JAMES WOOD HIGH SCHOOL 161 Apple Pie Ridge Road Winchester, VA (540) FAX (540)
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1 JAMES WOOD HIGH SCHOOL 161 Apple Pie Ridge Road Winchester, VA (540) FAX (540) Summer Math Packet Ms. K. Hill Honors Algebra Name N School o Welcome to Honors Algebra, May 4, 017 This is the summer math packet if you are entering Honors Algebra net year. Even if you register within two weeks of school at the beginning of the school year, you are responsible for these concepts before school starts in August. You can ask the guidance counselor for a packet. If you are entering Honors Algebra then you have been successful in Algebra 1 and Honors Geometry. This summer assignment will help you refresh your memory and allow us to jump right into math when school begins for the school year. If you have trouble working the problems, then I suggest looking at online resources, or asking a friend or parent for help. An older sibling might be able to assist you. Problems in this packet should be familiar and cover BASIC skills that you will need in order to help you achieve success in Honors Algebra. Top Online Resources: U-tube videos on the specific algebra topics are also very helpful This packet will be collected from each student the 1 st day back in August (16 th or 17 th ) and ALL WORK MUST BE SHOWN with each problem (as appropriate). The grade on this summer packet will count as a QUIZ GRADE. I will deduct 10 points for each day late. If not completed, then the grade will be a zero. I encourage you to join my Honors Algebra Google classroom (CODE: 991sg ). This packet is posted on that site in case you misplace your copy. Enjoy your summer and I look forward to meeting you in the fall! Kelly L. Hill James Wood High School Mathematics Department
2 A. Simplifying Polynomial Epressions I. Combining Like Terms - You can add or subtract terms that are considered like, or terms that have the same variable(s) with the same eponents E. 1 E. 5 7y y y + 3y 15 4y 8h 10h 1h 15h h 15h 8h 1h 3 5h 0h 3 3 As you write your final answer, the polynomial must be written with the highest degree on the first term and then each degree after that in descending order. II. Applying the Distributive Property - Every term inside the parentheses is multiplied by the term outside of the parentheses. Be careful if the term on the outside has a minus sign you must distribute the number as a negative. E. 1 3(9 4) E (5 6 ) III. Combining Like Terms and the Distributive Property - Sometimes problems will require you to distribute AND combine terms E. 1-3(4 ) + 13 E. 3(1 5 ) 9( ) -3 4 (-3) (-7)
3 PRACTICE SET 1 Simplify y y. 14y + 15y + 3y 3. 5n (3 4n) 4. -(11b 3) 5. 10q(16r + 11) 6. (5 6 ) 7. 3(18z 4w) + (10z + 6w) 8. (8c 3 ) + 1(4c 10) 9. (3a + 6) (4 + a ) 10. ( ) + ( ) 11. (8k + k 6) (-10k + 7 k ) 1. (13v 6v 4 + 8v ) ( v + 9v 7 )
4 B. Solving Equations I. Solving Two-Step Equations A couple of hints: 1. To solve an equation, UNDO the order of operations (PEMDAS) by working in the reverse order.. REMEMBER Addition if undone by subtraction, and vice versa. Multiplication is undone by division, and vice versa. 3. To remove a fraction in front of the variable, mulitply both sides of the equation by its reciprocal. E. 1 4 = 30 E. 87 = = 3 66 = = 8-6 = E Please know how to multiply by the reciprocal in order to isolate the variable as you perform your final step II. Solving Equations with variables on both sides or equations containing parentheses - When solving equations with variables on both sides of the equals sign, be sure to get all terms with variables on the SAME SIDE and all terms without variables on the opposite side. E = E. 5 5(4 7) = = = = = 4 0 = = 6 10 = = 8
5 PRACTICE SET Solve = = (3 4 ) = 19 there are ways 4. 8(3 4 ) = 19 this problem can be solved show both ways = 4(1 9 ) = = -(3 8 ) 8. (1 6 ) =
6 C. Solving and Graphing Inequalities When asked to solve an inequality the steps resemble solving an equation. - You are to isolate for the given variable using inverse operations - If you divide or multiply (at any step in the process usually the last step) and the term is negative, then you must flip the inequality sign - When graphing on a number line: <, > use an open dot <, > use a closed dot E. 1 Solve and Graph: E. Solve and Graph: PRACTICE SET 3 Solve and Graph each of the following on a number line or and 0
