NAME__________________________________
Student Number__________________________________
Algebra 1 Portfolio with evidence of mastery by standards.
I _________________________________________________ am a student at South Lake High School
in Lake County. This portfolio is evidence of my proof of mastery in Algebra 1.
Proof is provided by standard:
MAFS.912.A-APR 1.1
MAFS.912.A-APR 2.3
MAFS.912.A-APR 4.6
MAFS.912.A-CED 1.1
MAFS.912.A-CED 1.2
MAFS.912.A-CED 1.3
MAFS.912.A-CED 1.4
MAFS.912.A-REI 1.1
MAFS.912.A-REI 2.3
MAFS.912.A-REI 2.4
MAFS.912.A-REI 3.5
MAFS.912.A-REI 3.6
MAFS.912.A-REI 3.7
MAFS.912.A-REI 4.10
MAFS.912.A-REI 4.11
MAFS.912.A-REI 4.12
MAFS.912.A-SSE 1.1a
MAFS.912.A-SSE 1.1b
MAFS.912.A-SSE 1.2
MAFS.912.A-SSE 2.3
MAFS.912.F-BF 1.1
MAFS.912.F-BF 1.2
MAFS.912.F-BF 2.3
MAFS.912.F-IF 1.1
MAFS.912.F-IF 1.2
MAFS.912.F-IF 1.3
MAFS.912.F-IF 2.4
MAFS.912.F-IF 2.5
MAFS.912.F-IF 2.6
MAFS.912.F-IF 3.7
MAFS.912.F-IF 3.8
MAFS.912.F-IF 3.9
MAFS.912.F-LE 1.1
MAFS.912.F-LE 1.2
MAFS.912.F-LE 1.3
MAFS.912.F-LE 2.5
MAFS.912.F-LE 1.1
MAFS.912.N-RN 1.1
MAFS.912.N-RN 1.2
MAFS.912.N-RN 2.3
All work contained in this portfolio is my own and is done by me.
_______________________________________________
Student Signature
South Lake High School
Lake County Schools
0
NAME__________________________________
Student Number__________________________________
Evidence as proof of mastery of standard MAFS.912.A-APR.1.1 (DOK 1)
Understand that polynomials form a system analogous to the integers, namely, they
are closed under the operations of addition, subtraction, and multiplication; add,
subtract, and multiply polynomials.
Trisha is painting the walls in her room. The cost to paint is
foot. The total area of the walls is
dollars per square
. What is the total cost C, in dollars,
for Trisha to paint her room? Simplify your answer.
To meet the standard and solve this problem I had to ___________________________________
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1
NAME__________________________________
Student Number__________________________________
Evidence as proof of mastery of standard MAFS.912.A-Apr.2.3 (DOK 1) Identify
zeroes of polynomials when suitable factorizations are available, and use the zeroes to
construct a rough graph of the function defined by the polynomial.
What are the zeros of the polynomial y = x(x + 1) (x – 2)2
To meet the standard and solve this problem I had to ___________________________________
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2
NAME__________________________________
Student Number__________________________________
Evidence as proof of mastery of standard MSFS.912.A-APR.4.6 (DOK 2) Rewrite
simple rational expressions in different forms; write a(x)/b(x) in the form q(x) +
r(x)/b(x), where a(x), b(x), q(x), and r(x) are polynomials with the degree of r(x) less
than the degree of b(x), using inspection, long division, or, for the more complicated
examples, a computer algebra system.
Simplify the expression
2𝑥 2 +9𝑥𝑦+4𝑦 2
4𝑥+2𝑦
To meet the standard and solve this problem I had to ___________________________________
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3
NAME__________________________________
Student Number__________________________________
Evidence as proof of mastery of standard MAFS.912.A-CED.1.1 (DOK 2) Create
equations and inequalities in one variable and use them to solve problems. Include
equations arising from linear and quadratic functions, and simple rational, absolute,
and exponential functions.
