Geometry Reference Sheet: R R R RR RH R RH RH R
Geometry Reference Sheet: R R R RR RH R RH RH R
Geometry Reference Sheet: R R R RR RH R RH RH R
Geometry
r
Area = r
2 Reference Sheet
Circumference = 2 r Cylinder
Sector of Circle
r
central circumference × central angle
Rectangle 2 Arc Length =
Volume = r h angle 360º
h Surface Area = 2 r 2 + 2 rh total area × central angle
Area = lw Lateral Area = 2 rh r Sector Area =
w 360º
Perimeter = 2l + 2w
l
Trapezoid
b1 Sphere
Right Prism
1 h(b + b )
Area = – 4 r3
2 1 2 Volume = –
h r 3 Volume = base area × h
Surface Area = 4 r 2 Surface Area = base areas + face areas
h Lateral Area = sum of face areas
b2
Triangle
Area = bh Cone
Volume = –13 r h
2
h Rectangular Solid
s
h Surface Area = r 2+ rs
b
Lateral Area = rs h
r Volume = lwh
Parallelogram Surface Area = 2wl + 2l h + 2wh
w Lateral Area = 2(l + w)h
h Area = bh Right Pyramid l
b 1
Volume = –3
× base area × h
h
Pythagorean Theorem Surface Area = base area + face areas Trigonometry Formulas
c B
a2 + b2 = c2
b c a
h
a DISTANCE BETWEEN 2 2
C
TWO POINTS: d = (x2–x1) + ( y2– y1) A b
Cube
x1 + x2 y1 + y2 Area = 1– ab sin C
MID-POINT BETWEEN
( , ) 2
3 TWO POINTS: 2 2
Volume = s 2 a = b = c
Surface Area = 6s Law of sines:
SUM OF INTERIOR ANGLES sin A sin B sin C
OF AN n-SIDED POLYGON: 180 ( n – 2) 2 2 2
s Law of cosines: b = a + c – 2ac (cos B )
QuickTime™ and a
TIFF (Uncompressed) decompressor
are needed to see this picture. QuickTime™ and a
TIFF (Uncompressed) decompressor
are needed to see this picture.
QuickTime™ and a
TIFF (Uncompressed) decompressor
are needed to see this picture.
QuickTime™ and a
TIFF (Uncompressed) decompressor
are needed to see this picture.
Algebra Mind Maps By Frank Santos
1) Algebra Fundamentals 7) Rationals
2) Add/Sub Polynomials 8) Slopes & Linear Eqs.
3) Scientific Notation 9) Systems of Equations
4) Exponents 10) Graphing Inequalities
5) Mult. Polynomials 11) Relations & Functions
6) Factoring Polynomials 12) Radicals
13) Solving Quadratic Eqs.
ALGEBRA MIND MAP NOTES:
CH5-1&2 EXPONENTS.ppt CH7-3&6 Slope Int Eqs.ppt CH11-6&7 Add Radical & PhyT.ppt
CH5-4 SciNotation.ppt CH7-4,5,6&8 Lines&Eq2.ppt CH12-1A RelationsFunctions.ppt
CH5-5 DegOfPoly CH7-4,5&6 LinearEq.ppt CH12-4 Quad Eq Intro & Graph.ppt
CH5-5A Terms&Coefficients.ppt CH7-4A Intro Slopes.ppt CH12-4A QuadFunctions.ppt
CH5-7 BoxMeth Mult Polys.ppt CH7-4B SLOPES.ppt CH12-5&6 DirectIndirectVar.ppt
CH5-7&8 AddSub Polys.ppt CH7-6A AM170EqGivenSlope&Int.ppt CH13-1-5 Solve QuadEqMM.ppt
CH6-1&4 Factoring GCF&TriN.ppt CH7-6B AM171EqGivenSlope&Pt.ppt
CH13-2 SolveQuad SqRootRule.ppt
CH6-1A Factoring Basics.ppt CH7-6C AM172EqGivenTwoPts.ppt
Test Prep STATE STAR.ppt
CH6-2 Factoring Binomial.ppt CH7-6D AM174DescribeGraph.ppt
Test Prep District 3rdQ.ppt
CH6-3 Trinomial Square Pres.ppt CH7-8APar & Per Lines.ppt
CH7-8C AM173ParPerpLines.ppt
Q u ic k Tim e ™ a n d a Q u ic k Tim e ™ a n d a
G r a p h ic s d e c o m p r e s s o r G r a p h ic s d e c o m p r e s s o r
a r e n e e d e d t o s e e t h is p ic t u r e . a r e n e e d e d t o s e e t h is p ic t u r e .
