Date
Name
Math 8
EOST Review
Review the
"l Can" statement list for the main concepts of each unit
(1
-
Period for Units 1 - 4
4) covered this semester.
Unit 1: 1Can......
. . .
use order of operations to simplify and/or evaluate an expressions.
identify equations that have one solution, infinitely many solutions or no solutions. solve multistep one variable equations that have rational coefficients and variables on both sides.
Unit 2;
o o o o e . . . o . r o o o o
identify numbers as rational or irrational. apply the properties of integer exponents to simplify and evaluate numerical expressions. evaluate the square roots of small perfect squares and cube roots of small perfect cubes. understand that all non-perfect square roots and cube roots are irrational. estimate numbers as a product of a single digit and a power of ten. compare numbers expressed as a product of a single digit and a power of ten by a scale factor. represent very large and small quantities in scientific notation and use appropriate units. convert between decimal notation and scientific notation. perform mathematical operations with numbers in scientific notation. solve equations of the form x2 - p and x3 = p using square or cube roots. place irrational numbers on a number line. use approximations of irrational numbers to estimate the value of expressions. use the Pythagorean Theorem to solve problems finding a missing side use the Converse of the Pythagorean Theorem to determine if three sides form a right triangle usc the formula for volume of circular solids (cylinder, cone & sphere) to solve problems.
Unit 3:
o r o
identify relations that are functions (given ordered pairs, tables, mappings, graphs or equations) identify the domain & range for a function from list of ordered pairs, table, mapping or graph. find functions values given the function equation and value requested.
Unit 4:
e o o o .
find slope between coordinate points, a table, a graph or an equation and graph the linear equation identify the slope of horizontal or vertical lines graph a linear equation from a pair of points, table of values or an equation write the equation of a line given the slope & y-intercept, the slope & a point, two points or a graph. determine if a function is linear or non-linear from a table, graph or equation
Unit 1: Algebra Basics Simplifu the following:
L.32-5(6+4)+Z
Evaluate using x -- 2,Y = 7 gnd z =
a.
3(x
-
8y)
2. tO-2.52+L2
3.
5. 2x2 +5y -22
5. 5x-4y2 -72+8
18
-
2(3x + 7) + 5{x
4
-
1")
Solve:
8. 8-6x=4x+48
7.215x+71=lS
10.
.
-15-3x=4x-2x
9. 11+3x-7:r6x+5-3x
11.3x+2(5x-3)=7
Solve by writing an equation to represent the situation, and then answer the question.
12. Maria and Tom sold candy bars for a fundraiser. Maria sold 7 less than hlrice the number of candy bars that Tim sold. ln total, Maria and Tim sold 137 candy bars. Find the number of candy bars sold by each.
13. The length of a rectangle is 2 more than 3 times the width. If the perimeter is 92, find the dimensions of the rectangle.
14. Eleven diminished by 5 times a number
is the same as 4 times
the number increased by 20. Find the number.
Unit 2: Exponents, Scientific Notation, Radicals
Simpliff the following:
t.
rf
s.{r5
.ns
z. *0.
lnlL
b.mo
f
3.
b(fz.Lz fyf
4.
,
15' rsz
s.#
"
3.5asb'2c3 . 3a{b7c
10.
(m6)s
L1. (3zr)2
({3}0
14.
t-7y)0
15.
-7}p
L6.
TZx2yoz''
',.(#)
ls
(#)
,,
(,-q)'
zo
wo
22.
(2mI3
23.
(32)a
24.
a-zb4 3a-J
9.
(,C)'
13.
L
2L: ---2-3
12. (-5x)2
-
zs.# 15y'
zo. (2xzy){5x'Y}+
Find the following perfect square
1.
y'T60
z.
12t/
27.
(Zrtsz1't
28, ?xzys + 14x2y3
rootr and cuhe roots.
V&
3.
fi6-e
4.
iffi
Setween what turo whole numbers does the following squar€ root fall between?
s.
166'
6.
y'3I
7.
fi46
B.
Estlmate the tollowlng rguare roots to the nearest tenth,
9.
./Tq
10.
1ff0
11.
rm
tz,
€IT
1ffi
-
10x4y
Solve the following equations involving perfect squares and perfect cube variables.
L3.2x2-14=84
!4.
x2-L=12o
15.
x3
+L2=-15
16. 2x3=128
17. For the following numbers, circle ALL that are irational.
-% VTi6
3.26 -11
,lA
nn n
7L.L3
rc.2146
18. Change the following numbers from scientific notation to standard form.
2. 4.05 x 10-3
1. 3.271 x 106
3. 5.0809 x 10 -7
19. Change the following numbers from standard to scientific notation form. 1,
32,500,000
20, Compare the following
1. 1,160,000
2.
0.000477
3.
5,430,000,000,000
4. 0.0000000000234
as <, > or =.
