Download Quarter 1 Review Algebra 2 Block - Kraft Name Solve each equation

Quarter 1 Review
Algebra 2 Block - Kraft
Name _______________________
Solve each equation for x.
1) ½ x + 12 = 5
2) 7x + 2 – 3x = 12 – x
4) 3x = 27
5)
3) 5(x + 3) = -2(x -3)
8 z + 3 = 64
6) 2y  6  4  15
Standard: HS.A-CED.4 Rearrange formulas to highlight a quantity of interest, using the same reasoning as in solving
equations.
7) 2𝑦 − 6𝑥 = 7𝑤𝑣, solve for x
1
2
8) 𝐴 = 𝑏ℎ, solve for h
Write the equations for the following:
10) 10x – 5y = 25 (in slope-intercept form)
1
2
9) 𝐴 = ℎ(𝑏1 + 𝑏2 ), solve for 𝑏2
11) (-3, 5) and (7, 15) (in any form)
Standard: HS.A-CED.2 Create equations in two or more variables to represent relationships between quantities; graph
equations on coordinate plane.
** Graph the function.
3
12) 2𝑥 − 3𝑦 = −12
13) 𝑓(𝑥) = − 2 𝑥 − 5
y  x  4

16) 
1
y  x  1
2

15) −|𝑥 − 4|
Graph the following piecewise-defined function below.
 
2x  1


x  4
18) f x  
x 2
x 2
1
14) 𝑔(𝑥) = 3 |𝑥 − 5| − 2
𝑥 ≤3
17) { 𝑦 ≥ 0
𝑦 > 3𝑥 − 2
19) Write the equations for the given piece-wise function.
For each system, choose the method of solving that seems easier to use and solve. Show all work.
20)
3x  4y  13
5x  6y  19
20) _______________
22)
3x  y  5
y  4x  2
22) _______________
21)
2x  3y  6
6x  9y  9
21) _______________
23)
2x  3y  4
2x  5y  6
23) _______________
Standard: HS.F-IF.4* 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.
24) The bill for your cable company can be modeled by the linear function 𝑦 = 24.99 + 3𝑥 where y represents your
total bill due in dollars and x represents the number of premium channels you subscribe to.
a. What does the y-intercept represent? Explain.
b. What does the slope represent? Explain.
Standard: HS.A-CED.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.
25) A restaurant sells a regular size of pop for $2 and a large size of pop for $3.50. Lora and her friends buy 8 servings of
pop and spend a total of $19. Find the amount of large pops the friends bought and the amount of regular pops the
friends bought. Write your answer in a complete sentence.
26) Suppose you are buying two kinds of apps for school. An educational app costs $2, and a game app costs $4. You
must have at least 6 apps. The cost of the notebooks can be no more than $20. Write a system of inequalities to model
the situation, then graph and solve the system.
27) You and your friend are both knitting scarves for charity. You knit 8 rows each minute and already have knitted 10
rows. Your friend knits 5 rows each minute and has already knitted 19 rows. When will you both have knitted the same
number of rows?
A) Write an equation to represent your speed of knitting: y = ___________
B) Write an equation to represent your friend’s speed of knitting: y = ____________
C) After how many minutes will you and your friend have knitted the same number of rows?
1
28) You are given the equation 𝑦 = 3 𝑥 + 5. It is your task to find another linear equation to make a linear system that
will have:
a.
One solution
b. No solution
c. Infinite solutions
30) The accompanying table shows the enrollment of a preschool from 1980 through 2000. Write a linear regression
equation to model the data in the table.
A) Equation: _________________________
B) Using your equation from Part A, what would be the prediction for
enrollment in 2014?
C) During what year would the expected enrollment be 50?
Standard: HS.A-CED.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.
31) A sporting goods manufacturer makes a profit of $5 on soccer balls and a profit of $4 on volleyballs. Cutting requires
2 hours to make a soccer ball and 3 hours to make a volleyball. Sewing needs 3 hours to make a soccer ball and 2 hours
to make a volleyball. Cutting has 600 hours available and Sewing has 450 hours available.
Let
x = # of ___________________
y = # of ___________________
A)
Write a system of four inequalities
to show the constraints of this situation.
____________________________
____________________________
____________________________
____________________________
B)
Graph the constraints to find the feasible region.
C)
What are the vertices that represent the potential maximum profit?
_________________________________________________________________________
D)
Write the equation for the objective function.
_______________________________
E)
What is the maximum profit and how many of each item do we need to sell to achieve this profit?
_______________________________
_______________________________
Solve the following, make sure you check for extraneous solutions:
32) 2 3x  2  14
33) x  4  3  17
34) 3 4w  1  5  10
Standard: HS.F-BF.3* Identify the effect on the graph of replacing f(x) by f(x)+k, kf(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.
35)Write an equation for a translation on the parent graph 𝑦 = |𝑥| reflected over the x-axis and horizontally translated 4
units to the right and 3 units up.
36) Describe in words the transformation that leads 𝑓(𝑥) = 𝑥 2 to 𝑔(𝑥) = (𝑥 + 1)2 − 2.
37) Write an equation for a parabola whose vertex is higher than the following vertex:
38) Write a possible equation for the parabola pictured below:
39) Using the graph of the function f(x) in the diagram, graph the following transformations on f(x).
A) 𝑦 = 2𝑓(𝑥)
B) 𝑦 = 𝑓(𝑥) − 1
C) 𝑦 = 𝑓(𝑥 + 4)
________________
Standard: HS.SSE.2 Use the structure of an expression to identify ways to rewrite it.
Factor the quadratic expressions.
40) x 2  7 x  12
41) 4𝑐 2 + 4𝑐 + 1
42) 6 x 2  x  2
Standard: HS.APR.3 Identify zeros polynomials when suitable factorizations are available, and use the zeros to construct
a rough graph of the function defined by the polynomial.
Solve the equations by factoring.
43) 𝑥 2 − 2𝑥 − 24 = 0
44) 3𝑥 2 = 𝑥 + 4
Standard: HS.F-IF.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 f is the graph of the equation y =
f(x).
45) Error Analysis: A student claims that the relation {(0,3), (1,5), (3,8), (5,5)} is not a function because the ycoordinate 5 corresponds to more than one x-coordinate. Explain the students’ error, and justify your answer.
46) Is there a number that could be added for the missing input value to make this relation not a function? If yes, what
is the value? Explain.
_________________________________________________________________
_________________________________________________________________
_________________________________________________________________
_________________________________________________________________
47) Evaluate the given function for the given value: f(x) = 3x -1 for x = -2.
Identify the key features of the following quadratic graph.
48)
x
Vertex _________
Axis of symmetry _______
Max or min value _______
Domain _________
Range __________
y-intercept ______________
x-intercept(s) ______________
49) 𝑓(𝑥) = 2(𝑥 − 2)2 − 3
Vertex Form:
___________________________
50) 𝑦 = 2𝑥 2 − 12𝑥 + 19
Vertex Form:
___________________________
Standard Form: ___________________________
Standard Form: ___________________________
Vertex:
Vertex:
___________________________
___________________________
Axis of Symmetry: ___________________________
Axis of Symmetry: ___________________________
Max/Min:
___________________________
Max/Min:
___________________________
Domain:
___________________________
Domain:
___________________________
Range:
___________________________
Range:
___________________________
y-intercept:
___________________________
y-intercept:
___________________________
x-intercepts:
___________________________
x-intercepts:
___________________________