Raphael deposited
in a bank account which earns
How much money will Raphael have after 2.5 years?
interest each quarter.
To meet the standard and solve this problem I had to ___________________________________
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4
NAME__________________________________
Student Number__________________________________
Evidence as proof of mastery of standard MAFS.912.A-CED.1.2 (DOK 1) Create
equations in two or more variables to represent relationships between quantities;
graph equations on coordinate axes with labels and scales.
Nick deposited $500 in a bank that gives him 5% interest compounded annually.
Which equation can be used to find the total amount, in T dollars, in Nick’s account
after x years?
To meet the standard and solve this problem I had to ___________________________________
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5
NAME__________________________________
Student Number__________________________________
Evidence as proof of mastery of standard MAFS.912.A-CED.1.3 (DOK 3)
Represent constraints by equations or inequalities, and by systems of equations and/or
inequalities, and interpret solutions as viable or non-viable options in a modeling
context. For example, represent inequalities describing nutritional and cost constraints
on combinations of different foods.
To ensure a growing season of sufficient length, Mr. Brown has at most 16 days left
to plant his corn and potato crops. He can plant corn at the rate of 250 acres per day
and potatoes at a rate of 200 acres per day. He has at most 3500 acres available.
Which of the following ordered pairs represents a possible number of days Mr.
Brown can plant corn and potatoes?
Let x = the number of days corn will be planted and y = the number of days potatoes
will be planted.
To meet the standard and solve this problem I had to ___________________________________
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6
NAME__________________________________
Student Number__________________________________
Evidence as proof of mastery of standard MAFS.912.A-CED.1.4 (DOK 1)
Rearrange formulas to highlight a quantity of interest, using the same reasoning as in
solving equations. For example, rearrange Ohm’s Law V = IR to highlight resistance R.
John’s bank offers interest on deposits. The equation
represents the
amount of money A in the account 1 year after depositing the principal, P, at an
interest rate, r. Which of the following equations does not represent the equation
solved for the interest rate?
To meet the standard and solve this problem I had to ___________________________________
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7
NAME__________________________________
Student Number__________________________________
Evidence as proof of mastery of standard MAFS.912.A-REI.1.1(DOK 3) Explain
each step in solving a simple equation as following from the equality of numbers
asserted at the previous step, starting from the assumption that the original equation
has a solution. Construct a viable argument to justify a solution method.
Jake and Nikasha solved similar equations but did not know how to interpret their
work.
Jake’s work:
Nikasha’s work:
Which is a correct statement regarding their work?
A. Jake applied the Subtraction Property of Equality incorrectly.
B. Nikasha applied the Distributive Property incorrectly.
C. Jake’s equation has infinitely many solutions, and Nikasha’s equation has no
solution.
D. Nikasha’s equation has infinitely many solutions, and Jake’s equation has no
solution.
To meet the standard and solve this problem I had to ___________________________________
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8
NAME__________________________________
Student Number__________________________________
Evidence as proof of mastery of standard MAFS.912.A-REI.2.3 (DOK 2) Solve
linear equations and inequalities in one variable, including equations with coefficients
represented by letters.
What are the possible number of solutions of an absolute value equation of the form
, where a, b, and c are real numbers?
A. zero solutions
B. one solution
C. two solutions
D. zero, one, or two solutions
To meet the standard and solve this problem I had to ___________________________________
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9
NAME__________________________________
Student Number__________________________________
Evidence as proof of mastery of standard MAFS.912.A-REI.2.4 (DOK 2) Solve
quadratic equations in one variable. a. Use the method of completing the square to
transform any quadratic equation in x into an equation of the form (x – p)² = q that
has the same solutions. Derive the quadratic formula from this form.
Solve
.
To meet the standard and solve this problem I had to ___________________________________
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10
NAME__________________________________
Student Number__________________________________
Evidence as proof of mastery of standard MAFS.912.A-REI.3.5 (DOK 3) Prove
that, given a system of two equations in two variables, replacing one equation by the
sum of that equation and a multiple of the other produces a system with the same
solutions.