7 D. Solving Literal Equations - A literal equation is an equation that contains more than one variable - You can solve a literal equation for one of the variables by isolating that specific variable on one side of the equation - this is called solving for a variable. E. 1 3y = 18 Solve for E. 5a 10b = 0 Solve for a 3y = 18 5a 10b = 0 3y 3y + 10b +10b = 6 5a = b y a = 4 + b PRACTICE SET 4 Solve each equation for the specified variable. 1. Y + V = W, solve for V. 9wr = 81, solve for w 3. d 3f = 9, solve for f 4. d + t = 10, solve for 5. P = (g 9)180, solve for g y 6h = 10y, solve for n, solve for p 8. ml m = B, solve for m p
8 I. Reviewing the Distributive Property E. Binomial Multiplication - The distributive property is used when you want to multiply a single term by throughout an epression E. 1 8(5 + 9) II. Multiplying Binomials the FOIL Method - When multiplying two binomials (an epression with two terms), we use the FOIL method. This method uses the distributive property twice. - FOIL is the order in which you will multiply the terms F first terms of each binomial O the outer terms of the problem I the inner terms of the problem L the last terms of each binomial E. 1 ( + 6)(3 + 10) FIRST LAST First: 3 3 ( + 6)(3 + 10) Outer: INNER OUTER Inner: Last:
9 PRACTICE SET 5 Multiply. Be sure to simplify like terms as you write your final answer. 1. ( 5)( 9). ( 7)( 1) 3. (4 3)( 1) 4. ( 6)(3 5) 5. ( 1)(7 3) 6. ( 5) ( 5)( 5) 7. (3 7) 8. ( 5 y)(7 6 y) - When asked to multiply polynomials having more than terms, the FOIL method does not work. Some students will set up a chart in order to multiply the terms. E. ( 3)( 5 4) = = ( 5)( 7 8) 10. ( 4)(3 1)
10 F. Rules of Eponents Multiply common bases: a b a b (3 y )(4 y ) 34 y 1 y Division of common bases: Power to a power: ( ) a b a b ab ab 5 5 4m f 4 m f m f 3 m f m f ( abc) ( ) a b c 8ab c Negative power: Power of Zero: 0 a ; a a a 1 1 1e a a e y 5(1) y 5y ; 1e 5 3 PRACTICE SET 6 Simplify each epression ( c )( c)( c ). m m ( k ) 4. 0 d ( p q )( p q ) 6. 45y z 8 5yz fg m 9. 1ab 36ab c ( 5 ab)( abc)( 3 b) ( y ) b c
11 G. Factoring Polynomials I. Using the Greatest Common Factor (GCF) to factor - Always determine whether there is a GCF before starting any other factoring pattern E * in this eample the GCF is * divide each term by = 3 ( 11 30) GCF remaining trinomial 3 * Now, we must determine if the remaining polynomial in the parentheses is factorable. Can this trinomial be factored into two binomials? In order to determine this you can make a list of all the factors of Since the factors -5-6 = 30 AND = -11, we will choose these factors to help us create the binomial factors. 3 ( 11 30) 3 ( 5)( 6) II. Difference of Two Perfect Squares Pattern - This pattern will ONLY work with a subtraction sign and perfect squares. a b ( a b)( a b) * some students call this the square root pattern since you E. 1 take the square root of both terms ( 5)( 5)
12 PRACTICE SET 7 Factor each epression a b ab ab c n 8n g 9g 0 6. d 3d 8 7. z 7z m 18m
13 H. Radicals and the Quadratic Formula I. Simplifying Radical Epressions - To simplify a radical term, you need to find the Greatest Perfect Square of the number under the radical sign (the radicand) and then take the square root of this number. - There is a way to use factor trees in order to simplify. You can research this on the web for more instruction. List of perfect squares: 1, 4, 9, 16, 5, 36, 49, 64, 81, 100, 11, E E E BE CAREFUL WITH THIS ONE OR 16 3 MUST USE THIS PAIR 4 3 PRACTICE SET 8 Simplify the given radical epressions mn a b c H (continued) II. The Quadratic Formula - Need standard form: a b c 0 - The quadratic formula is used to solve quadratic equations where factoring is not an option. The quadratic formula will leave your answer in radical form and you MUST simplify the radical whenever possible. The Quadratic Formula: 4 int : ( ) b b ac a, where a 0 h b is always a positivevalue it helps to replace the values inside
14 E. 1 Solve: a, b 5, c 6 (5) (5) 4()( 6) () You may leave your answer in this form, you will not be epected to write it as separate answers, ie , 4 4 E. Solve: , 1, 8 a b c (1) 6 7 ( 1) ( 1) 4(1)(8) You must simplify: PRACTICE SET 9 Use the quadratic formula to solve each of the given quadratic equations. Be sure that each equation is in the proper form: a b c b 4b On the last page, solve the given quadratics for each bo where a quadratic equation is given. Use the strategy listed in the bo.
15 The Graphing Method The Quadratic Formula Ways for Solving a Quadratic Equation containing Real Roots (Zeros) Square Root Method 36 Factoring 7 0 Completing The Square
16
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