Edexcel FP2 2014 June — Question 2 6 marks

Exam BoardEdexcel
ModuleFP2 (Further Pure Mathematics 2)
Year2014
SessionJune
Marks6
PaperDownload PDF ↗
Mark schemeDownload PDF ↗
TopicModulus function
TypeSolve |quadratic| compared to linear: algebraic inequality
DifficultyStandard +0.8 This requires solving a modulus inequality involving a quadratic, which demands splitting into cases, solving two quadratic inequalities, and carefully combining solution sets. While systematic, it's more demanding than routine A-level questions and requires careful algebraic manipulation across multiple steps, placing it moderately above average difficulty.
Spec1.02g Inequalities: linear and quadratic in single variable1.02l Modulus function: notation, relations, equations and inequalities
2. Use algebra to find the set of values of \(x\) for which $$\left| 3 x ^ { 2 } - 19 x + 20 \right| < 2 x + 2$$
Question 2:
AnswerMarks Guidance
AnswerMark Guidance
\(3x^2 - 19x + 20 = 2x + 2 \Rightarrow 3x^2 - 21x + 18 = 0\)M1 Set equal and attempt to solve correctly. May be solved as inequality
\(x = 1,\quad x = 6\)A1 Both critical values seen
\(-(3x^2 - 19x + 20) = 2x + 2 \Rightarrow 3x^2 - 17x + 22 = 0\)M1 Negate expression, set equal to \(2x+2\), attempt to solve. May be solved as inequality
\(x = \frac{11}{3},\quad x = 2\)A1 Both critical values seen. Accept awrt 3.67
\(1 < x < 2,\quad \frac{11}{3} < x < 6\)A1, A1 Must be strict inequalities. Accept awrt 3.67. A1A0 if both correct apart from \(\leq\) seen. A1A0 if both correct and extra intervals seen 
# Question 2:

| Answer | Mark | Guidance |
|--------|------|----------|
| $3x^2 - 19x + 20 = 2x + 2 \Rightarrow 3x^2 - 21x + 18 = 0$ | M1 | Set equal and attempt to solve correctly. May be solved as inequality |
| $x = 1,\quad x = 6$ | A1 | Both critical values seen |
| $-(3x^2 - 19x + 20) = 2x + 2 \Rightarrow 3x^2 - 17x + 22 = 0$ | M1 | Negate expression, set equal to $2x+2$, attempt to solve. May be solved as inequality |
| $x = \frac{11}{3},\quad x = 2$ | A1 | Both critical values seen. Accept awrt 3.67 |
| $1 < x < 2,\quad \frac{11}{3} < x < 6$ | A1, A1 | Must be strict inequalities. Accept awrt 3.67. A1A0 if both correct apart from $\leq$ seen. A1A0 if both correct and extra intervals seen |

---
2. Use algebra to find the set of values of $x$ for which

$$\left| 3 x ^ { 2 } - 19 x + 20 \right| < 2 x + 2$$

\hfill \mbox{\textit{Edexcel FP2 2014 Q2 [6]}}
This paper (8 questions)
View full paper
Q1 6 Q2 6 Q3 8 Q4 10 Q5 12 Q6 10 Q7 11 Q8 12