Moderate -0.5 This is a straightforward algebraic manipulation question requiring cross-multiplication and collecting terms to isolate x. While it involves multiple steps (multiply both sides by denominator, expand, collect x terms, factorise), these are routine C1 techniques with no conceptual difficulty or problem-solving insight required, making it slightly easier than average.
each mark is for carrying out the operation correctly; ft
earlier errors for equivalent steps if error does not
simplify problem;
some common errors:
y (x + 3) = 1 − 2x yx + 3 = 1 − 2x M0
yx + 3x = 1 − 2x M0 yx + 2x = −2 M1 ft
yx + 5x = 1 M1 ft x (y + 2) = −2 M1 ft
x (y + 5) = 1 M1 ft −2
x= M1 ft
x= 1 M1 ft y+2
y+5
for M4, must be completely correct;
y (x + 3) = 1 − 2x
yx + 3x = 1 − 2x M0
yx + 5x = 1 M1 ft
x (y + 5) = 1 M1 ft
1
x= M1 ft
Answer
Marks
y+5
yx + 3 = 1 − 2x M0
yx + 2x = −2 M1 ft
x (y + 2) = −2 M1 ft
−2
x= M1 ft
y+2
Question 3:
3 | yx + 3y = 1 − 2x oe or ft
yx + 2x = 1 − 3y oe or ft
x (y + 2) = 1 − 3y oe or ft
]1−3y
[
x= oe or ft as final answer
y+2 | M1
M1
M1
M1 | for multiplying to eliminate
denominator and for expanding
brackets,
or for correct division by y and writing
1 2x
as separate fractions: x+3= − ;
y y
for collecting terms; dep on having an
ax term and an xy term, oe after division
by y,
for taking out x factor; dep on having an
ax term and an xy term, oe after division
by y,
for division with no wrong work after;
dep on dividing by a two-term
expression; last M not earned for triple-
decker fraction as final answer | each mark is for carrying out the operation correctly; ft
earlier errors for equivalent steps if error does not
simplify problem;
some common errors:
y (x + 3) = 1 − 2x yx + 3 = 1 − 2x M0
yx + 3x = 1 − 2x M0 yx + 2x = −2 M1 ft
yx + 5x = 1 M1 ft x (y + 2) = −2 M1 ft
x (y + 5) = 1 M1 ft −2
x= M1 ft
x= 1 M1 ft y+2
y+5
for M4, must be completely correct;
y (x + 3) = 1 − 2x
yx + 3x = 1 − 2x M0
yx + 5x = 1 M1 ft
x (y + 5) = 1 M1 ft
1
x= M1 ft
y+5 | yx + 3 = 1 − 2x M0
yx + 2x = −2 M1 ft
x (y + 2) = −2 M1 ft
−2
x= M1 ft
y+2