Question 9:
--- 9(a) ---
9(a) | Shows how this particular value
has been calculated
As in typical solution
Or (–6.51 – (–6)) ÷ (3.1 – 3) | AO1.1b | B1 | (–6.51 – (–6)) ÷ 0.1
(b) | Calculates values for (x + h) and
f(x + h) CAO | AO1.1b | B1 | 3.01, –6.0501
–5.01
Calculates value for gradient | AO1.1b | B1
(c) | Infers suggested limit | AO2.2b | B1 | – 5
(d) | Recalls and applies formula for
gradient | AO1.2 | M1 | 𝑓(3+ℎ)−𝑓(3)
Gradient =
ℎ
(3+ℎ)−(3+ℎ)2−(3−32)
=
ℎ
−ℎ2−5ℎ
=
ℎ
= −ℎ−5
As h → 0, gradient → −5
When x = 3 gradient = –5
Substitutes correct expressions for
f(3 + h) and f(3) | AO1.1b | A1
Simplifies to obtain -h – 5 | AO1.1b | A1
Evaluates gradient at x = 3 and
shows that it is the required value.
Constructs rigorous mathematical
argument to show the required
result.
Only award if they have a
completely correct solution, using
h → 0 (not =0) | AO2.1 | R1
Total | 8
(d) | Alternative
Recalls and applies formula for
gradient | AO1.2 | M1 | 𝑓(𝑥+ℎ)−𝑓(𝑥)
Gradient =
ℎ
(𝑥+ℎ)−(𝑥+ℎ)2−(𝑥−𝑥2)
=
ℎ
−ℎ2−(2𝑥−1)ℎ
=
ℎ
= −ℎ−(2𝑥−1)
As h → 0, gradient → −(2𝑥−1)
When x = 3 gradient = –5
Substitutes correct expressions for
f(x + h) and f(x) | AO1.1b | A1
Simplifies to obtain -h – (2x - 1) | AO1.1b | A1
Evaluates gradient at x = 3 and
shows that it is the required value.
Constructs rigorous mathematical
argument to show the required
result.
Only award if they have a
completely correct solution, which
is clear, easy to follow and contains
no slips. | AO2.1 | R1
Total | 4
Q | Marking Instructions | AO | Marks | Typical Solution