Determine the number of solutions of the system of linear equations below.
𝑥 + 2𝑦 = −1
{
2𝑥 + 4𝑦 = −2
To meet the standard and solve this problem I had to ___________________________________
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11
NAME__________________________________
Student Number__________________________________
Evidence as proof of mastery of standard MAFS.912.A-REI.3.6 (DOK 1) Solve
systems of linear equations exactly and approximately (e.g., with graphs), focusing on
pairs of linear equations in two variables.
Which ordered pair, (x, y), represents the solution to the system of equations?
𝑥 + 𝑦 = 12
{
2.5𝑥 + 7.5𝑦 = 75
To meet the standard and solve this problem I had to ___________________________________
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12
NAME__________________________________
Student Number__________________________________
Evidence as proof of mastery of standard MAFS.912.A-REI.3.7 (DOK 2) Solve a
simple system consisting of a linear equation and a quadratic equation in two
variables algebraically and graphically. For example, find the points of intersection
between the line y = –3x and the circle x² + y² = 3.
Which numbers are the y-values of the solutions of the system of equations
To meet the standard and solve this problem I had to ___________________________________
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13
NAME__________________________________
Student Number__________________________________
Evidence as proof of mastery of standard MAFS.912.A-REI.4.10 0 (DOK 1)
Understand that the graph of an equation in two variables is the set of all its solutions
plotted in the coordinate plane, often forming a curve (which could be a line).
y
5
4
3
2
1
–5
–4
–3
–2
–1
–1
1
2
3
4
5
x
–2
–3
–4
–5
Which of the following piecewise-defined functions represent the graph above?
A.
B.
C.
D.
To meet the standard and solve this problem I had to ___________________________________
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14
NAME__________________________________
Student Number__________________________________
Evidence as proof of mastery of standard MAFS.912.A-REI.4.11 (DOK 2) Explain
why the x-coordinates of the points where the graphs of the equations y = f(x) and y =
g(x) intersect are the solutions of the equation f(x) = g(x); find the solutions
approximately, e.g., using technology to graph the functions, make tables of values, or
find successive approximations. Include cases where f(x) and/or g(x) are linear,
polynomial, rational, absolute value, exponential, and logarithmic functions.
Which of the following systems of linear equations has exactly one solution?
A.
C.
y
4
–4
–3
–2
B.
3
6
2
4
1
2
–1
–1
1
2
3
4 x
–2
–6
–4
–2
–2
–4
–3
–6
–4
–8
D.
y
–3
–8
–2
4
–4
y
8
2
2
1
1
2
3
4 x
6
8 x
1
2
3
4 x
y
3
1
4
4
3
–1
–1
2
–4
–3
–2
–1
–1
–2
–2
–3
–3
–4
–4
To meet the standard and solve this problem I had to ___________________________________
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15
NAME__________________________________
Student Number__________________________________
Evidence as proof of mastery of standard MAFS.912.A-REI.4.12 (DOK 2) Graph
the solutions to a linear inequality in two variables as a half-plane (excluding the
boundary in the case of a strict inequality), and graph the solution set to a system of
linear inequalities in two variables as the intersection of the corresponding halfplanes.
Which of the following ordered pairs satisfies both inequalities below?
𝑦+𝑥 >4
{
2𝑥 ≤ 𝑦 + 6
To meet the standard and solve this problem I had to ___________________________________
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16
NAME__________________________________
Student Number__________________________________
Evidence as proof of mastery of standard MAFS.912.A-SSE.1.1b (DOK 2)
Interpret expressions that represent a quantity in terms of its context. b. Interpret
complicated expressions by viewing one or more of their parts as a single entity. For
example, interpret as the product of P and a factor not depending on P.
A rectangular pool table has an area of
What is the length of the other side?
. The length of one side is
.
