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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%

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(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)

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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)

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12

[2n a (n+ −1)d].

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Question 2 continued

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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)

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Question 3 continued

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(Total 7 marks)

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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)

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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)

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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)

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