Name:__________________________________________________

TAC MathPractice Quiz: Solving Equations & Inequalities

Please show all work for full credit!

1. Evaluate 2b (4 a – c2) if a = 5, b = , and c = 11.

2. Evaluate – | 3c – d | if c = –1 and d = 5.

3. Simplify 2(x + 3) + 5(2x – 1)

4. Solve for b.

5. Solve for n.

Section 1 Review

Name: _________________________________ Date: __________________ TAC Mathematics – Review for test 1

1. Evaluate given a = 12, b = 0.5, c = -3, and d = 13

9c abc�

2. Simplifying expressions 2m + 7n – 6m – 5n -5(a – 4b) + 4b 3. Solving Equations

x – 6 = -20 3 14 7 2w w� �

4. Solve the literal Equations:

solve for x, Ax + By = C solve for r, 3rxy – h = B

Section 2 Review

5. Solving Absolute Value Equations (Watch for Special Cases!) 3 6 36x � � � 4 5 25x

6. Solving Inequalities (Includes Graphing!) � !7 28w 3 4 19x � t

2 3 7 8 2 12� t � �z z( )

7. Compound Inequalities & Absolute Value Inequalities (Includes Graphing & Special Cases!)

3 2 7m� � or 2 1 13m� ! � � � d1 3 2 9( )y

2 9 27y � d � � � ! �3 1 1 2x

3 11 1b� ! � � � !3 4 6 0x

Graph… x ! �1 or x � �5 x ! 5 and x � 8

Word Problems!

8. Mrs. Denney is renting a car during her next trip. The rental charge is $19.50 a day plus 18 cents per mile. Write an expression to represent the cost given she drove m miles. (Ignoring the price of gas!)

The company she works for will reimburse her up to $33. How many miles can she drive and have it completely reimbursed?

9. Find the equation of the line having the given slope and containing the given point.

m = (6, -2)

10. Find the slope, if it exists, of the line that contains the points (10, -3) and (10, - 5).

11. Use the equation to complete the table. Use the table to list some of the ordered pairs that satisfy the equation.

y = -2x + 5

x y (x, y)

-2

-1

4

12. Graph the equation using intercepts.

y=2+x

13. The cost of printing a magazine is $4,000 to typeset and prepare copy for printing and $2 per copy to print. This expressed as an equation is y = 2x + 4,000, where x is the number of copies printed and y is the total cost of printing x copies. Find the cost of printing 11,000 copies. Find the cost of printing 20,000 copies.

(11,000 copies) ____________________

(20,000 copies) ____________________

14. Graph the inequality: x - y < 5

15. Graph the line that passes through the points (-1, 2) and (-1, -2). Identify the line as having a positive slope, a negative slope, a zero slope, or an undefined slope.

16. Find the slope of the line in the figure. Then write the equation of the given line.

17. Find the slope and the y-intercept of the line whose equation is: y= x+4

(slope) _______________

(y-intercept) ___________

18. Locate point R by giving the amount of horizontal and vertical movement from the origin.

19. Determine whether (2,9) is a solution of 5x - 10y = 158.

(circle) Yes No

Horizontal movement of point R from the origin:

____________

Vertical movement of point R from the origin:

___________

R

20. Write an equation of the line containing the given point and parallel to the given line. Write the equation in standard form.

(6, -5); 9x - 7y = 3

21. Find the equation of the line containing the given pair of points (3, 2) and (9, 5)

22. State the coordinates of the points graphed in the figure below.

A. ______________

B. ______________

C. ______________

D. ______________

E. ______________

F. ______________

A B

C F

E

D

23. Create a table of four coordinate points for the equation y = -4x + 5, and then graph the equation.

24. Find five ordered pairs to the equation y= x+4 then graph.

25. Find the equation of the line that passes through (1, -10) and is perpendicular to 2x + 7y = -5. Write the equation in standard form.

26. Write the equation of the line with the given slope and y-intercept value.

m = 5, b = -5

27. Find the slope, if it exists, of the line containing the pair of points (1, -1) and (1, -4).

28. The cost of printing a magazine is $8,000 to typeset and prepare copy for printing and $2 per copy to print. This is expressed as an equation y = 2x + 8,000, where x is the number of copies printed and y is the total cost of printing x copies. Find the cost of printing 12,000 copies. Find the cost of printing 20,000 copies.

(12,000) ___________________

(20,000) ___________________

Name_________________________________________________Date____________________ Topics in Applied College Mathematics (TAC) FORMATIVE

Directions: Solve Systems of Linear Equations Graphically Solve by graphing. State the solution to the system in proper notation.

1. x – y = 7 3x + y = 9

Solving Systems of Equations & Inequalities

Exceeding (4) Meeting Expectations (3) Approaching (2)

In addition to meeting all of the level 3 indicators, students must be able to:

In order to meet expectations for this indicator, students must be able to:

□ Problem Solving Using Systems of Linear Equations

□ Solve Systems of Linear Equations Graphically

□ Solve Systems of Linear Equations Addition Method

□ Solve Systems of Linear Equations Substitution Method

□ Problem Solving Using Systems of Linear Equations

Students approaching expectations will be able to meet between 1 and 2 of the level 3 indicators.

Section 3 Review

2. y = 2x - 3

y = x + 2

3) x + y = 10

x - y = 2

Directions: Graph the system of inequalities and shade the portion on the graph represented by the solution set.

4) x – 2y < - 1

x + 2y > 3

5) x – 4y < -7

x + 4y > 1

Directions: Solve the system of equations using the addition method. 6) a – 8b = 28 2a + 8b = -16

7) x – 2y = - 9 -x – 7y = - 27

8) 4x - 3y = 19 - 2x – 4y = -4

9) 4x + y = 18 3x – 3y = 21 10) 7x – 5y = - 4 3x – 5y = - 16

Direction: Find the solution to the system of equations by substitution.

11) 2a + 5b = 65 a = 15 + b

12) 1 x – y = 4 5 x – 5y = 20

13) 9x – 8y = 0 2x – y = 7

14) 10x – 8y = -4 5x + 12y = 10

15) 3x + 6y = 18 4x + 8y = 32

Directions: Problem Solving 16) Building A is 200 feet shorter than Building B. The total height of the two buildings is 1510 feet. Find the height of each building. (Simplify your answer. Type an integer or a decimal.) What is the height of building A? ft What is the height of building B ft 17) In a discount clothing store, all sweaters are sold at one fixed price and all shirts are sold at another fixed price. If one sweater and three shirts cost $40, while four sweaters and two shirts cost $70, find the price of one sweater and the price of one shirt. The price of a sweater is $ The price of a shirt is $ 18) At a concession stand, three hot dog(s) and four hamburger(s) cost $12.00; four hot dog(s) and three hamburgers(s) cos $10.75. Find the cost of one hot dog and the cost of one hamburger. What is the cost of one hot dog? What is the cost of one hamburger?

19) You invested $3,000 between two accounts paying 4% and 9% annual interest, respectively. If the total interest earned for the year was $170.00, how much was invested at each rate? $ Was invested at 4% and $ was invested at 9%

20) You invested $4000 between two accounts paying 4% and 6% annual interest, respectively. If the total interest earned for the year was $180, how much was invested at each rate?

$ Was invested at 4% and $ was invested at 6%

Section 4 Review