Question 7 - A-Level Maths

AQA Paper 1 Specimen — Question 7 4 marks

Exam Board	AQA
Module	Paper 1 (Paper 1)
Session	Specimen
Marks	4
Paper	Download PDF ↗
Mark scheme	Download PDF ↗
Topic	Discriminant and conditions for roots
Type	Find k for equal roots
Difficulty	Moderate -0.3 This is a standard discriminant problem requiring students to apply the condition b² - 4ac = 0 for equal roots, then solve the resulting quadratic equation in k. It's slightly easier than average because it follows a well-practiced procedure with no conceptual surprises, though algebraic manipulation requires care.
Spec	1.02d Quadratic functions: graphs and discriminant conditions

Find the values of \(k\) for which the equation \((2k - 3)x^2 - kx + (k - 1) = 0\) has equal roots. [4 marks]

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Question 7:

Answer	Marks	Guidance
7	Clearly states that
equal roots b2 4ac0	AO2.4	B1

k24(2k3)(k1)0

7k2 20k120

6 k  ,k 2

7 Forms quadratic expression in k

Answer	Marks	Guidance
(allow one error)	AO1.1a	M1

Obtains correct quadratic equation in k

Answer	Marks	Guidance
(PI by correct values for k)	AO1.1b	A1

Obtains correct values for k for ‘their’

Answer	Marks	Guidance
quadratic equation	AO1.1b	A1F
Total	4
Q	Marking Instructions	AO

Question 7:
7 | Clearly states that
equal roots b2 4ac0 | AO2.4 | B1 | b24ac0for equal roots
k24(2k3)(k1)0
7k2 20k120
6
k  ,k 2
7
Forms quadratic expression in k
(allow one error) | AO1.1a | M1
Obtains correct quadratic equation in k
(PI by correct values for k) | AO1.1b | A1
Obtains correct values for k for ‘their’
quadratic equation | AO1.1b | A1F
Total | 4
Q | Marking Instructions | AO | Marks | Typical Solution

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Find the values of $k$ for which the equation $(2k - 3)x^2 - kx + (k - 1) = 0$ has equal roots.
[4 marks]

\hfill \mbox{\textit{AQA Paper 1  Q7 [4]}}

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Q1 1 Q2 1 Q3 3 Q4 6 Q5 8 Q6 4 Q7 4 Q8 7 Q9 8 Q10 10 Q11 8 Q12 8 Q13 3 Q14 10 Q15 8 Q16 5 Q17 6