Pre-U Pre-U 9794/1 Specimen — Question 1 3 marks

Exam BoardPre-U
ModulePre-U 9794/1 (Pre-U Mathematics Paper 1)
SessionSpecimen
Marks3
TopicModulus function
TypeSolve |linear| < constant (pure inequality)
DifficultyEasy -1.8 This is a straightforward application of the basic modulus inequality rule |ax + b| < c ⟹ -c < ax + b < c, requiring only algebraic manipulation to solve. It's a routine one-step problem testing recall of a standard technique with no problem-solving or conceptual challenge.
Spec1.02l Modulus function: notation, relations, equations and inequalities
1 Find the set of all real values of \(x\) which satisfy the equation $$| 2 x + 5 | < 7$$
Use method to deal with modulus sign: M1
*EITHER*: Subtraction before division in solving \(-7 < 2x + 5 < 7\)
*OR*: squaring both sides to obtain 3 term quadratic and attempt factorizing or formula
AnswerMarks Guidance
*OR*: sketching \(y =2x + 5 \) with correct intersection points with axes and \(y = 7\) and locating (perhaps implicitly) their intersections
Obtain critical values of \(-6\) and \(1\) B1
Obtain \(-6 < x < 1\) A1
Total: 3
Use method to deal with modulus sign: M1

*EITHER*: Subtraction before division in solving $-7 < 2x + 5 < 7$

*OR*: squaring both sides to obtain 3 term quadratic and attempt factorizing or formula

*OR*: sketching $y = |2x + 5|$ with correct intersection points with axes and $y = 7$ and locating (perhaps implicitly) their intersections

Obtain critical values of $-6$ and $1$ B1

Obtain $-6 < x < 1$ A1

**Total: 3**
1 Find the set of all real values of $x$ which satisfy the equation

$$| 2 x + 5 | < 7$$

\hfill \mbox{\textit{Pre-U Pre-U 9794/1  Q1 [3]}}
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