Download Algebra 1 Math TAKS-STAAR-STAAR-M Comparison

Algebra 1 Math
TAKS-STAAR-STAAR-M Comparison
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(1) Foundations for functions. The student understands that a function represents a dependence of one quantity on another and can be
described in a variety of ways. The student is expected to:
(A) describe independent and dependent quantities in functional relationships; (Supporting Standard)
TAKS 2009
STAAR RELEASED ITEM
STAAR MODIFIED RELEASED ITEM
11 During a sale at a shoe store, all shoes
1 The sales tax rate at a clothing store is
1 The sales tax rate at a clothing
were 25% off the original price. Which
8.75%. Sales tax on an item is a function of
store is 8.75%. Sales tax on an item
statement best describes the functional
its price. Which of the following is the
is a function of its price. What is the
relationship between the sale price of a pair
dependent quantity in this function?
dependent quantity in this function?
of shoes and the original price?
A The sales tax rate on the item
A The sales tax rate on the item
A The sale price is dependent on the original
B The item’s price
price.
C The amount of sales tax on the item
B The item’s price
B The original price is dependent on the sale
D The item’s size
C The amount of sales tax on the item
price.
C The sale price and the original price are
independent of each other.
D The sale price is dependent on the number
of pairs of shoes purchased.
(1) Foundations for functions. The student understands that a function represents a dependence of one quantity on another and can be
described in a variety of ways. The student is expected to:
(B) gather and record data and use data sets to determine functional relationships between quantities; (Supporting Standard)
TAKS 2009
STAAR RELEASED ITEM
STAAR MODIFIED RELEASED ITEM
44 The function table shows the values of
2 Which of the following relations is a
2 Which relation is a function?
f(n) for
function?
A {(0, 0), (0, 1), (0, 2)}
given values of n.
B {(0, 0), (1, 1), (1, 4)}
C {(0, 0), (1, 2), (2, 2)}
Which function best represents the
relationship between the quantities in the
table? J
F I, II, and III only
G I and II only
H II and III only
J III and IV only
(1) Foundations for functions. The student understands that a function represents a dependence of one quantity on another and can be
described in a variety of ways. The student is expected to:
(E) interpret and make decisions, predictions, and critical judgments from functional relationships. (READINESS STANDARD)
TAKS 2009
31 The function below shows a relationship
between x and y.
y = 7x + 3
If the value of x increases by 1, what
happens to the value of y?
A The value of y increases by 3.
B The value of y increases by 7.
C The value of y increases by 10.
D The value of y increases by 21.
STAAR RELEASED ITEM
3 Southern Phone Company is promoting a
new cell phone service plan: a customer can
make up to 500 minutes of calls each month
for $39.99. If the number of minutes used in
a month exceeds 500, then the function
c = 0.40(m – 500) + 39.99
describes the monthly charge, c, in dollars in
terms of m, the total number of minutes
used. Which of the following statements best
describes this function?
A If the total number of minutes used is more
than 500, then every minute beyond 500
costs 40 cents.
B Every minute used costs 40 cents,
regardless of the total number of minutes
used.
C The first 500 minutes used costs 40 cents
each, after which there is an additional
charge
of$39.99.
D If the total number of minutes used is
more than 500, then every minute used
costs 40 cents
STAAR MODIFIED RELEASED ITEM
3 Southern Phone Company has a
new cell phone service plan. A
customer can use up to 500 minutes
of service each month for $39.99. If
the number of minutes used in a
month is more than 500, then the
c = 0.40(m – 500) + 39.99
describes the monthly charge, c, in
dollars in terms of m, the number of
minutes used. Which statement best
describes this function?
A If more than 500 minutes are used,
then every minute over 500 costs 40
cents.
B Regardless of the number of
minutes used, every minute costs 40
cents.
C If more than 500 minutes are used,
then every minute costs 40 cents.
(2) Foundations for functions. The student uses the properties and attributes of functions. The student is expected to:
(B) identify mathematical domains and ranges and determine reasonable domain and range values for given situations, both
continuous and discrete (READINESS STANDARD)
TAKS 2008
STAAR RELEASED ITEM
STAAR MODIFIED RELEASED ITEM
27 The perimeter of an equilateral triangle is 4 What is the domain of the function graphed 4 What is the domain of the function
36 meters or less.
below?
graphed below?
Which set describes the domain for l, the
length of one side of the triangle?
