Post on 07-Dec-2021
Save My Exams! – The Home of Revision For more awesome GCSE and A level resources, visit us at www.savemyexams.co.uk/
Quadratic EquationsQuestion Paper 2
Level A LEVEL
Exam Board Edexcel GCE
Subject Mathematics
Module Core 1
Topic Algebra and Functions
Sub-Topic Quadratic Equations
Booklet Question Paper 2
Time Allowed:
Score:
Percentage:
52 minutes
/ 43
/100
Grade Boundaries:
A* A B C D E U
>85% 777.5% 70% 62.5% 57.5% 45% <45%
Save My Exams! – The Home of Revision For more awesome GCSE and A level resources, visit us at www.savemyexams.co.uk/
(4)
8. The equation x2 + 2px + (3p + 4) = 0, where p is a positive constant, has equal roots.
(a) Find the value of p.
(b) For this value of p, solve the equation x2 + 2px + (3p + 4) = 0.(2)
________________________________________________________________________________________________________________________________
________________________________________________________________________________________________________________________________
________________________________________________________________________________________________________________________________
________________________________________________________________________________________________________________________________
________________________________________________________________________________________________________________________________
________________________________________________________________________________________________________________________________
________________________________________________________________________________________________________________________________
________________________________________________________________________________________________________________________________
________________________________________________________________________________________________________________________________
________________________________________________________________________________________________________________________________
________________________________________________________________________________________________________________________________
________________________________________________________________________________________________________________________________
________________________________________________________________________________________________________________________________
________________________________________________________________________________________________________________________________
________________________________________________________________________________________________________________________________
________________________________________________________________________________________________________________________________
________________________________________________________________________________________________________________________________
________________________________________________________________________________________________________________________________
________________________________________________________________________________________________________________________________
________________________________________________________________________________________________________________________________
________________________________________________________________________________________________________________________________
________________________________________________________________________________________________________________________________
________________________________________________________________________________________________________________________________
________________________________________________________________________________________________________________________________
________________________________________________________________________________________________________________________________
________________________________________________________________________________________________________________________________
________________________________________________________________________________________________________________________________
________________________________________________________________________________________________________________________________
________________________________________________________________________________________________________________________________
________________________________________________________________________________________________________________________________
________________________________________________________________________________________________________________________________
Save My Exams! – The Home of Revision For more awesome GCSE and A level resources, visit us at www.savemyexams.co.uk/
9. An arithmetic series has first term a and common difference d.
(a) Prove that the sum of the first n terms of the series is
(4)
Sean repays a loan over a period of n months. His monthly repayments form an arithmetic
sequence.
He repays £149 in the first month, £147 in the second month, £145 in the third month, and
so on. He makes his final repayment in the nth month, where n > 21.
(b) Find the amount Sean repays in the 21st month.
(2)
Over the n months, he repays a total of £5000.
(c) Form an equation in n, and show that your equation may be written as
n2 – 150n + 5000 = 0.
(3)
(d) Solve the equation in part (c).
(3)
(e) State, with a reason, which of the solutions to the equation in part (c) is not a sensible
solution to the repayment problem.
(1)
__________________________________________________________________________
__________________________________________________________________________
__________________________________________________________________________
__________________________________________________________________________
__________________________________________________________________________
__________________________________________________________________________
__________________________________________________________________________
__________________________________________________________________________
__________________________________________________________________________
__________________________________________________________________________
__________________________________________________________________________
__________________________________________________________________________
__________________________________________________________________________
__________________________________________________________________________
12
[2n a (n+ −1)d].
Save My Exams! – The Home of Revision For more awesome GCSE and A level resources, visit us at www.savemyexams.co.uk/
Question 2 continued
__________________________________________________________________________
__________________________________________________________________________
__________________________________________________________________________
__________________________________________________________________________
__________________________________________________________________________
__________________________________________________________________________
__________________________________________________________________________
__________________________________________________________________________
__________________________________________________________________________
__________________________________________________________________________
__________________________________________________________________________
__________________________________________________________________________
__________________________________________________________________________
__________________________________________________________________________
__________________________________________________________________________
__________________________________________________________________________
__________________________________________________________________________
__________________________________________________________________________
__________________________________________________________________________
__________________________________________________________________________
__________________________________________________________________________
__________________________________________________________________________
__________________________________________________________________________
__________________________________________________________________________
__________________________________________________________________________
__________________________________________________________________________
__________________________________________________________________________
__________________________________________________________________________
__________________________________________________________________________
__________________________________________________________________________
__________________________________________________________________________
__________________________________________________________________________
__________________________________________________________________________
__________________________________________________________________________
__________________________________________________________________________
Save My Exams! – The Home of Revision For more awesome GCSE and A level resources, visit us at www.savemyexams.co.uk/
8. The equation 2x2 + 2kx + (k + 2) = 0, where k is a constant, has two distinct real roots.
(a) Show that k satisfies
k2 – 2k – 4 > 0(3)
(b) Find the set of possible values of k.(4)
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
Save My Exams! – The Home of Revision For more awesome GCSE and A level resources, visit us at www.savemyexams.co.uk/
Question 3 continued
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
(Total 7 marks)
Save My Exams! – The Home of Revision For more awesome GCSE and A level resources, visit us at www.savemyexams.co.uk/
4. The equation
( + 2)k x3 6+ +x k = ,5 where k is a constant,
has two distinct real solutions for x.
(a) Show that k satisfies
2k k− −2 24 < 0(4)
(b) Hence find the set of possible values of k.(3)
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
Save My Exams! – The Home of Revision For more awesome GCSE and A level resources, visit us at www.savemyexams.co.uk/
8. The equation 2x k+ −( 3)x + (3− 2k) = 0, where k is a constant, has two distinct realroots.
(a) Show that k satisfies
2k k+ −2 3 0(3)
(b) Find the set of possible values of k.(4)
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
Save My Exams! – The Home of Revision For more awesome GCSE and A level resources, visit us at www.savemyexams.co.uk/
7. The equation kx2 + 4x + (5 – k) = 0, where k is a constant, has 2 different real solutionsfor x.
(a) Show that k satisfiesk2 – 5k + 4 > 0.
(3)
(b) Hence find the set of possible values of k.(4)
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________