Radicals
Q u ic k Tim e ™ a n d a Q u ic k Tim e ™ a n d a
2
G r a p h ic s d e c o m p r e s s o r G r a p h ic s d e c o m p r e s s o r
a r e n e e d e d t o s e e t h is p ic t u r e . a r e n e e d e d t o s e e t h is p ic t u r e .
Visual to REMEMBER
+
ALGEBRA FUNDAMENTALS ALGEBRA FUNDAMENTALS
-b b 4ac
2
With the emphasis on FUN
PROPERTIES
PS • OF
X=
2a 1A
SOLVING
Perfect Square times Other Factor
12 QUADRATIC
11 EQUATIONS
1
13
10
Scientific
9.54x107 miles
Notation
1.86x107 miles
Makes
per mile These
Systems of Equations
Given 2 linear equations
Numbers
Easy
The single point where they 9
intersect is the solution.
3
Q u ic k Tim e ™ a n d a
TI FF ( Un c o m p r e s s e d ) d e c o m p r e s s or
a r e n e e d e d t o s e e t h is p ic t u r e .
• POWER TO A POWER
Q u ic k Tim e ™ a n d a
TI FF ( Un c o m p r e s s e d ) d e c o m p r e s s or
a r e n e e d e d t o s e e t h is p ic t u r e .
4 THIS IS A
7 POWERFUL
IDEA
6 EXPONENTS
RISE
SLOPE= 5
RUN
QuickTime™ and a
TIFF (Uncompressed) decompressor
are needed to see this picture.
Traditional Method Number Sets Additive & Multiplicative
WHAT PERCENT OF 30 is 6? Commutative Properties
1,2,3... NATURAL
LET’ S
SWITCH
SWITCH
COMMUTES
COMMUTES
(For any rational numbers a & b)
Q uic k Tim e™ and a
30
G r aphic s dec om pr es s or
ar e needed t o s ee t his pic t ur e.
0,1,2..
YEAH!
WHOLE
Part 6 x
(Percent) ... 2,1,0,1,2,... INTEGERS
Whole 30 100
a
,b 0 RATIONAL abba
6 x b
100 100
30 100
6
non repeating,never ending
Rational & Irrational
IRRATIONAL
REAL
a b b a
20% x 0 Negative _ SquareRoots
IMMAGINARY
SWITCH PLACES
WHAT = X
WHAT % = X /100 What Percent is What???
What about Subtraction & Division?
OF = • (Times)
IS = = (Equals)
WHAT PERCENT OF 30 is 6? 30
x
• 30 6
100 ALGEBRA FUNDAMENTALS Adding Fractions
100 x 100
• 30 6 1 3 4
• With common denominators
30 100 30 7 7 7 (ADD NUMERATORS)
6
With the emphasis on FUN 1 3 • With uncommon denominators
x 20% 0
8 7 (CONVERT TO COMMON DENOMINATOR
7 24 31 AND ADD)
56 56 56
• With mixed numbers
1 3 (CONVERT FRACTIONS TO COMMON
2 5 DENONINATOR AND ADD WHOLE
8 7 NUMBERS AND FRACTIONS)
7 24 31
2 5 7
56 56 56
Principle of Balanced Equations
One side of an equal sign is
balanced with the other side. Equation Solving & Like Terms
Anything that you do to one Subtracting Fractions
side of a balanced equation • Maintaining Balance Same rules but sometimes you have to borrow a whole
x 3 5
must be done to the other side.
• Simplify Each Side First • BORROWING A WHOLE NUMBER
1 3
-3 -3 • A Like Term is a number and variable or variables 5 1
7 7 A whole number can be equivalent to a
fraction with the same numerator and
denominator.
• Only Like Terms can be combined 1 1 7 8
x2
5 4 4
7 7 7 7
2 3 45 1
1
2 3 45 1
3x & 5x 2x
8 3 5 7
Using 7 1 you can subtract the fraction
4 1 3
7 7 7 part of the mixed number.
7y 2 & 4 y 2 11y 2
56xb 4 & 6xb 4 50xb 4
Unlike Terms can not be combined
Additive & Multiplicative
DISTRIBUTIVE Property
(For any rational numbers a & b)
Closure
(For any rational numbers a & b)
a(b c) ab ac
Distribute outside term to each a b Is a rational number
term inside the parenthesis ab Is a rational number
Additive & Multiplicative
Inverse Properties
a (a) 0 -a is the Additive Inverse Additive & Multiplicative
Commutative Properties
1
LET’ S
1
COMMUTES
YEAH!
Associative Properties
QuickTime™ and a TIFF (Uncompressed) decompressor
QuickTime™ and a
TIFF (Uncompressed) decompressor are needed to see this picture.
TIFF (Uncompressed) decompressor are needed to see this picture.
are needed to see this picture.
