 by completing the square.
………………………
(Total 2 marks)
PiXL PLC 2017 Certification
Question 3.
Solve � 2 + 10� − 7 = 0 by completing the square.
Leave your answers in surd form.
………………………
(Total 3 marks)
Question 4.
Solve 2� 2 − 10� + 2 = 0 by completing the square.
Give your answers to 3 significant figures.
………………………
(Total 4 marks)
TOTAL /10
PiXL PLC 2017 Certification
Quadratic equations (completing the square) 2
Grade 8
Objective: Solve quadratic equations by completing the square.
Question 1.
Rewrite � 2 + 6� + 7 in the form (� + �)2 − �
………………………
(Total 1 mark)
Question 2.
Solve � 2 − 10� + 9 = 0 by completing the square.
………………………
(Total 2 marks)
PiXL PLC 2017 Certification
Question 3.
Solve � 2 − 8� − 12 = 0 by completing the square.
Leave your answers in surd form.
………………………
(Total 3 marks)
Question 4.
Solve 4� 2 + 28� − 24 = 0 by completing the square.
Give your answers to 3 significant figures.
………………………
(Total 4 marks)
TOTAL /10
PiXL PLC 2017 Certification
Quadratic equations (completing the square) 3
Grade 8
Objective: Solve quadratic equations by completing the square.
Question 1.
Naomi correctly completes the square on the expression � 2 + �� + � to get (� + 4)2 − 13.
What are the values of p and q?
� =……………
� =……………
(Total 2 marks)
Question 2.
Ralph has a rectangular field to enclose with 500m of fencing.
He must decide on a length, �, and width, �, such that he maximises the area of the field.
a) Show that this problem can be modelled by the quadratic equation � = 250� − �2
(1)
b) Solve by completing the square and write down the maximum area
Area = ………………………m2
(3)
(Total 4 marks)
PiXL PLC 2017 Certification
Question 3.
A small company that makes portable mobile phone chargers has a daily production cost C,
in pounds, given by the relation � = 0.5� 2 − 16� + 850, where � is the number of chargers
made.
a) How many chargers should be made to minimise production cost?
� =………………………
(3)
b) What is the cost when this many chargers are made?
� =………………………
(1)
(Total 4 marks)
Total /10
PiXL PLC 2017 Certification
Quadratic equations (completing the square) 4
Grade 8
Objective: Solve quadratic equations by completing the square.
Question 1.
The sketch shows the graph of a quadratic.
The minimum point of the graph is (4, 1).
Write down two possible equations of the graph in
the form � = �� 2 + �� + �.
� =..……………………………………… or � =..………………………………………
(Total 3 marks)
Question 2.
The height of a projectile in the air � seconds after it is shot can be modelled by the function
� = −15� 2 + 150� + 25, where � is measured in metres.
Complete the square to find the maximum height the projectile reaches and the time taken to
reach this height.
� =………………………m
� =………………………s
(Total 3 marks)
PiXL PLC 2017 Certification
Question 3.
Each month a cupcake stall sells 1400 cupcakes at £2 each. They are reconsidering their
pricing and know that for each £1 increase in price they would sell 100 less cupcakes.
What price should the cupcakes be to maximise the stall’s revenue?
………………………
(Total 4 marks)
Total /10
PiXL PLC 2017 Certification