A {0 < l < 3}
B {0 < l < 6}
C {0 < l < 12}
D {0 < l < 36}
F0<x≤5
G2<x≤5
H0<x≤4
J0<x<2
A0<x≤5
B2<x≤5
C0<x≤4
(4) Foundations for functions. The student understands the importance of the skills required to manipulate symbols in order to solve
problems and uses the necessary algebraic skills required to simplify algebraic expressions and solve equations and inequalities in problem
situations. The student is expected to:
(A) find specific function values, simplify polynomial expressions, transform and solve equations, and factor as necessary in
problem situations (READINESS STANDARD)
TAKS 2010
STAAR RELEASED ITEM
STAAR MODIFIED RELEASED ITEM
2
18 Look at the polynomial expression
5 In the quadratic equation x – x + c = 0, c
5 In the quadratic equation x2 – 3x +
modeled below with algebra tiles.
represents an unknown constant. If x = −3 is c = 0, c represents an unknown
one of the solutions to this equation, what is
constant. If x = 1, what is the value
the value of c? -12
of c? 2
Record “A” on the front of your answer
Record “A” on the front of your
document. Then, fill in the bubbles for
your numeric answer on the BACK of the
answer document. Then, fill in
scantron in section Griddable D on
Which of the following expressions is
the bubbles for your numeric
problem number 1.
equivalent to the polynomial expression
answer on the BACK of the
modeled above?
scantron in section Griddable D on
2
F 2x + 7x + 9
G 2x4 + 11x2 + 9
H 2x4 + 30x2 + 20
J 2x2 + 11x + 9
problem number 1.
(5) Linear functions. The student understands
representations. The student is expected to:
(C) use, translate, and make connections
(READINESS STANDARD)
TAKS
28 Which equation best represents the line
graphed below?
that linear functions can be represented in different ways and translates among their various
among algebraic, tabular, graphical, or verbal descriptions of linear functions.
STAAR RELEASED ITEM
6 Which of the following is not a correct
description of the graph of the function
y = -2x - 7?
F The graph of the function contains the point
(−2, −3), and when the value of x increases
by 1 unit, the value of y decreases by 2
units.
G The graph of the function contains the
points (−1, −5), (2, −11), and (4, −15).
H The graph of the function is a line that
passes through the point (0, −7) with a slope
of −2.
J The graph of the function contains the
points (0, −7), (1, −9), and (3, −1).
STAAR MODIFIED RELEASED ITEM
No STAAR-M Item released for this TEKS.
F 7x + 4y = 35
G 4x − 7y = 35
H 4x + 7y = − 35
J 7x − 4y = − 35
(6) Linear functions. The student understands the meaning of the slope and intercepts of the graphs of linear functions and zeros of linear
functions and interprets and describes the effects of changes in parameters of linear functions in real-world and mathematical situations. The
student is expected to:
(A) develop the concept of slope as rate of change and determine slopes from graphs, tables, and algebraic representations; (Supporting
Standard)
TAKS
STAAR RELEASED ITEM
STAAR MODIFIED RELEASED ITEM
52 What is the slope of the linear equation
7 If (2k, k) and (3k, 4k) are two points on
6 If (2, 1) and (3, 4) are two points
101x + 53y = 12? H
the graph of a line and k is not equal to 0,
on the graph of a line, what is the
what is the slope of the line?
slope of the line?
A3
B 3k
C
D Not here
A3
B 11
C
(6) Linear functions. The student understands the meaning of the slope and intercepts of the graphs of linear functions and zeros of linear
functions and interprets and describes the effects of changes in parameters of linear functions in real-world and mathematical situations. The
student is expected to:
(F) interpret and predict the effects of changing slope and y-intercept in applied situations (READINESS TEKS)
TAKS 2009
STAAR RELEASED ITEM
STAAR MODIFIED RELEASED ITEM
43 Tyler wants to buy a video-game system
8 The amount an appliance repairman
7 A repairman charges a total amount
for $375. He can pay for the system in 12
charges for each job is represented by the
for each job he completes.
months if he pays $75 now and $25 each
function
• This total amount, t, can be found
month. How will the number of monthly
t = 50h + 35, where h represents the
using the function t = 50h + 35,
payments be affected if Tyler pays $75 now
number of hours he spent on the job and t
where h represents the number of
and $30 each month?
represents the total amount he charges in
A He will make 10 fewer monthly payments.
dollars for the job. The repairman plans to
hours he spent on the job.
change the amount he charges for each job.
• The repairman plans to change the
B He will make 2 fewer monthly payments.
The amount he plans to charge is represented
amount he charges for each job.
C He will make 3 fewer monthly payments.
by the function t = 50h + 45. What will be
• The function t = 50h + 45 can be
the effect of this change on the amount he
D He will make 5 fewer monthly payments.
used to find the total amount charged
charges for each job?
F The total amount he charges for each job
for each job after this change.
will increase by $10.
What will be the effect of this change
G The total amount he charges for each job
on the amount he charges for each
will decrease by $10.
job?
H The amount he charges per hour will
A The total amount he charges for
increase by $10.
J The amount he charges per hour will
each job will increase by $10.
decrease by $10.
B The total amount he charges for
each job will decrease by $10.
C The amount he charges per hour
will increase by $10.
