Algebra 2 Summer Recommendations

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1 Algebra Summer Recommendations Book section 0.1 Representing Functions Terminolog Quadrants, Relations, Functions, Domain, Range, Mapping 1. State the domain and range of each relation in set notation. Determine whether the relation is a function, circle es or no. a) b) c) D: D: D: R: R: R: Function: Yes No Function: Yes No Function: Yes No. Name the quadrant in which each point is located. a) (, ) b) (, - ) c) ( -7, -1 ) d) (, 0 ) Book Section 0. FOIL Terminolog FOIL (First, Inner, Outer, Last). Find each product using FOIL. Combine like terms to simplif. a) ( )( 7) b) ( )( ) c) ( 7)( 11). Monica s current office is square with each side being units. a. Find the area of her office in terms of b. If her new office will be feet wider and feet longer, in terms of the new dimensions will be: Width Length c. Use FOIL to multipl and simplif the epression for the her new office dimensions. d. If her current office is 7ft b 7ft, how much LARGER will her new office be (in sq. ft)

2 Book Section Epressions and Formulas Terminolog Variables, Epressions, Order of Operations. Formula. Evaluate each epression if =, = -, and z = z a) ( z) b) ( z ) ( F ). The formula C represents the temperature conversion from Farenheit to Celsius. 9 a. Find the Celsius temperature corresponding to 7 0 F. (nearest tenth) b. Find the Farenheit temperature corresponding to 0 C. Book Section 1. Properties of Real Numbers Terminolog Groups of Numbers (Natural,Whole,Integers,Rational,Irrational,Real) Properties Commutative, Associative, Distributive, Identit, Inverse, Closure 7. Name the sets of numbers to which each number belongs a) b) 0 c) 11 d) 7 1. Simplif the epression: ( 9) ( 1) 9. Find the additive AND multiplicative inverse of each number: a) 1. 1 b) 0. Book Section 1. Solving Equations (1 variable) Terminolog Equation (vs. epression), Solution, Order of Operations BACKWARDS 10. Solve each equation for. 1 a) 1 7 b) (1 0) (1 1) 11. Solve each formula for the specified variable. a) a b c Solve for a. b) a b z Solve for.

3 Book Section 1. Solving Absolute Value Equations (1 variable) Terminolog Etraneous Solutions 1. Evaluate each epression if = -, =, and z = - a) z b) z 1. Solve each equation. Check our solutions. a) 0 b) Book section 1. Solving Inequalities Important point When to reverse the inequalit smbol. 1. Solve each inequalit AND graph the solution set on a number line. 9 a) 0 b) 1 c) 1 1. Write AND solve an inequalit using as for the following sentence. The difference of times a number and is greater than the number. Book section 1. Compound Inequalities and Absolute Value Inequalities Terminolog Compound Inequalit. Important Distinction: And vs. Or 1. Solve each compound inequalit and graph its solution set on a number line. a) 7 or b) ( ) and 1 c) Solve each absolute value inequalit and graph the solution set on a number line a) 10 c) b) d) Write absolute value inequalities for each number line shown. a) b)

Book section.1 Relations and Functions Terminolog Discrete vs. Continuous relation. Vertical line test. One to one functions, Independent vs. Dependent Variables. 19.

a) b) c) d) 0. Use the given functions to find each value. f ( ) g( ) a) f ( ) b) g (1) c) f () g() Book Section.

4 Book section.1 Relations and Functions Terminolog Discrete vs. Continuous relation. Vertical line test. One to one functions, Independent vs. Dependent Variables. 19. For each graph below, state the domain and range of the relation. THEN, determine whether or not the relation is a function. If it is, determine if it is a one to one function. a) b) c) d) 0. Use the given functions to find each value. f ( ) g( ) a) f ( ) b) g (1) c) f () g() Book Section. Linear Relations and Functions Terminolog Linear Function, Standard Form, X and Y intercepts 1. Is each equation a linear function? Yes or No? a) b) 0 c) 7 d) 10 e) 10. Write each equation in standard form. Find the and intercepts and graph. 1 a) b) 1 1

m ( -, ) ( -, r ) Book section. Writing Linear Equations Terminolog Slope Intercept Form, Point-slope form, Parallel, Perpendicular.

5 Book section. Rate of Change and Slope. Terminolog Rate of change, slope. Determine the rate of change of each equation (the slope) a) 0 b) 1. Find the slope of the line that passes through the two given points. a) ( -, 1 ) ( -, - ) b) (, - ) ( 1, -7 ). Find the value of r so that a line with the given slope passes through both points. m ( -, ) ( -, r ) Book section. Writing Linear Equations Terminolog Slope Intercept Form, Point-slope form, Parallel, Perpendicular. Write an equation in slope intercept form for a line that has the given characteristics. a) m passes through the point (1,) b) passes through the two points (, -1) and (, 1) c) passes through ( -, ) and is parallel to d) passes through (, -1 ) and is perpendicular to 1 e) passes through ( 9, - ) and is vertical f) passes through ( -, 7 ) and is horizontal 7. Write an equation in slope intercept form for each of the graphs below. a) b)

6 Book Section.1 Solving Sstems of Equations Terminolog Consistent, Inconsistent, Independent, Dependent, Substitution, Elimination. Describe each sstem as Independent, Dependent, or Inconsistent a) b) 10 c) Solve each sstem using substitution a) b) 9 d c d c 0. Solve each sstem using elimination a) z w z w b) 1 b a b a 1. Solve each sstem b graphing each equation and finding the intersection. a) b)

C) x m A) 260 sq. m B) 26 sq. m C) 40 sq. m D) 364 sq. m. 7) x x - (6x + 24) = -4 A) 0 B) all real numbers C) 4 D) no solution

C) x m A) 260 sq. m B) 26 sq. m C) 40 sq. m D) 364 sq. m. 7) x x - (6x + 24) = -4 A) 0 B) all real numbers C) 4 D) no solution Sample Departmental Final - Math 46 Perform the indicated operation. Simplif if possible. 1) 7 - - 2-2 + 3 2 - A) + - 2 B) - + 4-2 C) + 4-2 D) - + - 2 Solve the problem. 2) The sum of a number and its