ALGEBRA TILES
•Makes X’s & Algebra Visible
•Combine Like Terms
•Show Factoring
1 -1
x x2 -x -x2
Subtract polynomials
Example: Subtract (–3x5 –5x) – (6x + 8 – 8x5)
Since subtraction is the same as “adding the opposite ”, we
can change this problem to addition by changing all of
the signs of the polynomial to be subtracted...
(–3x5 –5x) + (–6x – 8 + 8x5)
Now, find your like terms …
–3x5 –5x + –6x – 8 + 8x5
5x5– 11x – 8
ANOTHER METHOD
Changing from Standard
Ex. 6800 Notation to Scientific Notation Changing from Scientific
Ex. 4.5 x 10-3 Notation to Standard Notation
6800 1. Move decimal to get
a single digit # and
3 2 1 count places moved 1. Move decimal the same
68 x 10 3 2. Answer is a single
digit number times
00045 number of places as the
exponent of 10. Scientific
the power of ten of
3 2 1 (Right if Pos. Left if Neg.)
Notation
places moved.
9.54x107 miles
If the decimal is moved left the power is positive.
If the decimal is moved right the power is negative.
1.86x107 miles
Makes
What is Scientific Notation per second These
A number expressed in scientific notation is
(3 x 104)(7 x 10–5)
Multiply two numbers
expressed as a decimal number between 1 and 10
multiplied by a power of 10 ( eg, 7000 = 7 x 103 or Number
in Scientific Notation
s Easy
0.0000019 = 1.9 x 10 -6)
6.20 x 10–5 DIVIDE USING SCIENTIFIC .2 x 10 3 + 3.0 x 10 3 1. Make exponents of 10 the same
2. Add 0.2 + 3 and keep the 103 intact
8.0 x 103 NOTATION
= .2+3 x 10 3
The key to adding or subtracting numbers
in Scientific Notation is to make sure the
= 3.2 x 10 3
6.20 10-5 exponents are the same.
1. Divide the #’s &
8.0 103 Divide the powers of ten
(subtract the exponents) 2.0 x 10 7 - 6.3 x 10 5
= 0.775 x 10 -8
2. Put Answer in Scientific 2.0 x 10 7 -.063 x 10 7 1. Make exponents of 10 the same
= 7.75 x 10–9 Notation 2. Subtract 2.0 - .063 and
= 2.0-.063 x 10 7 keep the 10 7 intact
= 1.937 x 10 7
Changing from Standard
Ex. 6800 Notation to Scientific Notation
2. Answer is a single
68 x 10 3 digit number times
the power of ten of
places moved.
If the decimal is moved left the power is positive.
If the decimal is moved right the power is negative.
Anything to the
zero power X X X X X
2 3 2 2 2 222
X6
equals 1 THIS IS A
POWERFUL
IDEA
EXPONENTS
EXPONENTIAL NOTATION
Simplify
3x 3 y 4
2
7z
Take A Power
To A Power
2 IS THE EXPONENT
INVERTING A NEGATIVE
EXPONENTS CHANGES ITS SIGN 3x 3 y 4 34 x 3•4 y1•4 1. Multiply the outside
2
21 1
X 2
2z 2 4 z 2•4
power to the inside
powers.
X 2
2. Simplify
X 2
X IS THE BASE
34 x12 y 4 81x12 y 4
4 8
X X 2 2 z 16z 8
MULTIPLYING EXPONENTS DIVIDING EXPONENTS
ADD THE EXPONENTS SUBTRACT THE EXPONENT OF THE
DENOMINATOR FROM THE EXPONENT
A B
X X X
A B
OF THE NUMERATOR XA
X AB
XB
6x-3 Multiply a Binomial by a Trinomial
c +d +e
7x8 42x5
a ac ad ae
7x8¥6x-3=42x5
b bc bd bc
(a+b)(c+d+e)= ac+ad+ae
bc+bd+be
(3x 2 x) 2 Multiply
14 x Adding Rationals
Rationals 2 with uncommon
5
x(3x 1) 2 x denominators
1. Factor each numerator and
2 x
14 x denominator if possible. 5
x x The Key is to:
1
x(3x 1) 2 2. Cancel and/or Reduce 2 5x 5x 2 1. Make Denominators
7 14 x x x x Common
2. Add Numerators &
(3x 1) Simplify
7
x 1 x 1 Divide
2
x 1 x 2x 1
2
Rationals
6 Solving Rational
x 1 x 2 2x 1 x 5
1. INVERT 2nd Fraction & x Equations (2nd Deg)
x 2 1 x 1 MULTIPLY
x 1 (x 1)(x 1) 6
2. FACTOR each numerator xx 5x 1. Bust fractions by
(x 1)(x 1) x 1 x
and denominator if possible. multiplying bymon
x 2 6 5x 6
3 2 denominator.
