Standard +0.8 This question requires understanding modulus equations to find x values, then substituting into a more complex modulus expression. It demands careful case analysis and algebraic manipulation beyond routine modulus problems, but uses standard C3 techniques without requiring novel insight.
4 It is given that \(| x + 3 a | = 5 a\), where \(a\) is a positive constant. Find, in terms of \(a\), the possible values of
$$| x + 7 a | - | x - 7 a |$$
Allow solution leading to \(a=\frac{1}{2}x\) (B1) and \(a=-\frac{1}{8}x\) (M1A1)
Attempt to find second value of \(x\)
M1
By solving equation with signs of \(x\) and \(5a\) different, or by squaring both sides and attempting solution of quadratic equation with three terms. If using quadratic formula to solve equation, substitution must be accurate
Obtain \(-8a\)
A1
And no other values of \(x\)
Substitute each of at most two values of \(x\) (involving \(a\)) leading to one final answer in each case and showing correct application of modulus signs in at least one case
M1
Obtain \(4a\) as final answer
A1
Obtained correctly from \(x=2a\)
Obtain \(-14a\) as final answer
A1
Obtained correctly from \(x=-8a\)
[6]
# Question 4:
| Answer | Marks | Guidance |
|--------|-------|----------|
| Obtain $2a$ as one value of $x$ | B1 | Allow solution leading to $a=\frac{1}{2}x$ (B1) and $a=-\frac{1}{8}x$ (M1A1) |
| Attempt to find second value of $x$ | M1 | By solving equation with signs of $x$ and $5a$ different, or by squaring both sides and attempting solution of quadratic equation with three terms. If using quadratic formula to solve equation, substitution must be accurate |
| Obtain $-8a$ | A1 | And no other values of $x$ |
| Substitute each of at most two values of $x$ (involving $a$) leading to one final answer in each case and showing correct application of modulus signs in at least one case | M1 | |
| Obtain $4a$ as final answer | A1 | Obtained correctly from $x=2a$ |
| Obtain $-14a$ as final answer | A1 | Obtained correctly from $x=-8a$ |
| **[6]** | | |
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4 It is given that $| x + 3 a | = 5 a$, where $a$ is a positive constant. Find, in terms of $a$, the possible values of
$$| x + 7 a | - | x - 7 a |$$
\hfill \mbox{\textit{OCR C3 2015 Q4 [6]}}