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Page 1 of 6
Mark schemes
Q1.
(a) ( x โ 10)( x + 10)
either order ignore fw B
Additional Guidance
( x + 10)( x + โ10)
B
Condone missing bracket at end only
( x โ 10)( x + 10
B
( x โ 10( x + 10)
B
( x โ 10)( x + 10) followed by attempt to solve, e.g. answer x = 10, x = โ 10
B
answer only x = 10, x = โ 10
B
(b) 7 x โ 2 x > 1 โ 6 or 5 x > โ 5
or 6 โ 1 > 2 x โ 7 x or 5 > โ 5 x
or 1 > โ x
oe collecting terms M
x > โ 1 or โ1 < x
SC1 incorrect sign e.g. x โฅ โ1 or x = โ 1
or answer of โ 1 A
Additional Guidance
M1A
SC
x > โ1 with -1 or 0, 1, 2, โฆ.. as the answer M1A [3]
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Q2.
(a) 4 x โค 13 + 7 or x โ โค oe
M
x โค 5
SC1 x < 5 or x = 5 or x โฅ 5
A
(b)
B [4]
Q3.
(a) Open circle at โ2 with line going right to at least 4
or
arrow (of any length) to the right Strand (i) If line is marked with any sort of circle at the RHS this is Q Q
(b) 3 x โค 11 โ 5 or 3 x โค 6 or x โ 2 โค 0
Working with = sign must be recovered to โค to gain any credit M
x โค 2
Must have x โค on answer line
SC1 for x < 2
A [3]
Q4.
(a) 4 x + 12 = 17 or x + 3 =
4 x + 3 = 17 is M
M
Page 4 of 6
or x โ
or x โฅ
oe M
x โฅ 8
SC1 8
SC1 x โฅ 3.6 or x โฅ
A
(b)
B1 x <
or
condone missing arrow for B2 or B B
Additional Guidance
Intention must be clear to indicate x < 4 with minimum of a line drawn to the
left of hollow circle positioned at 4
Is B
implies is B [4]
Q8.
3 x > 13 + 5
oe 3x > 18
3 x โ 18 > 0
x โ 6 > 0
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M
x > 6
SC1 x โฅ 6
A [2]
Q9.
3x < โ9 or x < โ 3
oe M
โ 4
SC1 For x โค โ 4
A [2]
Q10.
(a) or 2 โค w ........ or ........ w < 6
M
2 โค w < 6 or 2 โค w โค 5
A 2 3 4 5
ft M1 A0 and inequality of form a โค w < b or a โค w โค b
SC2 Answer 2 3 4 5 6 or 3 4 5 with M SC1 Answer 6 9 12 15 with M
SC
A1ft
(b) 16 B
(c) their min from (a) โ 3 M
โ 1 ft their min from (a) A1ft [6]
Q11.
5 d โ d > 17 + 3
Allow one sign or arithmetic error
e.g. 4d > 21 or 5 d โ d > 17 โ 3
M
d > 5
A [2]
