* Your assessment is very important for improving the workof artificial intelligence, which forms the content of this project
Download CP Algebra / Honors Algebra
Survey
Document related concepts
Location arithmetic wikipedia , lookup
Georg Cantor's first set theory article wikipedia , lookup
Foundations of mathematics wikipedia , lookup
Large numbers wikipedia , lookup
Fundamental theorem of algebra wikipedia , lookup
Proofs of Fermat's little theorem wikipedia , lookup
System of polynomial equations wikipedia , lookup
Real number wikipedia , lookup
Mathematics of radio engineering wikipedia , lookup
History of algebra wikipedia , lookup
Transcript
2013-2014 Algebra 1 Summer Math Packet Dear Students and Parents: The purpose of this packet is to review pre-algebra concepts as you look forward to Algebra 1 next year. All concepts in this packet have been previously covered in Pre-Algebra. Following the review of this packet, there will be an assessment on these skills in the first couple weeks when you return in September. Please use this summer to assure all pre-requisite concepts have been understood. You will have access to the online Holt series through summer, if needed. Show all your work for each problem. Have a wonderful summer! Ms. Weil [email protected] Order of Operations 1) 2 2) 5 – (12 ÷ 2 x 3) ÷ 9 + 15 (18 − 9) 0 +15 3•12 − 6 • 4 3) 3 4[3 – 5(8 – 6)] ÷ 2 + 11 Adding/Subtracting/Multiplying/Dividing Positive and Negative Numbers 4) 5 – 3 + 12 – (-9) 5) 7) -4 + -9 – 3(-6) 8) −4 ⎛ 3 ⎞ ⎜ ⎟ ⎝ 4 ⎠ 1 7 2 − 3 9 6) (−2)(4) − (−5)(−1) 9) ⎛ 2 ⎞ ⎛ 5 ⎞ ⎜ ⎟ ÷ ⎜ 1 ⎟ ⎝ 3 ⎠ ⎝ 9 ⎠ 1 Evaluating Expressions 10) 12) 7b – 2a, when a = -3 and b = 4 11) 2r + 7 , when r = 12 and t = 3 t 3x2 + 5x + 1, when x = -2 13) (3x)2 – 7y2, when x = 3 and y = -2 Solving Equations Check: 3b + 2 = 6(3 – b) 3b + 2 = 18 – 6b -2 -2 3b = 16 – 6b +6b + 6b 9b = 16 9 9 16 b= 9 16) 22 − 6x ≤ −63− x 19) 2a 2 = 7 3 16 16 ) + 2 = 6(3 – ( ))? 9 9 16 11 + 2 = 6( ) 3 9 16 6 22 + = 3 3 3 22 22 = ✓ 3 3 Does 3( 17) Here is an example: The check is a required step Solve the equation & inequalities. Include a check. 1 15) d +2=3 4 5(g − 7) + 2"# g − 3(g − 5)$% = 0 3 18) 1− (v + 2) = −5 4 20) 7x + 6 ≤ 14(x – 4) 2 Properties of Real Numbers Match each equation on the left with the property it illustrates on the right. 21) 4 + (9 + 6) = (4 + 9) + 6 A. Identity Property of Addition 22) x + 12 = 12 + x B. Associative Property 23) (3 + y) + 0 = 3 + y C. Distributive Property 24) x 1 = x D. Identity Property of Multiplication 25) 5(x + y) = 5x + 5y E. Commutative Property Classification of Real Numbers 26) Explain the difference between a rational and an irrational number. 27) Classify the following numbers as rational or irrational. a) ½ b) 8 c) 6 d) 16 e) π 28) List the set of all natural numbers. 29) List the set of whole numbers less than 4. 30) List the set of integers such that –3 < x < 5. 31) Classify the following numbers as real, rational, irrational, natural, whole and/or integer. (A number may belong to more than one set) a) –3 c) 3 b) 4 2 3 d) 0 True or False? 32) All whole numbers are rational numbers. 33) All integers are irrational numbers. 3 34) All natural numbers are integers Properties of Exponents 35) 38) d7 • d9 = 5 6 4 ( −c h ) = 36) x 2 e • x8 e = 39) 417 = 414 Monomials and Polynomials 41) What the difference between. a monomial and polynomial? 43) (3p2 - 2p + 3) - (p2 - 7p + 7) 42) 44) 37) (7q ) (12q r ) = 40) ⎛ −4s 6 ⎞ ⎜ 3 5 ⎟ = ⎝ t r ⎠ 5 3 5 3 (d2 - d + 5) - (-d2 + d + 5) (x3 - 3x2y + 4xy2 + y3) - (7x3 - 9x2y + xy2 + y3) 2x - 2 3x -10 45) Find the length of each side of the triangle if the perimeter is 33 cm. 3x + 5 Slope and Linear Equations 45) Find the slope of the line through the given points. a) (-1, 2) and (-5,10) b) (-7, 10 ) and (1, 10) 47) Rewrite 3y = 2x – 7 in slope-intercept form. Identify the slope and y-intercept. 