To meet the standard and solve this problem I had to ___________________________________
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17
NAME__________________________________
Student Number__________________________________
Evidence as proof of mastery of standard MAFS.912.A-SSE.1.2 (DOK 2) Use the
structure of an expression to identify ways to rewrite it. For example, see x4- y4 as
(x²)² – (y²)², thus recognizing it as a difference of squares that can be factored as
(x² – y²)(x² + y²).
Simplify the polynomial expression and write in standard form.
To meet the standard and solve this problem I had to ___________________________________
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18
NAME__________________________________
Student Number__________________________________
Evidence as proof of mastery of standard MAFS.912.A-SSE.2.3 (DOK 2) Choose
and produce an equivalent form of an expression to reveal and explain properties of
the quantity represented by the expression. a. Factor a quadratic expression to reveal
the zeros of the function it defines
What are the factors of the quadratic function whose graph is shown?
y
7
6
5
4
3
2
1
–3
–2
–1
–1
1
2
3
4
5
6
7
x
–2
–3
To meet the standard and solve this problem I had to ___________________________________
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19
NAME__________________________________
Student Number__________________________________
Evidence as proof of mastery of standard MAFS.912.F-BF.1.1 (DOK 3) Write a
function that describes a relationship between two quantities. c. Compose functions.
For example, if T(y) is the temperature in the atmosphere as a function of height, and
h(t) is the height of a weather balloon as a function of time, then T(h(t)) is the
temperature at the location of the weather balloon as a function of time.
Which quadratic equation represents the data?
x
2
3
4
5
6
f(x)
7
9
13
19
27
A.
B.
C.
D.
To meet the standard and solve this problem I had to ___________________________________
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20
NAME__________________________________
Student Number__________________________________
Evidence as proof of mastery of standard MAFS.912.F-BF.1.2 (DOK 2) Write
arithmetic and geometric sequences both recursively and with an explicit formula, use
them to model situations, and translate between the two forms.
A digital picture is made up of many small dots called pixels. Rayma has a picture
that is 40 pixels wide and wants to enlarge it. Every time she increases the size, the
width of the picture doubles. Write an explicit formula that gives the width of the
picture after doubling it n times.
To meet the standard and solve this problem I had to ___________________________________
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21
NAME__________________________________
Student Number__________________________________
Evidence as proof of mastery of standard MAFS.912.F-BF.2.3 (DOK 2) Identify
the effect on the graph of replacing f(x) by f(x) + k, k f(x), f(kx), and f(x + k) for specific
values of k (both positive and negative); find the value of k given the graphs.
Experiment with cases and illustrate an explanation of the effects on the graph using
technology. Include recognizing even and odd functions from their graphs and
algebraic expressions for them.
Alondra wants to translate the graph of
to the right 3 units and down 2
units. Which of the following functions will translate the graph the specified
amount?
A.
B.
C.
D.
To meet the standard and solve this problem I had to ___________________________________
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22
NAME__________________________________
Student Number__________________________________
Evidence as proof of mastery of standard MAFS.912.F-IF.1.1 (DOK 1) Understand
that a function from one set (called the domain) to another set (called the range)
assigns to each element of the domain exactly one element of the range. If f is a
function and x is an element of its domain, then f(x) denotes the output of f
corresponding to the input x. The graph of is the graph of the equation y = f(x).
Which of the following relations is a function?
A. I and III only
B. II only
C. I and II only
D. I, II, and III
To meet the standard and solve this problem I had to ___________________________________
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23
NAME__________________________________
Student Number__________________________________
Evidence as proof of mastery of standard MAFS.912.F-IF.1.2 (DOK 2) Use
function notation, evaluate functions for inputs in their domains, and interpret
statements that use function notation in terms of a context.
If
and
, what is the value of
?
To meet the standard and solve this problem I had to ___________________________________
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24
NAME__________________________________
Student Number__________________________________
Evidence as proof of mastery of standard MAFS.912.F-IF.1.3 (DOK 2) Recognize
that sequences are functions, sometimes defined recursively, whose domain is a subset
of the integers. For example, the Fibonacci sequence is defined recursively by f(0) = f(1)
= 1, f(n+1) = f(n) + f(n-1) for n ≥ 1.