3. SIMPLIFY
x 1 (x 1)(x 1) x 2 5x 6 0 5 2. Set Eq =0
3. Factor
(x 1)(x 1) x 1 (x 3)(x 2) 0
4. Set Each Factor = 0
x 1 x 30 x 20
& Solve
x 1 x 3 x 2
Find the slope of a line Find the Slope of a Write this equation in
Standard Form
Obj. 169
Comparison of AM 170, 171 & 172
Write Equation in
Through (3,4) &(-2,6) line between 2 Points Ax+By=C
3
Standard Form or SUMMARY AM 170 SUMMARY AM 171 SUMMARY AM 172
Ex #4. y 8 x 4 Slope Intercept Form Write Equation of a Line Write Equation of a Line Write equation of a line
x1 y1 x2 y2 3
Given Slope and y-intercept Given Slope and a point given two points on the line.
y y
8 y x4 8 1. Put points into m 2 1
(3,4) & (-2,6) 1. Write x 1,y1,x2,y2 over numbers 8 1. Bust Fractions by multiplying to find slope.
x 2 x1
by LCD
8y=+3x+32
y 2 y1 6 4 2. Write Formula and Substitute -3x -3x
2. Move x-term to LHS 1. USE Y=MX+B & SOLVE FOR B 2. USE Y=MX+B & SOLVE FOR B
Slope (Left Hand Side) of equation 2. PUT M&B INTO INTO
3. PUT M&B
x 2 x1 2 3 x1,x2,y1,y2 values. -3x+8y=32 or 1. PUT M&B INTO Y=MX+B FOR EQUATION Y=MX+B FOR EQUATION
Note: Mult. both sides of the Eq. Y=MX+B FOR EQUATION (4,3) (6,7)
2 3 5
x y
5 y=mx+b
(4,3)
y=mx+b
y=mx+b
Slope of 2
-8 -8 -8 -8
y=2x-5
Y & X-Intercepts -5=b 2. -5=b
3. y=2x-5
SLOPE is a measure of
Q uic k Tim e™ and a
TI FF ( Unc om pr es s ed) dec om pr es s or
ar e needed t o s ee t his pic t ur e.
Y
Q uic k Tim e™ and a
TI FF ( Unc om pr es s ed) dec om pr es s or
ar e needed t o s ee t his pic t ur e.
SLOPE= RISE
X Slope Is -2
(0,Y) Neg Recip 1. Solve the equation for y to
y=-2x+6
Is 1/2 find slope. (Use Neg Recip)
1
1 5 b
(6,4)
There are 3 Forms of Line Equations 4 •
3 RISE 2
• Standard Form: ax+by=c 2 (3,2)
•
Negative Slope
1 RUN 3 Positive Slope Is Down the Hill
• Slope Intercept Form: y=mx+b Is Up the Hill
(0,0) 1 2 3 4 5 6
• Point-Slope Form y-y1=m(x-x1)
All 3 describe the line completely but are
NO Slope
used for different purposes. You can Vertical Drop
convert from one form to another.
ZERO Slope Horizontal
Y & X-Intercepts
Y
Y is the Y-Intercept
X is the X-Intercept
(X,0)
X
(0,Y)
Review of an Equation & It’s Solution y x 3 AM 186&7 SOLVING Systems
of Eq. By ELIMINATION/ADD
Is (5,4) a y x 3 Determine if a given point
y x 1 solution? y x 1 is a Solution to a Sys of Eq.
SOLUTIONS ARE THE GRAPH
The graph of one variable equation is a number on y x 3 1. Line up equation variables 4 5 3? Not True 1. Put (x,y) point into
and #.
the number line. (3x=21 • ) x=7 1 2 3 4 5 1? True
each equation.
2. Combine Like Terms
0 7
2. If both equations
The graph of an inequality is a dot and heavy line & 11 3. Solve for 1 variable.
arrow on a number line. (3x>21 0 ) x>7 y x 1 4. Put answer into either are true the point is
7 equation and solve for (5,4) IS NOT A SOLUTION a solution.
The graph of a linear equation is a line. 1 2 1 the other variable.
(2,1)
11 5. CHECK ANS. BY PUTTING
y=x-1 (0,-1) ANS. BACK INTO EACH EQ.
Input
Inputs
x={1,5,-8} h={1,-4,7}
Outputs Outputs
f(x)=7x-2 y=? f(h)=2h-1 ?
100x 2
2x radical and other factor in 2nd) 5x 2
a 2 36 100 2. Solve for unknown variable
x 2
5 Simplify radical if needed
10x 2x 2. Take square root of first
a 2 64
radical x 5
a 64 8
x x ?