4 Translating Expressions and Equations Set up an algebraic expression or equation to represent each verbal expression. DO NOT SOLVE. Example: 18 less than the quotient of a number and 3. à let n = a number ; n − 18 3 48) The sum of six times a number and 25 49) 7 less than fifteen times a number 50) Four times the square of a number increased by five times the same number 51) The sum of a number and 23 is 78. 52) The sides of a rectangle are a number and 4 less than that same numbers. The perimeter is 56 meters. 53) If a number is decreased by 6, and the result is multiplied by 3, then the answer is 15. Find the unknown number. Consecutive Number Problems Include a let statements and checks for each problem. 54) The sum of two consecutive integers is 61. 55) The sum of three consecutive even integers is 156. 56) Find two consecutive odd whole numbers whose sum is 2 less than 6 times the first number. 5 Miscellaneous Word Problems Write an equation to mode each word problem. Include let statements and checks for each problem. 57) Joelle had $24 to spend on seven pencils. After buying them she had $10. How much did each pencil cost? Example: Let x = cost per pencil 7x + 10 = 24 -10 -10 7x = 14 7 7 x=2 58) Sarah already has 45 stamps in her collection, and she gets 7 new stamps each month. How long will it take before she has 129 stamps in her collection? Check: Does 7(2) + 10 = 24? 14 + 10 = 24 24 = 24 ✓ Each pencil cost 2 dollars. 59) The perimeter of a trapezoid is 90 cm. The parallel bases are 24 cm and 38 cm long. The lengths of the other two sides are consecutive odd integers. What are the lengths of these other two sides? 60) Lynn took a cab from her office to the airport. She had to pay a flat fee of $2.05 plus $0.90 per mile. The total cost was $5.65. How many miles was the taxi trip? 61) Luke has $5 more than Sam. Together they have $73. How much money does each have? 62) The length of a rectangle is 3 inches more than the width. Find the length and width if the perimeter of the rectangle is 98 in. 64) A ladder is leaning against the side of a 10m house. If the base of the ladder is 3m away from the house, how tall is the ladder? Round your answer to the nearest hundredth. Please draw a diagram and show all work. 6 67) In any triangle the sum of the measures of the angles is 180 degrees. In Triangle ABC, ∠ A is twice as large as ∠B. ∠B is 4 degrees larger than ∠C. Find the measure of each angle. 69) Four times a number increased by 25, is 13 less than 6 times the number. Find the number. 68) The sum of 38 and twice a number is 124. Find the number. 70) 15% of what number is 12? (Set up a proportion). Put an X on in the box where you think you belong: I was not at all confident completing this packet in my own. I found this packet to be extremely easy to complete on my own. Here are some websites you might find useful in completing your summer assignment. 1. 2. 3. 4. 5. 6. 7. 8. 9. 9. 10. my.hrw.com (use your 7th grade log-in) http://www.regentsprep.org – use the Math A site http://www.math.com – use both Algebra and Pre-Algebra http:// library.thinkqest.org http://www.mathgoodies.com/lessons/toc_vol5.html – http://www.teacherschoice.com.au/Maths_Library/Algebra/Alg_1.htm http://education.jlab.org/solquiz http://w3.fiu.edu/math/cine_math/fast/pie.htm -- solving equations http://www.algebrahelp.com/worksheets/ http://www.math.com/homeworkhelp/Algebra.html http://www.math.com/homeworkhelp/PreAlgebra.htm My child completed this packet over the summer and will be ready to submit it by the end of the first week back to school in September. 7 Parent Signature _______________________________ 8