Algebra 2 C Midterm Exam Review Topics Exam Date: A2: Wednesday, January 21 st A4: Friday, January 23 rd

Transcription

1 Algebra C Midterm Exam Review Topics Exam Date: A: Wednesday, January 1 st A4: Friday, January rd Chapter 1 Properties and Operations Number Sets Properties of Real Numbers Square Roots Simplifying Algebraic Equations Properties of Exponents Relations and Functions Transformation of Functions Chapter Linear Functions Solving Linear Equations & Inequalities Proportional Reasoning Graphing / Writing Linear Functions Linear Inequalities in Variables Linear Regression Absolute-Value Equations and Inequalities and Functions Chapter Linear Systems Solving Linear Systems using Graphs and Tables Solving Linear Systems Algebraically: (elimination / substitution) Solving Systems of Linear Inequalities Solving Linear Systems in Variables Chapter 4 Matrix Operations Matrices and Data Multiplying Matrices Adding / Subtracting Matric Helpful Vocabulary Domain Linear Range Relation Slope Standard Form Systems of Equations Vertical Line Test x-intercept y-intercept Preparing for the Exam Complete the review problems. Plan your time wisely. Do not wait until the night before the exam to study. Review your notes. Review all the quizzes you have taken. Write down and Review all the concepts or skills that stumped you. Check in with your teacher on any problems you could not resolve. Do not stay up late the night before the exam. Get plenty of rest. Eat a good breakfast.

2 Algebra II-C Midterm Review Formulas and Tips Quadrants II III I IV Absolute Value Equations and Inequalities x a x a x a a x a x a a x a x a x a or x a x a x a or x a Slope-Intercept Form of a Line y mx b, where m is slope and b is the y-intercept Point-Slope Form of a Line ( y y1) m( x x1 ) Slope y y1 m x x1 Absolute Value Functions in Vertex Form Vertex Form: y a x h k Vertex ( x, y ) ( h, k) Equation for axis of symmetry: Domain x-values Range y-values x h x- and y-intercepts of Linear Equations x-intercept: Set y 0 ; solve for x. (x, 0) y-intercept: Set x 0 ; solve for y. (0, y) Laws of Exponents Zero Exponent a 0 1 n 1 1 Negative Exponent a or n n a a m n m n Product of Powers a a a m a m n Quotient of Powers a n a m n m a Power of a Power n m m Power of a Product Power of a Quotient a m ab a m a b a b b m m n a Linear Inequalities If you multiply or divide by a negative number, flip the inequality symbol. Use a solid dot for and symbols. Use an open dot for < and > symbols.

3 Name Algebra II-C Midterm Review Packet NOTE: The following problems will serve as a good start to prepare for the mid-term exam. You should also study your notes and be sure you can explain important mathematical vocabulary terms. 1. Is (, ) a solution to y 4x 8? 1.. State the quadrant for each of the following points: a. (, ) a. b. (, ) b. c. (, ) c. d. (, ) d. e. ( 0, ) e.. Graph the following equations. a.) 4x y 1 b.) y Simplify 5. Find the slope of the line containing each pair of points. 4. a. ( 4, ) and (, ) 5a. b. (4, ) and (4, ) 5b. 6. Write an equation for the line that contains the given pair of points (1, 16) and (6, 8). a. Write your final answer in slope-intercept form. 6a. b. Write your final answer in point-slope form. 6b.

4 7. Represent real numbers greater than or equal to seven using: a. set notation 7a. b. interval notation 7b. 8. Represent even numbers between 6 and 6, inclusive using roster notation Represent (, 7] using set notation Represent x -5 x 7 using interval notation Classify by all subsets of real numbers to which it belongs Classify by all subsets of real numbers to which it belongs Evaluate f () for f ( x) x x Given the relation 1, ), (1, 6), (, 5), (, 6), (4, 9) (, find the: a. Domain 14a. b. Range 14b. 15. Solve for x: ( x ) x Solve each inequality for the variable given and graph the final solution on a number line. a. 8k 16 16a. b. ( w 8) 9 (4 w) 4 16b.

5 1 c x 10 16c. 17. Solve each equation for the indicated variable. 1 a. A bh for b. 17a. b. V IR for R. 17b. c. C r for r. 17c. 18. Graph the following linear equation. y 1 x Find the x- and y- intercepts; then graph the following linear equation. 19. x y 1 0. What is the slope of the following equation : y 5 ( x 1)? 0.

6 1. Solve for x in 9x 6x 1 x Explain how you can tell if a set of points is an example of a function.. Explain how you can tell if a graph is an example of a function. 4. For each relation shown, state: i.) the domain ii.) the range iii.) whether the relation is a function. If not, state why. a.) b.) y 1, x y, x domain: range: function or relation? why? domain: range: function or relation? Why? 5. Simplify each expression. Do not leave any answer with negative exponents. a. 5x 8 x 4 5a. b. 0 5 a a 5b. c. 7 5x y 4 15x y 8 5c.

7 4 d. 0 9x y z 5d. e a b 4 a b 5e. f. a b 8 5f. 6. Solve for the variable. a. b x b b a. 6b. 7. Simplify or perform the operations and then simplify. a. 60 7a. b b. c. 10 7c. d d. e e. f f.

8 g g. h h. i. 5 7i. j. 6 7j. k k. l l. 8. Determine the vertex of each absolute value function: a. f ( x) x 4 6 8a. b. f ( x) x 4 6 8b. c. f ( x) x 4 6 8c. d. f ( x) x 4 6 8d. 9. Solve and graph on a number line: x Solve each absolute value inequality, then graph on a number line: a. x 10 0a. b. x 15 0b.

9 c. 4 x 5 0c. d. 5 x 1 0d. 1. Leona earns $500 per week plus 7% of her weekly sales. a. Write a function (in function notation) to represent the situation. 1a. b. What is her salary if she sells $500 worth of equipment? 1b.. Write the equation of a line in slope-intercept form of a line that is. parallel to y x 1 and passes through (, 8).. Are the following pairs of lines parallel, perpendicular, or neither? 1 y x 6 a. 4 y 4x 6 a. b. c. y x 5 y x 7 y x 5 y x 1 b. c.

10 4. A consumer group is studying how hospitals are staffed. Here are the results from eight randomly selected hospitals in a state. Hospital Beds Full-Time Employees Full-Time Hospital Employees a. Make a scatter plot of the data on separate graph paper. b. Draw a line of best fit and determine the equation for that line. 4b. c. Use your model to predict the number of beds in a 4c. hospital with 80 full-time employees. d. Use the linear regression feature of your calculator to find the equation of the best fitting line for the data. 4d. e. What is the correlation coefficient? Explain what it means. 4e. 5. Given the function f ( x) x 1 : a. State the direction of opening. 5a. b. State the coordinates of the vertex of the absolute value graph. 5b. c. Write the equation for the axis of symmetry. 5c. d. Complete a table of values: x y e. Sketch the graph. Good Luck. Remember this is the bonus for your midterm as well as a homework grade. This is due on the day of your exam, currently slated for the week of, January 0 th. This will change if we have a snow day.