Easy -1.2 This is a straightforward algebraic manipulation requiring three basic steps: multiply by c, add 5, then square both sides. It tests routine rearrangement skills with a single surd, which is simpler than typical C1 questions that involve multiple techniques or problem-solving.
M1 for each of 3 correct or ft correct steps s.o.i. leading to \(y\) as subject
\(ac + 5 = \sqrt{y}\) o.e.
M1
\([y] = [(ac + 5)^2\) o.e. isw
M1
or some/all steps may be combined; allow B3 for \([y] = [(ac + 5)^2\) o.e. isw or B2 if one error
Question 4(i)
Answer
Marks
Guidance
\(2 - 2x > 6x + 5\)
M1
or \(1 - x > 3x + 2.5\)
\(-3 > 8x\) o.e. or ft
M1
for collecting terms of their inequality correctly on opposite sides eg \(-8x > 3\)
\(x < -3/8\) o.e. or ft isw
M1
allow B3 for correct inequality found after working with equation allow SC2 for \(-3/8\) o.e. found with equation or wrong inequality
Question 4(ii)
Answer
Marks
Guidance
\(-4 < x < 1/2\) o.e.
2
accept as two inequalities M1 for one 'end' correct or for \(-4\) and \(1/2\)
Question 5(i)
Answer
Marks
Guidance
\(7\sqrt{3}\)
2
M1 for \(\sqrt{48} = 4\sqrt{3}\) or \(\sqrt{27} = 3\sqrt{3}\)
Question 5(ii)
Answer
Marks
Guidance
\(\frac{10 + 15\sqrt{2}}{7}\) www isw
3
B1 for 7 [B0 for 7 wrongly obtained] and B2 for \(10 + 15\sqrt{2}\) or B1 for one term of numerator correct; if B0, then M1 for attempt to multiply num and denom by \(3 + \sqrt{2}\)
$ac = \sqrt{y - 5}$ o.e. | M1 | M1 for each of 3 correct or ft correct steps s.o.i. leading to $y$ as subject
$ac + 5 = \sqrt{y}$ o.e. | M1 |
$[y] = [(ac + 5)^2$ o.e. isw | M1 | or some/all steps may be combined; allow B3 for $[y] = [(ac + 5)^2$ o.e. isw or B2 if one error
## Question 4(i)
$2 - 2x > 6x + 5$ | M1 | or $1 - x > 3x + 2.5$
$-3 > 8x$ o.e. or ft | M1 | for collecting terms of their inequality correctly on opposite sides eg $-8x > 3$
$x < -3/8$ o.e. or ft isw | M1 | allow B3 for correct inequality found after working with equation allow SC2 for $-3/8$ o.e. found with equation or wrong inequality
## Question 4(ii)
$-4 < x < 1/2$ o.e. | 2 | accept as two inequalities M1 for one 'end' correct or for $-4$ and $1/2$
## Question 5(i)
$7\sqrt{3}$ | 2 | M1 for $\sqrt{48} = 4\sqrt{3}$ or $\sqrt{27} = 3\sqrt{3}$
## Question 5(ii)
$\frac{10 + 15\sqrt{2}}{7}$ www isw | 3 | B1 for 7 [B0 for 7 wrongly obtained] and B2 for $10 + 15\sqrt{2}$ or B1 for one term of numerator correct; if B0, then M1 for attempt to multiply num and denom by $3 + \sqrt{2}$