(8) Linear functions. The student formulates systems of linear equations from problem situations, uses a variety of methods to solve them,
and analyzes the solutions in terms of the situation. The student is expected to:
(A) analyze situations and formulate systems of linear equations in two unknowns to solve problems; (Supporting Standard)
TAKS
STAAR RELEASED ITEM
STAAR MODIFIED RELEASED ITEM
5 A restaurant sold a total of 418 large and
9 The sum of the perimeters of two different
8 Read the information below about
small hamburgers during one day. Total
squares is 32 centimeters, and the difference
two squares.
hamburger sales were $1077. Large
between their perimeters is 8 centimeters. If
• The side length of the larger
hamburgers sold for $3, and small
x represents the side length of the larger
square can be represented by x.
hamburgers sold for $1.50. Which system of
square and y represents the side length of
• The side length of the smaller
linear equations can be used to find l, the
the smaller square, which of the following
number of large hamburgers sold, and s, the
systems of equations could be used to find
square can be represented by y.
number of small hamburgers sold?
the dimensions of the squares?
• The sum of the perimeters of the
A l + s = 1077
A x + y = 32
two squares is 32 centimeters.
x−y=8
3l + 1.50s = 418
•
The
difference between their
B l + s = 418
B 4x + 4y = 32
perimeters is 8 centimeters.
3l + 1.50s = 1077
4x − 4y = 8
C 1.50l + 3s = 418
Which system of equations could be
l + s = 1077
C 2x + 2y = 32
used to find the side length of each
2y − 2x = 8
D l + s = 418
square?
1.50l + 3s = 1077
D 4x + 2y = 32
A 4x + 4y = 32
4x − 2y = 8
4x − 4y = 8
B 2x + 2y = 32
2y − 2x = 8
C 4x + 2y = 32
4x − 2y = 8
(8) Linear functions. The student formulates systems of linear equations from problem situations, uses a variety of methods to solve them,
and analyzes the solutions in terms of the situation. The student is expected to:
(B) solve systems of linear equations using concrete models, graphs, tables, and algebraic methods (READINESS STANDARD)
TAKS
STAAR RELEASED ITEM
STAAR MODIFIED RELEASED ITEM
10 Some values for two linear equations are
Some values for two linear equations
shown in the tables below.
are shown in the tables below.
No Released Item for this TEKS on TAKS.
What is the solution to the system of
equations represented by these tables?
F (2, 3)
G (3, 5)
H (−1, 1)
J (5, 11)
What is the solution to the system of
equations represented by these
tables?
A (3, 5)
B (−1, 1)
C (5, 11)
(9) Quadratic and other nonlinear functions. The student understands that the graphs of quadratic functions are affected by the parameters
of the function and can interpret and describe the effects of changes in the parameters of quadratic functions. The student is expected to:
(D) analyze graphs of quadratic functions and draw conclusions. (READINESS STANDARD)
TAKS
STAAR RELEASED ITEM
STAAR MODIFIED RELEASED ITEM
58 The graph below represents the
11 The graph of a quadratic function is
relationship between the density of water and shown below.
the temperature of water.
Which statement about this graph is not true?
A The graph has a y-intercept at (0, 8).
B The graph has a maximum point at (-1, 9).
C The graph has an x-intercept at (2, 0).
D The graph has the y-axis as a line of
symmetry
According to the graph, which of the following
intervals best represents the temperature at
which the density of water is greater than
999.9 kilograms per cubic meter?
F Less than 1°C
G Between 0°C and 4°C
H Between 4°C and 8°C
J Between 1°C and 7°C
No STAAR-M Item released for this TEKS.
(10) Quadratic and other nonlinear functions. The student understands there is more than one way to solve a quadratic equation and solves
them using appropriate methods. The student is expected to:
(A) solve quadratic equations using concrete models, tables, graphs, and algebraic methods (READINESS STANDARD)
TAKS
STAAR RELEASED ITEM
STAAR MODIFIED RELEASED ITEM
43 What is the solution set for the equation
12 The graph of a quadratic function is
10 The graph of a quadratic function
2x 2 − 16x − 96 = 0?
shown below.
is shown below.
A {4, 12}
B {−4, 12}
C {−4, −12}
D {4, −12}
What is the best estimate of the positive
value of x for which this function equals 8?
F2
G4
H 13
What is the best estimate of the
positive value of x for which this
function equals 8?
A2
B4
C7
J7
(11) Quadratic and other nonlinear functions. The student understands there are situations modeled by functions that are neither linear nor
quadratic and models the situations. The student is expected to:
(C) analyze data and represent situations involving exponential growth and decay using concrete models, tables, graphs, or algebraic
methods. (Supporting Standard)
TAKS
STAAR RELEASED ITEM
STAAR MODIFIED RELEASED ITEM
13 A population of 1500 deer decreases by
11 A population of 1500 deer
1.5% per year. At the end of 10 years, there
decreases by 1.5% per year. At the
will be approximately 1290 deer in the
end of 10 years, there will be
population. Which function can be used to
approximately 1290 deer in the
determine the number of deer, y, in this
population. Which function can be
population at the end of t years?
A y = 1500(1 – 0.015)t
used to determine the number of
No Released Item for this TEKS on TAKS.
t
deer, y, in this population at the end
B y = 1500(0.015)
C y = 1500(1 + 0.015)t
D y = 1500(1.5)t
of t years?
A y = 1500(1 – 0.015)t
B y = 1500(1 + 0.015)t
C y = 1500(1.5)t