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Name: ________________
Class: ________
Date: ________________________
Grade 9 Math
Number Sense Unit Test Review Package
Assessment Date: Thursday November 27th
Outcomes that will be assessed
A3 demonstrate an understanding of the meaning and uses of irrational numbers
A5 compare and order real numbers
B2 add, subtract, multiply, and divide rational numbers in fractional and decimal forms using the most appropriate
method
B3 apply the order of operations in rational number computations
A1 solve problems involving square root and principal square root
B1 model, solve, and create problems involving real numbers
B4 demonstrate an understanding of, and apply the exponent laws for, integral exponents
B5 model, solve, and create problems involving numbers expressed in scientific notation
This review package will help you review the material from the Number Sense Unit.

If you need help with a concept:
o Use your math journal,
o Ask Ms. Maier for help and/or
o Watch the videos on Ms. Maier’s website.

Copy and complete each question on loose-leaf and check your answers on the answer
key as you go.
Part A: Comparing and Ordering Real Numbers
1) Draw a number line from -2 to +2 and label with the following numbers.
0.3, (-0.4),
3
,
4
1
,
10
0.01,
3,  4
2) List the following numbers from least to greatest.
0.05,
-0.4,
5
,
10

1
,
10
2 110
0.01,
,
9
Part B: Operations with Decimals and Fractions
a) 5.73 + 15.69 =
b) 8.52 – 3.9 =
c) 1.8 x 6.4 =
d)
0.05 3.2055
a)
5 3
 =
3 4
f)
5 2
 
6 3
g)
7 2

5 3
h)
2 5

5 3
Challenge
i) 2.1 x (-2.3) x (-0.3) =
k)
 2 13   34   0.2) 
j) 5.2 – 9.4 =
l) (-1.305) ÷ 0.5 =
Part C: Order of Operations


Complete each question below using the correct order of operations (BEDMAS)
Make sure to show all steps and put a box around your final answer.
1)
52  4  2  6  3
2)
4(2 2  5)   3 110
3)
1 2 1 1
  
2 3 2 4
4)
3.4  2  0.3  0.75
6)
(1.4)  (2.3)(1.5)  0.2
Challenge
2
3 3  1
 1
5)         
4 2  2
 2
2
Part D: Problem Solving


Complete each question below use the 4 step model for problem solving.
Remember the 4 steps are:
a) Explore
What I know:
What I want to find out:
b) Plan
Plan:
Estimate:
c) Solve
Show and explain all steps below:
d) Examine
Did you answer what was asked?
Does your answer seem reasonable?
1) A school policy requires that there be at least one chaperone for every 16 students on a field
trip. How many chaperones are required for a field trip with 76 students?
Challenge
2) At the Superstore oranges are 10 cents each and apples are 25 cents each. How many
oranges and apples can you buy for exactly $1.95
Part E: Exponent Laws
Multiplying Powers
1) am x an =
2) a5 x a3 =
3) a5b3 x a2b10 =
4) 10a5b33 x 5ab10 =
Dividing Powers
5) am ÷ an =
6) a3 ÷ a2 =
y 10
7) 7 
y
10 x 7 y 5 z 15

8)
2 x 2 y 3 z 15
Power of a Power
9) (am)n =
10) (a10)2 =
11) (510)0 =
12) (a-10)-20 =
Challenge – Write all answers using positive exponents only, and simplify using the
exponent of zero rule if necessary.
13) (32 x 43)5 =
15)
3
 5a 2 
 
14) 
 3b 
2
5
16) 4a b c  5ab c
2
40a 3 b 3

20a 4 b
4
4

Part F: Square Roots and Pythagorean Theorem
1) List the perfect square numbers from 1 to 144
2) Estimate the square root of each of the following. Show your steps and/or
explain how you estimated.
a)
b)
5
80
3) For each Pythagorean theorem question:
 Draw a diagram and label with the information you are given.
 Apply the Pythagorean Theorem (a2 + b2 = c2 or b2 = c2 – a2)
 Solve, (show all of your steps)
 Include units for your answer.
 Put a box around your final answer.
a) Find the length of the missing side of the triangle.
i)
?
2cm
7cm
ii)
12m
4m
?
b) The bottom of a ladder must be placed 5 feet from a wall. The ladder is 10 feet long.
How far above the ground does the ladder touch the wall?
Challenge
c) The area of a square is 64 cm2. Find the length of a side. Find the length of the
diagonal.
Part G: Scientific Notation
1) Write each number in scientific notation.
45000
0.0043
2) Write each of the following numbers in standard form.
5.23 x 103
7.17 x 10-4
3) Add or Subtract each of the following. Keep numbers in scientific notation. DO
NOT convert numbers to standard form.
(2.7 x 109) + (3.4 x 109) =
(5.3 x 10-7) + (1.2 x 10-7) =
(4.7 x 109) - (1.4 x 109) =
(5.6 x 10-10) - (2.7 x 10-10) =
4) Multiply or divide each of the following. Keep numbers in scientific notation. DO
NOT convert numbers to standard form.
(1 x 1010) x (2 x 1020) =
(1.5 x 10-10) x (2.3 x10-2) =
(8 x 1012) ÷ (2 x 103) =
(5.25 x 107) ÷ (5 x 103) =
Challenge
5) Rewrite in proper scientific notation
32 x 1010
0.25 x 10-4
6) Add or subtract and then rewrite each answer in proper scientific notation.
(1.7 x 108) + (43 x 107) =
(9.8 x 10-7) - (50 x 10-8) =
7) Multiply or divide and then rewrite each answer in proper scientific notation.
(3.7 x 10100) x (4.8 x 1010) =
(9.76 x 10-7) ÷ (2 x 10-8) =
8) Problem Solving using numbers in scientific notation.
For each problem:
 Complete on loose-leaf.
 Write down what you know and what you want to find out.
 Show all steps.
 Keep all numbers in scientific notation.
 Write your final answer in a sentence.
a) The world population is approximately 6 x 109. The total land area of the Earth is
approximately 1.5 x 108 km2. Approximately how are there per km2 of Earth’s
surface?
Write your answer in scientific notation and in standard form.
Challenge
b) If the speed of light is 3 x 108 meters/second. How many seconds does it take
light to reach the Earth, if the sun is 1.5 x 1011 meters from Earth?
Write your answer in scientific notation.