On Monday, Anthony invited 2 friends to join his online group. The next day, both of
his friends invited 2 more people each. If this pattern continues, how many people
will have been invited by Friday?
To meet the standard and solve this problem I had to ___________________________________
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25
NAME__________________________________
Student Number__________________________________
Evidence as proof of mastery of standard MAFS.912.F-IF.2.4 (DOK 2) For a
function that models a relationship between two quantities, interpret key features of
graphs and tables in terms of the quantities, and sketch graphs showing key features
given a verbal description of the relationship. Key features include: intercepts;
intervals where the function is increasing, decreasing, positive, or negative; relative
maximums and minimums; symmetries; end behavior; and periodicity.
Troy is selling homemade wooden horses. The equation
represents the
profits he can make for each horse made. What is the greatest number of horses
Troy can make before he is making a negative profit?
To meet the standard and solve this problem I had to ___________________________________
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26
NAME__________________________________
Student Number__________________________________
Evidence as proof of mastery of standard MAFS.912.F-IF.2.5 (DOK 2) Relate the
domain of a function to its graph and, where applicable, to the quantitative
relationship it describes. For example, if the function h(n) gives the number of personhours it takes to assemble n engines in a factory, then the positive integers would be an
appropriate domain for the function.
A manufacturer produces 3 chairs every 2 hours. Which graph represents this
situation?
To meet the standard and solve this problem I had to ___________________________________
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27
NAME__________________________________
Student Number__________________________________
Evidence as proof of mastery of standard MAFS.912.F-IF.2.6 (DOK 2) Calculate
and interpret the average rate of change of a function (presented symbolically or as a
table) over a specified interval. Estimate the rate of change from a graph.
A construction company is building a new office complex. The following table shows
the percentage of the building that is complete versus the amount of time remaining
before the complex is finished.
Percentage
Time
Complete, p Remaining,
d
0
90 days
20
72 days
40
54 days
60
36 days
80
18 days
Which of the following equations represents the time remaining in terms of the
percentage completed?
A.
B.
C.
D.
To meet the standard and solve this problem I had to ___________________________________
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28
NAME__________________________________
Student Number__________________________________
Evidence as proof of mastery of standard MAFS.912.F-IF.3.7 (DOK 2) Graph
functions expressed symbolically and show key features of the graph, by hand in simple
cases (linear and exponential) and using technology for more complicated cases.
A ball is launched straight up. The function
gives the ball’s speed, , in
feet per second, in terms of time, , in seconds as it reaches its maximum height
before falling back to the ground. Which graph below models the function?
To meet the standard and solve this problem I had to ___________________________________
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29
NAME__________________________________
Student Number__________________________________
Evidence as proof of mastery of standard MAFS.912.F-IF.3.8 (DOK 2) Write a
function defined by an expression in different but equivalent forms to reveal and
explain different properties of the function. b. Use the properties of exponents to
interpret expressions for exponential functions. For example, identify percent rate of
change in functions such as 𝑦 = (1.02) , 𝑦 = (0.97) 𝑡 , 𝑦 = (1.01) 12𝑡 , 𝑦 = (1.2) 𝑡⁄10, and
classify them as representing exponential growth or decay.
A tennis ball is launched from a small catapult. The height of the tennis ball is
modeled by the function
where is the height in feet and is the
elapsed time in seconds. Which of the following is the maximum height of the ball?
To meet the standard and solve this problem I had to ___________________________________
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30
NAME__________________________________
Student Number__________________________________
Evidence as proof of mastery of standard MAFS.912.F-IF.3.9 (DOK 2) Compare
properties of two functions each represented in a different way (algebraically,
graphically, numerically in tables, or by verbal descriptions). For example, given a
graph of one quadratic function and an algebraic expression for another, say which
has the larger maximum.
