Download review guide #1- number system unit summative assessment

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REVIEW GUIDE #1- NUMBER SYSTEM UNIT SUMMATIVE ASSESSMENT
1) Without using the square root button on your calculator, estimate √800 as
accurately as possible to 1 decimal place.
2) Write two equivalent expressions that represent the situation. Demonstrate or
model why these two expressions are the same.
"Mt. Everest, the highest elevation in Asia, is 29,028 feet above sea level. The Dead
Sea, the lowest elevation, is 1,312 feet below sea level. What is the difference
between these two elevations?"
3) The temperature was +3∘ C at midday.
By evening, the temperature was −5∘ C.
(a) Some of the calculations below show how to figure out the temperature change.
Circle any that apply.
(b) What was the change in temperature? Explain your answer.
4) What is the distance between 6 and −6? between 24 and 17? between 17 and
24? between 𝑡 and 4? The distance between two points is always positive. If 𝑎 and 𝑏
are two points on a number line, the distance is therefore either 𝑎 − 𝑏 or 𝑏 − 𝑎,
whichever is nonnegative. This is an example of an 𝑎𝑏𝑠𝑜𝑙𝑢𝑡𝑒 − 𝑣𝑎𝑙𝑢𝑒 calculation,
and the result is written ∣ 𝑎 − 𝑏 ∣. What is the meaning of ∣ 𝑏 − 𝑎 ∣?
5) The three seventh grade classes at Sunview Middle School collected the most
boxtops for a school fundraiser, and so they won a $600 prize to share among them.
Mr. Aceves’ class collected 3,760 box tops, Mrs. Baca’s class collected 2,301, and Mr.
Canyon’s class collected 1,855. How should they divide the money so that each class
gets the same fraction of the prize money as the fraction of the box tops that they
collected?
6) Think about the following then state the opposites of the problems below.
What is the value of 3 + (−3)? What is the value of (−10.4) + 10.4? These pairs of
numbers are called 𝑜𝑝𝑝𝑜𝑠𝑖𝑡𝑒𝑠. What is the sum of a number and its opposite? Does
every number have an opposite?
State the opposite of:
(a) −2.341
1
(b) 3
(c) 𝑥
(d) 𝑥 + 2
(e) 𝑥 − 2
7) In what situations does the order in which you subtract two numbers not
matter? (i.e., when does 𝑎 − 𝑏 = 𝑏 − 𝑎)
8) On the number line below, the numbers a and b are the same distance from 0.
What is a+b? Explain how you know.
9) Describe the relationship between the following pairs of numbers:
(a) 24 − 11 and 11 − 24
(b) 𝑥 − 7 and 7 − 𝑥
(c) ∣ 𝑥 − 7 ∣ and ∣ 7 − 𝑥 ∣
10) On a number line, what number is halfway between
(a) −4 and 11
(b) 𝑚 and 𝑛?
11) Make a dot somewhere between 0 and 0.5 on a number line, and label it 𝑘. Place
each of the following on the same number line as accurately as you can.
(a) −𝑘
(b) 2𝑘
(c) 𝑘 2
(d) 𝑘 − 2
(e)√𝑘
12) Mark a random number 𝑥 between 1 and 2 (at a spot that only you will think of)
on a number line. Plot the 𝑜𝑝𝑝𝑜𝑠𝑖𝑡𝑒 of each of the following:
(a) 𝑥
(b) 𝑥 + 5
(c) 𝑥 − 4
(d) 6 − 𝑥
13) The current balance of Alex’s account is 727.1rmb. He withdrew
78.34 rmb from his savings account. What is his balance after the withdrawal?
Show work.
14) Write two equivalent expressions that represent the situation. Demonstrate or
model why these two expressions are the same.
"Roman Civilization began in 509 B.C. and ended in 476 A.D. How long did Roman
Civilization last?"
15) 27) Represent each of the following rational numbers in fraction form. (8.NS.1)
a)
0.47
b)
-0.405
c)
-6.94
16) The numerical expression
3 12
5
-64 +
· 5 = is equal to what rational
8 105 6
number? Show your work.
17) Approximate the decimal equivalent to the hundredths place.
a)
38
b)
93
c)
174
18) Circle all of the rational numbers from the list below and explain why it
is rational.
a)
b)
17
196
c)
4.68
d)
-2p
e)
4.303003000...
f) 96
19) Simplify the following perfect squares:
a)
324
b)
225
d)
5184
e)
9604
20) Find the value of the expression:
-2.6 · 5 +
c)
f)
256
1156
(-3.8 + 0.2)
=
-0.6