Algebra 2 Midterm Exam – Homework Handlers

                                                                           Name:                                                          
Directions:  Use what you have learned in this course to answer thefollowing questions. Justify your responses completely. Each question is worth5 points.
1. Solve for n:  –6(n – 8) = 4(12 – 5n) + 14n.
2.  For f(x)= 2|x+3| – 5, name the type of function and describe each of thethree transformations from the parent function f(x) = |x|.

3.  Determine whether f(x) = –5 – 10x + 6has a maximum or a minimum value.  Findthat value and explain how you know.
4. The median weeklyearnings for American workers in 1990 was $412 and in 1999 it was $549.Calculate the average rate of change between 1990 and 1999.
5. Find the roots of the parabolagiven by the following equation.      
                                                2×2+ 5x – 9 = 2x

6.  Describe the end behavior and determinewhether the graph represents an odd-degree or an even-degree polynomialfunction. Then state the number of real zeros.
7. GEOMETRY Recall the formula for finding the area of arectangle.  Define a variable for thewidth and set up an equation to find the dimensions of a rectangle that has anarea 144 square inches, given that the length is 10 inches longer thanits width. 
     DIMENSIONS:
     Length­:                                                            Width:                                    

8. Theamount f(t) of a certain medicine, in milligrams, in a patient’sbloodstream t minutes after being taken is given by f(t) =  . 
       Find the amount of medicinein the blood after 20 minutes.
9.  Graph f(x) = x2 + 2x – 3, label the function’s x-intercepts, y-interceptand vertex with their coordinates.  Alsodraw in and label the axis of symmetry.

10. Determine whether the relation shown is afunction. Explain how you know.

11.  Solve the inequality and graph the solution on a numberline.
       –3(5y – 4) ≥ 17

 
12.  Assume that the wooden triangle shown is a right triangle.
​​

a. Write an equation usingthe Pythagorean Theorem and the measurements provided in the diagram.
    Hint: (leg 1)2 + (leg 2)2 = (hypotenuse)2
b. Transform each side ofthe equation to determine if it is an identity.

13.Use longdivision or synthetic division to find the quotient of   .

14. Simplify (9 + 8 – 6)(4 – 5).

15.  Find the inverse of h(x) = .

16.  If f(x) = 2x – 1 and g(x)=  – 2, find [g◦ f](x).

17.  Graph the function y =  – 2.  Then statethe domain and range of the function. 

                                                                           Domain:
                                                                             Range: 
18. If f(x)= 3×2 – 2 and g(x)= 4x + 2, what is the value of (f+ g)(2) ?
Theprice of a sweatshirt at a local shop is twice the price of a pair of shorts.The price of a T-shirt at the shop is $4 less than the price of a pair ofshorts. Brad purchased 3 sweatshirts, 2 pairs of shorts, and 5 T-shirts for atotal cost of $136.
19.  Let w represent the price of onesweatshirt, t represent the price of one T-shirt, and h representthe price of one pair of shorts. Write a system of three equations thatrepresents the prices of the clothing.
20.Solve the system. Find the cost of each item.
 
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