Question 1 - A-Level Maths

OCR H240/01 2021 November — Question 1 4 marks

Exam Board	OCR
Module	H240/01 (Pure Mathematics)
Year	2021
Session	November
Marks	4
Paper	Download PDF ↗
Topic	Discriminant and conditions for roots
Type	Find range for two distinct roots
Difficulty	Moderate -0.8 This is a straightforward discriminant question requiring only the standard formula b²-4ac > 0 and basic algebraic manipulation to solve for k. It's a routine textbook exercise testing recall of a single technique with minimal problem-solving, making it easier than average.
Spec	1.02d Quadratic functions: graphs and discriminant conditions

1 Determine the set of values of \(k\) such that the equation \(x ^ { 2 } + 4 x + ( k + 3 ) = 0\) has two distinct real roots.

Show mark scheme Show mark scheme source

Question 1:

Answer	Marks	Guidance
Answer	Marks	Guidance
\(16 - 4(k+3)\)	M1*	Attempt discriminant; allow \(b^2 + 4ac\) for M1, but nothing else
\(-4k - 12 + 16 > 0\)	A1	Obtain correct inequality; not necessarily expanded
\(4k - 4 < 0\)	M1dep*	Attempt to solve their inequality or equation for \(k\)
\(k < 1\)	A1	Obtain \(k < 1\)

OR (completing the square or differentiating):

- M1* – attempt to complete the square, or differentiate, and link minimum point to 0

- A1 – obtain \((k+3) - 4 < 0\)

- M1d* – solve their inequality or equation

- A1 – obtain \(k < 1\)

OR (using perfect square):

- M1* – link \(k+3\) to 4

- A1 – obtain \(k + 3 < 4\)

- M1d* – solve their inequality or equation

- A1 – obtain \(k < 1\)

# Question 1:

| Answer | Marks | Guidance |
|--------|-------|----------|
| $16 - 4(k+3)$ | M1* | Attempt discriminant; allow $b^2 + 4ac$ for M1, but nothing else |
| $-4k - 12 + 16 > 0$ | A1 | Obtain correct inequality; not necessarily expanded |
| $4k - 4 < 0$ | M1dep* | Attempt to solve their inequality or equation for $k$ |
| $k < 1$ | A1 | Obtain $k < 1$ |

**OR** (completing the square or differentiating):
- M1* – attempt to complete the square, or differentiate, and link minimum point to 0
- A1 – obtain $(k+3) - 4 < 0$
- M1d* – solve their inequality or equation
- A1 – obtain $k < 1$

**OR** (using perfect square):
- M1* – link $k+3$ to 4
- A1 – obtain $k + 3 < 4$
- M1d* – solve their inequality or equation
- A1 – obtain $k < 1$

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1 Determine the set of values of $k$ such that the equation $x ^ { 2 } + 4 x + ( k + 3 ) = 0$ has two distinct real roots.

\hfill \mbox{\textit{OCR H240/01 2021 Q1 [4]}}

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