QuickTime™ and a
TIFF (Uncompressed) decompressor
are needed to see this picture.
x 6x 9
2 Square Roots of
Perfect Squares 4 8 3 8 8
Perfect squares
9
3 1. Factor any perfect
1, 4, 9, 16, …
Radicals
3
6 squares
(x 3)(x 3) (x 3) 2
Visual to REMEMBER
3x25
EVEN POWERED
2. Take square root of 3x25 9x50 EXPONENTS ARE
(x 3) 2
perfect square. SQUARES
x3
Divide Radicals
PS • OF 2
Rationalizing the
Perfect Square times Other Factor 3
Denominator
Simplifying Negative
2
2
3 1. Mult. Numerator & Denom.
3 3 3 By Denom. to get a Perfect
9 Square Roots 6m 8m Multiply Radicals Square in Denominator
6
2. Take the square root of the
1. Factor any perfect squares 9
Perfect Square
9 (4, 9, 16, 25, 36…) 6m 8m 1. Multiply to one radical
6
2. Simplify 3. Simplify
9 1
(& Put perfect squares in first
radical and other factor in 2nd)
48m 2 3
• Factor any perfect squares
3i 2. Take square root of first (4, 9, 16, x2, y6…)
radical
16m 2 3 • Take square root of first
3. The square root of -1 is radical
called IMAGINARY 4m 3
Solve with Perfect Solve Quadratic Eq.
(x 2) 49 2 x 2 5x 6 By Factoring
Square Binomial
x 2 5x 6 1. Set Eq = 0
(x 2) 49 2
1. Get Perfect Squares on 2. Factor
Both Sides of Equation.
x 2 5x 6 0 3. Set Each Factor = 0
x 2 7 2. Take Square Root of 4. Check Answers by
Perfect Squares (x 6)(x 1) 0 Putting into Original Eq.
3. Solve Positive Number
x 6 0 & x 1 0
x 2 7 x 2 7 & Neg. Number
4. Check Answers by x 6 x 1
x 9 x 5 Putting into Original Eq.
Q u ic k Tim e ™ a n d a Q u ic k Tim e ™ a n d a
G r a p h ic s d e c o m p r e s s o r G r a p h ic s d e c o m p r e s s o r
a r e n e e d e d t o s e e t h is p ic t u r e . a r e n e e d e d t o s e e t h is p ic t u r e .
SOLVING
Q u ic k Tim e ™ a n d a Q u ic k Tim e ™ a n d a
2
G r a p h ic s d e c o m p r e s s o r G r a p h ic s d e c o m p r e s s o r
a r e n e e d e d t o s e e t h is p ic t u r e . a r e n e e d e d t o s e e t h is p ic t u r e .
EQUATIONS
Exponent is 1 Exponent is 2
-b b 4ac
2
ax +by +c = 0 f(x) = ax2 +bx +c = 0
X= y = mx + b
2a
The Discriminant
The Discriminant equals b2-4ac
• If BX
B is isinthe
thebisector
interior of angle ABC:
CDA then the measure
The measure of angle
of angle ABX =
Angle
AngleBisector
AdditionTheorem
Axiom CDB
1/2 the+ measure
the measure of angle
of angle ABC;BDA
The=Measure
the measure of angle
of angle SBCCDA
= 1/2
the measure of angle ABC
Properties of Equality
Multiplication • If a = b then ac = bc
Reflexive • a=a
• If a = b then b = a
Symmetric:
Transitive
Name: Class: Date:
Remedial Plan
Indicate whether the statement is true or false.
constant of proportionality point-slope form standard form
constant of variation rise substitution
constant rate of change run system of equations
direct variation slope x-intercept
linear relationship slope-intercept form y-intercept
State whether each statement is true or false.
1. The x-intercept of a function is the x-coordinate of the point where the graph crosses the x-axis.
a. True
b. False
Determine whether each statement is true or false.
2.
a. True
b. False
State whether each statement is true or false.
3. The hypotenuse is the side adjacent to the right angle.
a. True
b. False
State whether each statement is true or false.
4. The constant ratio in a direct variation is called the constant of variation.
a. True
b. False
Remedial Plan
Determine whether each statement is true or false.
5.
a. True
b. False
State whether each statement is true or false.
6. The Pythagorean Theorem is used to find the ratio of the angle measures of two angles in a right triangle.
a. True
b. False
Determine whether each statement is true or false.
7. 7 < 11
a. True
b. False
State whether each statement is true or false.
8. A triangle is formed by three line segments that intersect only at their endpoints.
a. True
b. False
Remedial Plan
State whether each statement is true or false.
