Edexcel IGCSE Math A 3 sequences functions and graphs

Use this question-bank hub to move from sequence rules and function notation into coordinates, straight lines, graph interpretation and calculus skills.

Covered syllabus points

3.1 Sequences 3.2 Function notation 3.3 Graphs 3.4 Calculus

[Maximum number: 3]

Jalina left her home at 1000 to cycle to a park.
On her way to the park, she stopped at a friend's house and then continued her journey to the park.
Here is the distance-time graph for her journey to the park.

Figure for Question 3 Sequences, functions and graphs question 1 — Edexcel IGCSE Math A Higher

(a)

On her journey to the park, did Jalina cycle at a faster speed before or after she stopped at her friend's house?
Give a reason for your answer.

Jalina stayed at the park for 45 minutes.
She then cycled, without stopping, at a constant speed of $16 \mathrm{~km} / \mathrm{h}$ from the park back to her home.

[ 1 ]

$15 \mathrm{~km} / \mathrm{h}$ or $\frac{25}{6} \mathrm{~m} / \mathrm{sec}$ or $0.25 \mathrm{~km} / \mathrm{min}$ or $\frac{15}{4}$
oe
$12 \mathrm{~km} / \mathrm{h}$ or $\frac{10}{3} \mathrm{~m} / \mathrm{sec}$ or $0.2 \mathrm{~km} / \mathrm{min}$ or $\frac{9}{3}$ oe

'before' with
reason

1

B1

e.g. before as gradient is steeper
or before as speed before is 15
km / h speed after is $12 \mathrm{~km} / \mathrm{h}$ or
before as she goes over 11(allow
11-12 ) km in $\frac{3}{4}$ hour but only
goes 9 km in $\frac{3}{4}$ hour after oe
NB: any figures used for the
reason must be accurate if they
haven't used 'gradient is steeper'
oe

(b)

Show all this information on the distance-time graph.

[ 2 ]

Line from:
$(12{:}00,24)\to(12{:}45,24)\to(14{:}15,0)$

Marking guidance:
- B2 for the complete line
- If not B2, award B1 for either line segment, or for a time of 1.5 hours seen

[Maximum number: 4]

f is the function such that f(x)=4-3 x

(a)

Work out f(5)
g is the function such that $\mathrm{g}(x)=\frac{1}{1-2 x}$

[ 1 ]

(b)

Find the value of x that cannot be included in any domain of g

[ 1 ]

For $g(x)=\frac{1}{1-2x}$ , the denominator cannot be zero:
$1-2x\ne0$

Final answer:
$x\ne0.5$

(c)

Work out fg(-1.5)

[ 2 ]

$g(-1.5)=\frac{1}{1-2(-1.5)}=\frac14=0.25$ f(g(-1.5))=4-3(0.25)=3.25

Final answer:
3.25

[Maximum number: 6]

The curve C has equation $y=5 x^{3}-x^{2}-6 x+4$

(a)

Find $\frac{\mathrm{d} y}{\mathrm{~d} x}$

\frac{\mathrm{d} y}{\mathrm{~d} x}=

There are two points on the curve C at which the gradient of the curve is 2

[ 2 ]

Final answer:
$\frac{dy}{dx}=15x^{2}-2x-6$

B2 for correct differentiation.
B1 for two of $15x^{2}$ , -2x, and -6 correct.

(b)

Find the x coordinate of each of these two points.

Show clear algebraic working.

[ 4 ]

Set the gradient equal to 2:
$15x^{2}-2x-6=2$ $15x^{2}-2x-8=0$

Factorise:
(3x+2)(5x-4)=0

Final answers:
$x=-\frac23,\qquad x=\frac45$

Allow -0.66 or better for $-\frac23$ .

[Maximum number: 3]

Here are the first four terms of an arithmetic sequence.

$1\qquad4\qquad7\qquad10$

(a)

Find an expression, in terms of n, for the nth term of this sequence.

[ 2 ]

3n-2

M1 for 3n+k, where $k\ne -2$ , or equivalent.
A1 for 3n-2, or equivalent such as 1+(n-1)3.
Working not required, so a correct answer scores full marks unless from obvious incorrect working.

(b)

The nth term of a different arithmetic sequence is 5n+17.

Find the 12th term of this sequence.

[ 1 ]

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Covered syllabus points

3 Sequences, functions and graphs question 1

Question (a)

Question (b)

3 Sequences, functions and graphs question 2

Question (a)

Question (b)

Question (c)

3 Sequences, functions and graphs question 3

Question (a)

Question (b)

3 Sequences, functions and graphs question 4

Question (a)

Question (b)