CAIE P1 2017 March — Question 1 4 marks

Exam BoardCAIE
ModuleP1 (Pure Mathematics 1)
Year2017
SessionMarch
Marks4
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Mark schemeDownload PDF ↗
TopicDiscriminant and conditions for roots
TypeFind range for two distinct roots
DifficultyModerate -0.5 This is a straightforward discriminant problem requiring students to apply b²-4ac > 0 and solve a quadratic inequality. While it involves multiple steps (setting up discriminant, expanding, solving inequality), it's a standard textbook exercise with no novel insight required, making it slightly easier than average.
Spec1.02d Quadratic functions: graphs and discriminant conditions
1 Find the set of values of \(k\) for which the equation \(2 x ^ { 2 } + 3 k x + k = 0\) has distinct real roots.
Question 1:
AnswerMarks Guidance
AnswerMarks Guidance
\((3k)^2 - 4 \times 2 \times k\)M1 Attempt \(b^2 - 4ac\)
\(9k^2 - 8k > 0\) soi, allow \(9k^2 - 8k \geq 0\)A1 Must involve correct inequality. Can be implied by correct answers
\(0, \frac{8}{9}\) soiA1
\(k < 0, k > \frac{8}{9}\) (or 0.889)A1 Allow \((-\infty, 0)\), \((\frac{8}{9}, \infty)\)
Total: 4 marks
## Question 1:

| Answer | Marks | Guidance |
|--------|-------|----------|
| $(3k)^2 - 4 \times 2 \times k$ | M1 | Attempt $b^2 - 4ac$ |
| $9k^2 - 8k > 0$ soi, allow $9k^2 - 8k \geq 0$ | A1 | Must involve correct inequality. Can be implied by correct answers |
| $0, \frac{8}{9}$ soi | A1 | |
| $k < 0, k > \frac{8}{9}$ (or 0.889) | A1 | Allow $(-\infty, 0)$, $(\frac{8}{9}, \infty)$ |

**Total: 4 marks**

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1 Find the set of values of $k$ for which the equation $2 x ^ { 2 } + 3 k x + k = 0$ has distinct real roots.\\

\hfill \mbox{\textit{CAIE P1 2017 Q1 [4]}}
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