9. Slope is the ratio of the run, or horizontal change, to the rise, or vertical change.
a. True
b. False
10. Linear functions written in the form Ax + By = C are written in slope-intercept form.
a. True
b. False
Indicate whether the statement is true or false. If it is false, change the identified word(s) to make the statement
true.
State whether each sentence is true or false. If false, replace the underlined word or phrase to make a true
11. The rational exponent of a geometric sequence can be found by dividing any term by its previous term.
Write whether each sentence is true or false. If false, replace the underlined word or phrase to
make a true sentence.
12. A reflection is a transformation that moves all points of a figure the same distance in the same direction.
13. A translation maps each point to its image along a vector called the translation vector.
Remedial Plan
State whether each sentence is true or false. If false, replace the underlined word or phrase to make a true
14. Constants are monomials that are real numbers.
15. Exponential decay is when an initial amount decreases by the same percent over a given period of time.
16. The equation A = P is the general equation for compound interest.
17. The nth root of a quantity is the number rounded to the nearest power of 10.
Determine whether each sentence is true or false. If false, replace the underlined word or phrase
to make a true sentence.
18. Two angles are congruent if their measures have a sum of 90.
State whether each sentence is true or false. If false, replace the underlined word or phrase to make a true
19. Binomials of the form and , where a, b, c, and d are rational numbers are
conjugates.
20. The zero exponent property tells us that any nonzero number raised to the zero power is 1.
Remedial Plan
Indicate the answer choice that best completes the statement or answers the question.
Choose the correct term to complete each sentence.
21. Vertical angles are two ____________ angles formed by two intersecting lines.
a. nonadjacent b. collinear
22. Find the sixth term of the geometric sequence –16, 40, –100, ... .
a. –15,625 b. –6250
c. 6250 d. 1562.5
Use the figure.
23. Name the angle that is vertical to 3.
a. 1 b. 2
c. 3 d. 4
24. ABC has vertices A(–2, 1), B(–4, –1), and C(0, –1) and is reflected in the line x = 2. What is the coordinate
of ?
a. (2, 0) b. (2, –1) c. (4, –1) d. (–4, –1)
measure of ∠ B.
Remedial Plan
Use the graph to answer each question.
27. What is the domain of the relation?
a. {–4, –2, –1, 0, 1, 2, 3, 4} b. {–4, –1, 0, 2, 3, 4}
c. {–4, –2, –1, 0, 1, 4} d. {–4, 4}
28. Which is the equation for the nth term of the geometric sequence 6, 12, 24, ...?
29. Write a verbal expression for 2n + 7.
a. the product of 2, n, and 7 b. 7 more than twice a number
c. 7 less than a number times 2 d. 7 more than n and 2
30. Which figure shows and point G contained in plane R?
a. b.
c. d.
31. Name the image of under reflection in line m.
32. Find the coordinates of the image of P(–3, 1) after the composition of a reflection in the y-axis and a
translation 2 units left.
a. P′′(–1, 1) b. P′′(1, 1) c. P′′(3, 1) d. P′′(1, –3)
Remedial Plan
Graph each function.
33.
a. b.
c. d.
34. Jon enlarges a 4-inch by 6-inch photograph by 2.5x. What are the dimensions of the enlarged photograph?
a. 8-in. by 12-in. b. 10-in. by 15-in. c. 10-in. by 12-in. d. 15-in. by 10-in.
35. f(x) = 6x is compressed vertically by a factor of
a. g(x) = (6x)
b. g(x) = 4(6x)
c. g(x) =
d. g(x) = 64x
Remedial Plan
36. Write in radical form.
a. b.
c. d. x
37. BUSINESS A printing press valued at $120,000 depreciates 12% per year. What will be the approximate
value of the printing press in 7 years?
a. $19,200 b. $265,282 c. $49,041 d. $55,728
Tell how the transformed function compares to the parent function.
38. f(x) = 5.2x; g(x) = 5.2−x
a. Reflected across the x-axis
b. Reflected across the y-axis
c. Stretched vertically by a factor of –1
d. Compressed vertically by a factor of –1
39. If each lap around a track is 400 meters long, how many laps equal 3.1 miles? Round to the nearest tenth.
(Hint: 1 foot = 0.3048 meter)
a. 12.5 laps b. 39.2 laps
c. 121.9 laps d. 378.0 laps
40. Which unit would be most appropriate to measure the width of the basement of a house?
a. centimeters
b. meters
c. millimeters
d. kilometers
Use the graph to answer each question.