O
1.16 x
105
2. 0.0036
Q
s.o
* ro*
21. Put the following in least to greatest order. 1,,47
xL0'2,
L.47
xLO}, L4,700,
0.00147
22. Perform the following mathematical operations with scientific notation.
5.5x1.08+3.2x108
{7.1.x1.0-3X2.2x107)
8.4x106-3.4x105
(2.4x104X3.3x106)
X 1012
8.4 X 108
6.9
4.2 X 1-0s
2.3 X 1"0*3
Unit 2 Part 2: Volume of Circular Solids and Pythagorean Theorem
Volume
Cylinder:
Formulas: Cone: Sphere:
V = ntz h V =Yrnr2 h Y = 4/3nr3
Find the volume for each figure below, both in terms of TI and approximate, rounding to the nearest tenth.
Answer in terms of ?I
(exact)
Using 3.14 for ?I
1. Sphere with diameter of 8 in.
2, Cylinder with
a height of 3 cm and
radius of 5 cm
3.
Cone with a height of 7
ft. and
diameter of 12tt.
lt has a diameter of 6 inches and a height of I inches. lf the end of the funnel plugged, how much oil can the funnel hold before it overflows? Find your answer to the nearest tenth.
4. An oil funnel
is in the shape of a cone.
5. A cylindrical glass has a radius of 4 inches and a heighth of 10 inches. What glass can hold? Find your answer to the nearest tenth.
6.
is
is
the maximum amount of koot-aid :) the
A scoop of ice cream from Bruster's has a diameter of 4.8 inches. What is the volume of the scoop of ice cream to the
nearest tenth?
Pythagorean Theorem is the relationship between the sides of a right triangle: Find the length of the missing side of each right triangle, Estimate answers to the nearest tenth as needed.
7. find x
8. find
9. a=7,c=L(,findb
x
Determine whether the given side lenths form a right triangle, are they a Pythagorean Triple? Yes or No
10. 25 ft, 15 ft, 20
ft
tL. 7 in,4 in,5 in
L2. 4A cm,9 cm,4lcm
Using the Pythagorean Theorem, solve the following problems. Round answers to the nearest tenth as needed. Draw an
illustration if one is not provided. Answer the question with a complete sentence. 13. A 30 foot ladder is leaned against a wall. lf the base of the ladder is 12 feet from the wall, how high up the wall will the ladder reach?
14. A rectangle is 1.1 in wide and 13 in long. Find the length of its diagonal.
15. Megan lives 9 miles north of the mall. Cindy lives 12 miles east of the mall. What Megan and Cindy's homes?
is
the shortest distance between
Unit 3: Relations, Functions and Number System State the domain and range of each relation. Then determine whether each relation is a function.
1' sormain
Ramge
2.
21
25 30
Domain:
Domain:
Range:
Range:
Function: Yes/No
LinearlNon-Linear
Function: Yes/No
4. {(-3,4), (-2,4),(-1, -1)(3,
3.
Linear/Non-Linear
-t)}
Domain: Range:
LinearlNon-Linear
Function: YeslNo Domain: Range:
tunction: Yes/No Linear/Non-Linear Find the value if
/(r)
=
Zx
*
1
s./(0)
Find the value if
7' s{4)
6.
g(x) =
2
-
f(12)
Zx
a.g(-1)
Unit 4: Linear Equations Determine the slope:
l.
2. l-t,7)anO l-LL,7l
l-Lz, -1) and (-3, -4)
3,
x
v
-2
10
-4
4
-6 -8
-2
-10
-8 -L4
5.
Write a linear equatiort in slope intercept form using the given lnformation.
6. m * 1 and y-intercept
= -7
7. m = -4 and
passes thru (0, -5)
8. m =%
and passes thru (0, 1)
10. (0, 1) and (t-3, -7) are points on the line
ldentify the slope and y'intercept for the following: 11.
Y
L2.2x+5y*20
= -3x
13. Y=5x+8
Graph the following linear equations.
L4.
x=4
15. y=-2x+5
16.
x+y=-4
L7. y =-3
For the following problems, determine the rate of change (slope) then can you identify what is being compared (the
practlcal meaning for the probleml.
Time {min}
l#at*r kfi in p:ol fcall
Time
{Hltr}8$
fnrinl
15 30
T}U
13{}
1Ct
sn
45
1
?tl
rlD 4D 2r)
tlli
!4{}
3{r
4tt
*1{}
Fsnrt|ilH$sutflnnJt* ffinud Pythagorean Theorem:
Used to find the
of a right triangle, where a and b represent the
and c represents the
Know the formulas for the volume of circular solids:
Cylinder: Cone: Sphere:
Slope-lntercept Form:
m=
Used
andb= then move
Standard Form:
to identify the equation of
To graph using this form, start at
_
a
on the
connect the point to draw the line.
and
Also used to identify the equation of a
*Be able to convert to y s1x + b in order to graph or identify components of the line. =
Slope Formula;
*A zero "underneath" means
Used to find the slope between two ordered pairs: (xr, yrl
. A zero in the top means
trw Luffit{ ffi #ffi$r ffiefil
& lxr, yzl
