Integrated Algebra Mid-Term Review Packet:



Algebra I Mid-Term Review Packet Last one!:

|1)[pic] |2) [pic] |

|3)[pic] |4) Which of these sets of numbers contains no rational numbers? |

| |1) [pic] 2) [pic] |

| |3) [pic] 4) [pic] |

|5) If h represents a number, which equation is a correct translation of "Sixty|6) If A = [pic] and B = [pic]? |

|more than 9 times a number is 375"? | |

|1) |What is A + B? |

|[pic] | |

|3) |What is A – B? |

|[pic] | |

| | |

|2) | |

|[pic] | |

|4) | |

|[pic] | |

| | |

| | |

|7) Subtract [pic] from [pic]. |8) What is the product of [pic] and [pic]? |

| | |

|9) [pic] |10) [pic] |

|11) |

|Which of the following graphs represents the function f(x) = – x2 + 3? |

|1. [pic] 2. [pic] |

|3. [pic] 4. [pic] |

|12) |13) The following lines |

| |3y-6x=18 |

| |-4x+2y=10 |

| |are |

| |Parallel 2) perpendicular |

| |The same 4) intersecting |

|14) [pic] |15) [pic] |

|16) [pic] |17) |

| |[pic] |

|18) [pic] |19) What is the value of n in the equation [pic]? |

| | |

| | |

| | |

|20) |21) |

|[pic] |[pic] |

|22) |23) A candy store sells 8-pound bags of mixed hazelnuts and cashews. If c pounds of|

|[pic] |cashews are in a bag, the price p of the bag can be found using the formula [pic]. |

| |If one bag is priced at $18.11, how many pounds of cashews does it contain? |

| | |

| | |

| | |

|24) The following lines |25) Factor: |

|y-2x=1 |A [pic] B. 5x – 30 C [pic] |

|2y-x=6 | |

|are |Factor Completely: Hint, take out the GCF first |

|1) |D. [pic] E. [pic] |

|parallel | |

| | |

|2) | |

|The same | |

| | |

|3) | |

|perpendicular | |

| | |

|4) | |

|intersecting | |

| | |

| Calculate the domain of the function, f(x) = [pic] Show all work |27) Which function is what f(x) would become after a shift of 8 units right and 3 |

|algebraically, graphically and provide a sketch. |units up? |

| |f(x + 8) – 3 C) f(x + 8) + 3 |

| |f(x – 8) – 3 d) f(x – 8) + 3 |

|28) Simplify: [pic] | 29) Mike goes to a bakery and buys four cookies and three drinks for a total of |

| |$5.00, and Anna goes to the same bakery and buys six cookies and 2 drinks for a |

| |total of $5.85. How much does one cookie cost and how much does one drink cost? |

| |Only an algebraic solution will be accepted. |

| | |

| | |

| | |

Open Response: Continue

30) a) Find the equation of the parabola in the graph below.

b) For which interval does the parabola increases and which interval does the parabola decreases. Explain

31) Maya has a science lab due tomorrow. She launches a model rocket from the ground level at t = 0 sec. It reaches a height of h feet, where [pic].

a. Graph the equation (Label, Label, Label)

b. What is the maximum height the rocket reaches? _________________

c. How much time does the rocket take to reach its maximum height? ___________

32) Write a linear equation for each

|A) [pic] |B) |C) |

| |[pic] | |

D) A line that passes through (2,3) and (4,4) in all 3 forms (Point-slope form, slope-y intercept form, standard form)

33) The length of a rectangular door is 5 feet more than its width, w.  The area of the door is 36 square feet.  Write an equation which could be used to find the dimensions of the door? Find the door’s dimensions.