Edwin rented 4 movies for the weekend. DVDs cost $2 to rent and Bluray Discs cost
$5 to rent. If Edwin paid $11, which system of equations can be used to determine x,
the number of DVDs rented and y, the number of Bluray Discs rented?
A.
B.
C.
D.
To meet the standard and solve this problem I had to ___________________________________
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31
NAME__________________________________
Student Number__________________________________
Evidence as proof of mastery of standard MAFS.912.F-LE.1.1 : (DOK 3)
Distinguish between situations that can be modeled with linear functions and with
exponential functions. a. Prove that linear functions grow by equal differences over
equal intervals, and that exponential functions grow by equal factors over equal
intervals. b. Recognize situations in which one quantity changes at a constant rate per
unit interval relative to another. c. Recognize situations in which a quantity grows or
decays by a constant percent rate per unit interval relative to another.
Which of the following is NOT a geometric sequence?
A.
B.
C.
D.
To meet the standard and solve this problem I had to ___________________________________
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32
NAME__________________________________
Student Number__________________________________
Evidence as proof of mastery of standard MAFS.912.F-LE.1.2 (DOK 2) Construct
linear and exponential functions, including arithmetic and geometric sequences, given
a graph, a description of a relationship, or two input-output pairs (include reading
these from a table).
The length of time in minutes a remote control helicopter can fly varies indirectly
with how fast in miles per hour it is flying. Using the table below, which of the
following equations represents the flight time of the helicopter?
Flight Time
(min):
Speed (mph):
20
10
6.7
5
5
10
15
20
To meet the standard and solve this problem I had to ___________________________________
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33
NAME__________________________________
Student Number__________________________________
Evidence as proof of mastery of standard MAFS.912.F-LE.1.3 (DOK 2) Observe
using graphs and tables that a quantity increasing exponentially eventually exceeds a
quantity increasing linearly, quadratically, or (more generally) as a polynomial
function.
A line passes through the points (0, 4) and (3, 0). Which equation does not
represent an equation of this line?
To meet the standard and solve this problem I had to ___________________________________
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34
NAME__________________________________
Student Number__________________________________
Evidence as proof of mastery of standard MAFS.912.F-LE.2.5 (DOK 2) Interpret
the parameters in a linear or exponential function in terms of a context.
Maurice is traveling from Phoenix to the Grand Canyon. He averages 45 mi/h on the
220 mile trip. Which equation describes Maurice’s distance from the Grand
Canyon hours after he leaves Phoenix?
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NAME__________________________________
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Evidence as proof of mastery of standard MAFS.912.N-RN.1.1 (DOK 2) Explain
how the definition of the meaning of rational exponents follows from extending the
properties of integer exponents to those values, allowing for a notation for radicals in
terms of rational exponents. For example, we define 5 1⁄3 to be the cube root of 5
because we want (5 1⁄3 ) 3 = 5 (1⁄3)3 to hold, so (5 1⁄3 ) 3 must equal 5.
Identify the expression that is equivalent to the one given.
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NAME__________________________________
Student Number__________________________________
Evidence as proof of mastery of standard MAFS.912.N-RN.1.2 (DOK 1) Rewrite
expressions involving radicals and rational exponents using the properties of
exponents.
A cube has a volume of
cubic centimeters. Which of the following represents
the length of each of the cube’s edges?
A.
B.
C.
D.
To meet the standard and solve this problem I had to ___________________________________
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NAME__________________________________
Student Number__________________________________
Evidence as proof of mastery of standard MAFS.912.N-RN.2.3 (DOK 2) Explain
why the sum or product of two rational numbers is rational; that the sum of a rational
number and an irrational number is irrational; and that the product of a nonzero
rational number and an irrational number is irrational.  Find the sums and products
of rational and irrational numbers.
Ms. Robinson wrote the four numbers listed below.
3√2
7√6
4√7
2√18
She asked the students in her math class to identify two irrational numbers from the
list whose product results in a rational number. Which combination of numbers is
correct?
To meet the standard and solve this problem I had to ___________________________________
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