41. What is the domain of the relation?
a. {– 4, –1, 0, 2, 4} b. {– 4, – 2, – 1, 1, 4}
c. {–4, –2, –1, 0, 1, 2, 4} d. {– 1, 1}
Remedial Plan
42. A cable company charges an installation fee to install cable at a residence. There is also a monthly fee for the
cable service. The total costs for Months 2, 4, 6, and 8 are $145, $255, $365, and $475, respectively. How
much is the installation fee? Assume that the relationship between the two quantities is linear.
a. $35
b. $55
c. $90
d. $110
43. Evaluate 2(11 – 5) + 9 ÷ 3.
a. 18 b. 15 c. 30 d. 11
Use the graph to answer each question.
45. Which is a true statement about the relation?
a. The relation is not a function.
b. The value of x increases as y decreases.
c. The value of x increases as y increases.
d. The relation is a linear function.
For the next two questions, use the figure below.
46. Does the figure appear to have line symmetry? If so, state their number.
a. yes; 1 b. yes; 2 c. yes; 3 d. no
47. A number is divided by four. The result is added to five. This result is multiplied by three to give 27. What is
the number?
a. 16 b. 1 c. 21 d. 3
Remedial Plan
49. If h(r) = r – 6, what is the value of h(–9)?
50. Which object models a line?
a. a fly b. a wall
c. a meter stick d. a diskette
51. Solve the formula V = ℓwh for ℓ.
52. Given A is between Y and Z and YA = 5.5, AZ = 2x, and YZ = 41.5, find AZ.
a. 9 b. 18 c. 36 d. 47
Determine whether the pair of triangles is congruent. If yes, include the theorem or postulate that
applies.
53.
a. yes; The triangles are congruent by hypotenuse-angle congruence.
b. yes; The triangles are congruent by hypotenuse-leg congruence.
c. no; The triangles are not congruent.
d. There is not enough information to determine congruency.
54. Point E with coordinates (5, 7) is translated along a glide reflection to its image of (–7, 9). Which best
describes the glide reflection?
a. translation along and reflection in x-axis
b. translation along and reflection in y-axis
c. translation along and reflection in x-axis
d. translation along and reflection in y-axis
Remedial Plan
55. Solve –6d = –42.
a. –48 b. 7
c. –36 d. 252
56. Write a verbal expression for 3n – 8.
a. the product of 3, n, and 8 b. 8 less than the product of 3 and n
c. 3 times n less than 8 d. n minus 8 times 3
57. Solve |5k + 2| > 1.
a. b. Ø
c. d. {k | k is a real number.}
58. Point Q with coordinate (–2, 3) is rotated 270° about the origin. Which of the following could be the
coordinates of its image?
a. b.
c. d.
59. Marek paints a barrel in the shape of a cylinder. To paint 8 square feet of the barrel, he uses 1 quart of paint.
The height of the barrel is 4 feet and the radius of its base is 0.5 feet. If Marek does not paint the top lid of
the barrel, how much paint does Marek use to paint the barrel?
a. about 0.5 quart b. about 2 quarts c. about 1.75 quarts d. about 3.8 quarts
Tell how the transformed function compares to the parent function.
60. f(x) = 4x; g(x) = 4−x − 10
a. Reflected across the x-axis; translated left 10 units
b. Reflected across the x-axis; translated down 10 units
c. Reflected across the y-axis; translated left 10 units
d. Reflected across the y-axis; translated down 10 units
61. Which pair of ratios forms a proportion?
62. Evaluate .
a. 2 b. 4 c. 8 d. 32
Remedial Plan
63. A point K with coordinates (–1, 6) is translated along the vector and then reflected in the y-axis. What
are the coordinates of K"?
a. (1, 9) b. (1, –9) c. (–1, 9) d. (–1, –9)
64. POPULATION A city’s population is about 763,000 and is increasing at an annual rate of 1.5%. Predict the
population of the city in 50 years.
a. 1,335,250 b. 826,830,628
c. 358,374 d. 1,606,300
65. Find the reflection of the point A(6, –1) in the x-axis.
a. (6, –1) b. (–6, 1) c. (6, 1) d. (1, 6)
66. Point J with coordinates (–2, 1) is translated along and then reflected in the x-axis. What are the
coordinates of ?
a. (–5, –2) b. (2, 1) c. (–5, 2) d. (2, –1)
67. Simplify .
68. GEOMETRY The formula for the volume of a cone is V = πr2h, where V represents the volume, r
represents the radius of the base, and h represents the height. What is the height of a cone with a volume of
110 cubic centimeters and a base with a radius of 5 centimeters?
a. 21 cm b. 0.47 cm c. 4.2 cm d. 41.49 cm
69. Mandy begins bicycling west at 30 miles per hour at 11:00 A.M. If Liz leaves from the same point 20 minutes
later bicycling west at 36 miles per hour, when will she catch Mandy?
a. 2:00 P.M. b. 1:00 P.M. c. 1:30 P.M. d. 2:30 P.M.