34) Rewrite the following equation into standard quadratic form: [pic]

35) If f(x) = [pic] find the value of f(-3)

36) Solve the following compound inequality:

5. ≥ -2x+3 > 9

37) Look at the following graphs and answer the following questions

|x | | |

|F(x) |H(x) [pic] |g(x) = 2x |

| | | |

|0 | | |

|2 | | |

| | | |

|1 | | |

|5 | | |

| | | |

|2 | | |

|8 | | |

| | | |

|3 | | |

|11 | | |

| | | |

|4 | | |

|14 | | |

| | | |

|5 | | |

|17 | | |

| | | |

a. Name each function: Linear, Exponential, Quadratic.

b. Which function has a larger average rate of change from x = 1 to x = 5,

c. What is the domain and range of f(x)?

38) Find the solution for the following system graphically

y≥ 2x+1

y≤-x+3

39) Use the graph shown below to answer each of the following,

a. For which week(s) was Tara’s weight gain 2 pounds?

b. For which time intervals, in weeks, did Tara have a negative weight change?

40) Solve by Factoring:

[pic]

a. What is the extrema?

b. What are the solutions?

c. What is the axis of symmetry?

Unit 1

• I can simplify algebraic expressions by combining like terms and using the laws of exponents

• I can add and subtract polynomials

• I can translate verbal expressions to algebraic expressions

• I can multiply monomials

• I can multiply using double distribution

• I can divide a polynomial by a monomial

• I can solve algebraic equations to find all possible solutions.

• I can represent the solutions for an algebraic equation in words, a set notation, or a graphical representation on the number line.

• I can solve multi-step equations involve variables on both sides

• I can solve algebraic equations using the distributive property.

• I can solve algebraic equations by cross multiplying.

• I can solve algebraic inequalities in words, set notation and graphically.

• I can identify the solutions for equations and inequalities joined by“and” or “or”.

• I can solve algebraic equations or inequalities joined by “and”, or “or” in words, set notation, and graphically.

• I can solve compound inequalities in words, set notation, and graphically.

• I can write linear equations in the slope-intercept form, slope-point form, and standard form.

• I can write linear equations for horizontal and vertical lines.

• I can write linear equations to represent relationships looking at graphs, tables, and solve word problems.

• I can determine if two lines are parallel.

• I can determine if two lines are perpendicular.

• I can write linear inequalities.

• I can graph half planes for linear inequalities.

• I can rearrange literal equations in term of different variables.

Unit 2:

• I can solve a system of two linear equations graphically

• I can solve a system of two linear equations by substitution

• I can solve a system of two linear equations by addition

• I can solve a system of two linear inequalities graphically.

• I can solve a real-life system of linear equations and inequalities.

Unit 3:

• I understand the difference between Relations and Functions

• I can represent relations in a relation set, mapped diagram, tables and graphically.

• I can identify a function represented in a relation set, mapped diagram, tables and graphically.

• I can understand the difference between function input and output.

• I can evaluate an output when give an input of a function.

• I can state the domain and range of a relation looking at its graph.

• I can identify parent functions, their domains and ranges.

• I can identify different types of transformations

• I can graph transformed functions

• I can write a transformed parent function

• I can calculate the rate of change

• I can calculate the average rate of change

• I can identify linear functions in real life applications

• I can differentiate between linear and exponential functions.

• I can determine if a function is linear or exponential looking at graphs, tables, and equations.

Unit 4

• I can graph quadratic functions.

• I can identify the domain and range of a quadratic function over and interval.

• I can identify the x-intercepts, y-intercept, extrema or vertex, increasing and decreasing interval, and axis of symmetry of a parabola.

• I can identify functions in real-life.

• I can graph a quadratic equation in real life context using the graphic calculator with the appropriate window

• I can Evaluate quadratic functions in real life context

• I can calculate the rate of change over an interval in real life context.

• I can identify the Sum/product form of quadratic equations and their transformation.

• I can factor algebraic expressions using GCF

• I can factor algebraic expressions using DOPS

• I can factor a trinomial with a leading coefficient =1 using the diamond method.

• I can identify the roots of a quadratic looking at the graph

• I can calculate the roots from a graph using the calculator

• I can write the sum- product quadratic equation using the roots.

• I can solve quadratics in real-life.

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