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Date May 2018 Marks available 3 Reference code 18M.2.SL.TZ1.S_4
Level Standard Level Paper Paper 2 Time zone Time zone 1
Command term Sketch Question number S_4 Adapted from N/A

Question

Let g(x) = −(x − 1)2 + 5.

Let f(x) = x2. The following diagram shows part of the graph of f.

The graph of g intersects the graph of f at x = −1 and x = 2.

Write down the coordinates of the vertex of the graph of g.

[1]
a.

On the grid above, sketch the graph of g for −2 ≤ x ≤ 4.

[3]
b.

Find the area of the region enclosed by the graphs of f and g.

[3]
c.

Markscheme

* This question is from an exam for a previous syllabus, and may contain minor differences in marking or structure.

(1,5) (exact)      A1 N1

[1 mark]

a.

      A1A1A1  N3

Note: The shape must be a concave-down parabola.
Only if the shape is correct, award the following for points in circles:
A1 for vertex,
A1 for correct intersection points,
A1 for correct endpoints.

[3 marks]

b.

integrating and subtracting functions (in any order)      (M1)
eg  fg

correct substitution of limits or functions (accept missing dx, but do not accept any errors, including extra bits)     (A1)
eg 21gf,(x1)2+5x2

area = 9  (exact)      A1 N2

[3 marks]

c.

Examiners report

[N/A]
a.
[N/A]
b.
[N/A]
c.

Syllabus sections

Topic 5—Calculus » SL 5.5—Integration introduction, areas between curve and x axis
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