70. Omari drives a car that gets 18 miles per gallon of gasoline. The car’s gasoline tank holds 15 gallons. The
distance Omari drives before refueling is a function of the number of gallons of gasoline in the tank. Identify a
reasonable domain for this situation.
a. 0 to 18 miles b. 0 to 15 gallons
c. 0 to 270 miles d. 0 to 60 mph
Remedial Plan
Enter the appropriate value to answer the question or solve the problem.
Complete the sentence.
71. 3.7 kg = _____ lb
72. The area of a square carpet tile is 900 square centimeters. What is the length of one edge of the tile in
centimeters?
73. Find the sum of the measures, in degrees, of the interior angles of an 12-gon.
Find the value of x in each figure.
74.
Remedial Plan
75. The floors of houses in Japan are traditionally covered by tatami. Tatami are rectangular-shaped straw mats
that measure about 6 feet by 3 feet. If a room is 48 feet by 24 feet, how many tatami are needed to cover the
floor? Use the draw a diagram strategy.
Enter the appropriate word(s) to complete the statement.
coefficient multiplicative inverses properties
identity null set two-step
Choose from the terms above to complete each sentence.
76. A(n) ________________ contains two operations.
Choose the correct term or phrase to complete each sentence.
77. When a figure is moved without turning it, it is called a (rotation, translation).
Remedial Plan
Choose the correct term from the two choices given which makes the statement true.
78. A (radical sign, scientific notation), , is used to indicate a positive square root.
Choose the correct term or phrase to complete each sentence.
79. The original figure before a transformation is called a(n) (image, preimage).
Choose the correct term from the two choices given which makes the statement true.
80. (Scientific notation, Square root) is a compact way of writing numbers with absolute values that are very
large or very small.
Remedial Plan
State which metric unit you would probably use to measure each item.
81. length of a computer keyboard
Solve the equation.
82.
Name the reciprocal of the number.
83.
84. A can of soup has a volume of 20π cubic inches. The diameter of the can is 4 inches. What is the height of
the can?
Remedial Plan
Find each sum or difference.
85. –0.38 – (–1.06)
86. Stephanie wants to transfer the soil from a rectangular pot measuring 4 inches by 5 inches by 3 inches into a
cylinder-shaped pot. The soil in both pots should be leveled to the top. What should be the volume of the
cylindrical pot?
Use the figure below to answer the following questions.
87. Name three points on plane B.
Remedial Plan
89. Translate the following equation into a verbal sentence.
– 5 = x(y + 7)
Solve each equation.
90. 5(12 – 3p) = 15p + 60
Remedial Plan
Indicate the answer choice that best completes the statement or answers the question.
Determine whether each pair of segments is congruent.
91.
a. yes
b. no
Add, subtract, multiply, or divide.
92. –20(12)
a. –8
b. –32
c. –240
d. 240
93. SPORTS EQUIPMENT The price of a baseball glove is $8 more than half the price of spikes. The glove
costs $54. Solve the equation to find out how much the spikes cost.
a. $23
b. $128
c. $84
d. $92
94. Which of the following is as a fraction in simplest form?
a.
b.
c.
d.
Remedial Plan
Write the decimal as a fraction or mixed number in simplest form.
95. 0.
a.
b.
c.
d.
Remedial Plan
Answer Key
1. True
2. False
3. False
4. True
5. False
6. False
7. True
8. True
9. False
10. False
11. False - common ratio
12. False - translation
13. True
14. True
15. True
16. True
17. False - order of magnitude
18. False - complementary
19. True
20. True
21. a
22. d
23. b
24. c
25. d
26. a
27. c
28. c
29. b
Powered by Cognero Page 21
Name: Class: Date:
Remedial Plan
30. a
31. b
32. b
33. d
34. b
35. a
36. b
37. c
38. a
39. a
40. b
41. b
42. a
43. b
44. d
45. a
46. d
47. a
48. a
49. d
50. c
51. b
52. c
53. b
54. b
55. b
56. b
57. a
58. c
59. c
Remedial Plan
60. d
61. b
62. c
63. c
64. d
65. c
66. c
67. c
68. c
69. b
70. b
71. 8.1
72. 30
73. 1800
74. 48
75. 64
76. two-step equation
77. translation
78. radical sign
79. preimage
80. Scientific notation
81. centimeter
cm
82. 59
83.
84. 5
5 in
5 in.
5 inches
85. 0.68
86. 60 in3
Remedial Plan
87. Sample answer: T, U, V
88. 6
89. Three divided by y minus five equals x times the sum of y and 7.
90. 0
91. a
92. c
93. d
94. d
95. d