IB Pre-Calculus
Chapter 2 Review
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Full marks are not necessarily awarded for a correct answer with no working. Answers must be
supported by working and/or explanations. When an answer is incorrect, some marks may be given for a
correct method, provided this is shown by written working. You are therefore advised to show all
working.
1.
The quadratic function f is defined by 𝑓(𝑥) = 2𝑥 2 + 12𝑥 + 11.
(IBSL 2008 Paper 1)
a). Express f in the form 𝑓(𝑥) = 2(𝑥 − ℎ)2 + 𝑘
[3marks]
b). Write down the vertex of the graph.
[2 marks]
c). Write down the equation of the axis of symmetry of the graph of f.
[2 marks]
d). Find the y-intercept of the graph of f.
[2 marks]
e). The x-intercepts of f can be written as
p q
, where 𝑝, 𝑞, 𝑟 ∈ ℤ . Find the values of 𝑝, 𝑞, 𝑟.
r
[3 marks]
d). Use your findings and graph the function f showing your vertex, x and y-intercepts. [2 marks]
e). The graph of f is translated 4 units in the positive x-direction and 2 units in the positive
y- direction. Find the function g for the translated graph, giving your answer in the form
𝑔(𝑥) = 2(𝑥 − 𝑝)2 + 𝑞.
[4 marks]
2.
Let 𝑓(𝑥) = 𝑎(𝑥 − 4)2 + 3
a. Write down the coordinates of the vertex of the curve of f.
[2 marks]
b. Given that 𝑓(2) = 12, find the value of a.
[2 marks]
c. Find the y-intercept of the curve of f.
[2 marks]
3.
Find the zeros of the polynomial function and state the multiplicity of each.
𝑓(𝑥) = −9𝑥 3 (𝑥 − 5)2 (𝑥 + 4)5
[9 marks]
4.
Solve the equation:
5.
Find the equation of the line for which 𝑓(3) = 5 and 𝑓(8) = 2
6.
Find the vertex and axis of symmetry of the quadratic 𝑓(𝑥) = 3𝑥 2 − 12𝑥 + 3. [4 marks]
3
𝑥+2
+
6
𝑥 2 +2𝑥
=
3−𝑥
𝑥
[10 marks]
[4 marks]
7.
Find the quadratic that contains the point (6, −5) and vertex (4, 3).
[4 marks]
8.
Find the zeros of the polynomial 𝑓(𝑥) = 3𝑥 3 + 2𝑥 2 − 1𝑥.
[6 marks]
9.
Divide the polynomial 𝑓(𝑥) = 4𝑥 3 + 9𝑥 2 − 3𝑥 − 10 by 𝑔(𝑥) = 𝑥 + 4 and write a
summary statement in fraction form.
[6 marks]
10.
Sketch the general shape of the graph of the polynomial 𝑓(𝑥) = 𝑥(𝑥 − 3)2 (𝑥 + 5)3 .
[6 marks]
11.
Determine whether (𝑥 − 3) is a factor of 𝑓(𝑥) = 4𝑥 4 − 6𝑥 3 − 7𝑥 2 − 9. Show how you
arrived at your answer.
[5 marks]
12.
Write down the equation that will help you find the least perimeter for a rectangle with an
area of 400 square meters.
[8 marks]