Grade 9 / MYP 4
Extended Mathematics
Chapter 1, 2, and 3 Quiz
Name: ________________________________________
Date: __________________
(Note: You will be assessed based on Criteria A: Knowledge and Understanding and Criteria C:
Communication in Mathematics)
Simple problems in familiar contexts:
1) a) Write in algebraic form: The sum of a number and its square.
b) In proper mathematical vocabulary, express in your own words what is meant by 2a - a 3 .
2) Evaluate
3a - 2b
if a  6, b  5, c  4
c
3) Solve for x in each of the following and explain in the right hand column your logic and or reasoning for
each step, i.e justify each step. You do not need to use all the space provided and you may write outside
the space provided if you need to.
a)
3 7
=
Reasoning
2x 3
b)
5- 2x £11
Reasoning
4) Simplify each of the following expressions with positive exponents only.
15x 9 y 2
a)
=
3x 4 y 7
b)
(3x y )
-3 4 3
=
5) When two times a number is subtracted from eight, the result is -18. Write an algebraic equation that
describes this situation and use it to find the number.
6) Each positive whole number can be expressed as a product of prime numbers. Find a, b, c, and d .
a) 120 = 2 a ×3b × 5c
b) 1260 = 2 ×3 × 5 × 7
a
b
c
d
7) How many times larger is (6  1011) than (3  108)? Express your answer in scientific notation and
standard notation.
8) Expand: (4 + 3a)(4 – 3a)
More complex problems:
9) Solve for x in each of the following:
x x
a) - = 4
2 6
b) 3(4 x  2)  x  7  x
c) 2𝑥+1 ∙ 8𝑥 = 4
10) Expand and simplify the following:
11) Simplify the following:
4
3
27  64

( x + 3) ( x +1) ( x -1)
2
3
Challenging Problems in familiar contexts:
kg
kg
. If a substance has a greater density than 1000 3 it will sink in
3
m
m
kg
pure water. If a substance has a lower density than 1000 3 it will float in pure water. The planet
m
Saturn has a mass of 95.12 earths mass. Saturn has the volume of 763.6 earths volume. If the mass of
earth is 5.9736 ´10 24 kg and the volume of earth is 1.08321´1021 km3 , find the density of Saturn. If
Saturn could be placed in a pool of pure water, would Saturn sink or float?
12) The density of pure water is 1000
13) Expand and simplify the following: ( x  4)( x 2  2 x  1)
14) Express in your own words, two different ways to find the area of the large rectangle. Hence, or
otherwise, find the area of the large rectangle.
a
b
c
d
e
Option 1)
Option 2)
Area =
15) Jason rode his bike to his friend’s house traveling at 15kph-1. He traveled back home at 20 kph-1 . The
trip there was 60 minutes longer than the trip back. What was the distance to his friend’s house? Explain
your reasoning and logic in any equations you may use to solve the problem.
Distance
Rate
Time
Challenging Problems in unfamiliar situations:
16) 33 = 27, so the last digit of 33 is 7. What is the last digit of 3100? Is there an easy way to find it? Why
can’t the answer be found using your GDC?
17) Find the values for A and B given:
A
B
4x -1
+
=
for all x ¹1,-2
x -1 x + 2 (x -1)(x + 2)
Achievement Level Descriptor Criterion
Criterion A: Knowledge and Understanding
0 The student does not reach a standard described by any of the descriptors given below.
1–2 The student attempts to make deductions when solving simple problems in familiar contexts.
3–4 The student sometimes makes appropriate deductions when solving simple and more-complex problems
in familiar contexts.
5–6 The student generally makes appropriate deductions when solving challenging problems in a variety of
familiar contexts.
7–8 The student consistently makes appropriate deductions when solving challenging problems in a variety of
contexts including unfamiliar situations.
Criterion C: Communication
0 The student does not reach a standard described by any of the descriptors given below.
1-2
of
The student shows basic use of mathematical language and/or forms of mathematical representation. The lines
reasoning are difficult to follow.
3–4 The student shows sufficient use of mathematical language and forms of mathematical representation. The
lines of reasoning are clear though not always logical or complete. The student moves between different forms of
representation with some success.
5–6 The student shows good use of mathematical language and forms of mathematical representation. The lines of
reasoning are concise, logical and complete. The student moves effectively between different forms of representation.