Algebra 1 Mod 1 Review Worksheet I. Graphs Consider the graph below Please do this worksheet in your notebook, not on this paper. A) For the solid line; calculate the average speed from: 1) 1:00 pm to 3:00 pm. 2) 4:30 pm to 7:00 pm For the broken line; calculate the average speed from: 1) 1:00 pm to 5:00 pm 2) 6:15 pm to 8:30 pm C) Which line shows the car that drove for the greatest period of time? D) Which line show the car that probably stopped driving first? For the three graphs below, determine which graph represents a piecewise linear function, which represents a quadratic function and which represents an exponential function. A) C)
II. Identifying Functions from data sets. For each data set below, determine if the set represents a linear, quadratic or exponential function. Explain how you know. A) y 11 13 17 23 31 y 2 8 26 80 242 C) y 4 0-4 - 8-12 III. Polynomials A) classify the following polynomials by both degree (linear, quadratic, cubic, quartic or number) and number of terms (monomial, binomial, trinomial or polynomial) i) 5x 4 ii) - 3x 2 + x iii) 7x 6 3x 2 1 iv) 6 + 4x 2-11x 3 + 9x Perform the indicated operations with the given polynomials. i) (8x 2 3x + 2) + (3x 2x 2 + 9) ii) 2(4x 8 3x 5 + 4x) (9x 6x 5 + x 6 ) iii)!"#!!!!!!!"#!!"!!"! iv) (4x 5y + 6z)3 (6x + 7y 3z)2 v) (3x 2 5x)(2x 4 6x 3 + x) vi) (x - 1) 3 vii) (x - 1) (x 10 + x 9 + x 8 + x 7 + x 6 + x 5 + x 4 + x 3 + x 2 + x + 1) viii) (4x 5)(3x + 7) ix) (2x 3) 2 C) Find the area of the rectangle with sides of 3x + 2 cms and 5x 1 cms. Draw the picture. D) Find the volume of the rectangular prism with a length of 2x + 1 in. width of x + 2 in. and height of x 1 in. Draw the picture. IV. Number Systems A) True or False if false state a counter example that shows the statement to be false. 1) All whole numbers are natural numbers. 2) All natural numbers are rational. 3) All integers are whole numbers. 4) All irrational numbers are real numbers. Name two different ways to express an irrational number. C) From the list of the following numbers, circle the irrational numbers and underline the rational numbers. 1 8.23 0-55 12 π 22 16 0!! ½ 9.121314 8.314 5. 23 1.328 D) Consider the irrational number 5, perform the indicated operation and determine if you answer is rational or irrational i) 5 + 5 2) 5 * 5 3) 5-5 4) 5 5 E) Now attempt to use all four operations (+ - * and ) with the irrational numbers 3 and 7. Explain what happens in each case.
V) Use the Pythagorean Theorem to find the shortest distance between points. A) Stan drives 12 miles north, turns east and drive for 12 more miles. What is the shortest distance from Stan to his starting point? Debbie walks from her house, seven blocks west, turns north and walks an additional five blocks. If Debbie is to walk the shortest possible distance to her house, how far will she walk? VI) Commutative, Associative and Distributive Properties A) Identify which property is being used, for the commutative and associative properties, be sure to indicate if the property is of addition or of multiplication. i) 3x(2x 6x 2 ) = 6x 2 18x 3 ii) 3x(2y*4z) = (3x*2y)4z iii) (6x y + 2z) = 6x + y 2z iv) 7*x *3*x = 7*3*x*x v) 4 + (3 + 2) = (3+2) +4 vi) 13 + (12 + 11) = (13 + 12) + 11 Fill in the missing parts of the proof: Prove that (2x + 3(y+2)) + 5z = 6 + (3y + 5z +2x) Statements Reason 1) (2x + 3(y+2)) + 5z Given 2) (2x + 3y + 6) + 5z 2) 3) (2x + 6 + 3y) + 5z 3) 4) 2x + (6 + 3y + 5z) 4) 5) (6 + 3y + 5z) + 2x 5) 6) 6 + (3y + 5z + 2x) 6)
ANSWER KEY A) 1) 50 m.p.h. 1) 68.75 m.p.h. 2) 80 m.p.h. 2) 0 m.p.h. C) The dotted or broken line. D) The solid line. Graph A: Exponential Graph B: Piecewise Linear Graph C: Quadratic II. A) quadratic: the second difference is constant exponential: the differences are being multiplied by 3 C) linear: The first difference is constantly - 4 III. A) i) quartic monomial ii) quadratic binomial iii) degree 6 trinomial iv) cubic polynomial i) 6x 2 + 11 ii) 8x 8 x 6 - x iii) 1 iv) 6x 22y + 12z v) 6x 6-28x 5 +30x 4 +3x 3-5x 2 vi) x 3-3x 2 +3x- 1 vii) x 11-1 viii) 12x 2 +13x- 35 ix) 4x 2-12x + 9 C)15x 2 +7x- 2 cms 2 D) 2x 3 +3x 2-3x- 2 IV) A) 1) false, 0 is W but not a N 2) true 3) false, there are an infinite number of negative Z that are not W b/c whole numbers do not include negative 4) true 1) i) as a decimal with three dots after it, for example 4.123124 ii) the square root of a non- perfect square, for example 13 C) irrational numbers rational numbers 8.23 12 π 9.121214 0-55 22 16 0!! 8.314 5.23 1.328!! D) i) 2 5 I (Irrational) ii) 5 Q (Rational) iii) 0 Q iv) 1 Q E) i) 3 + 7 = 3 + 7 they are not like terms I ii) 21 I iii) 3-7 = 3-7 they are not like terms I iv)!"! I don t expect you to know this yet. This is also an I (irrational Number) V) Pythagorean Theorem A) approximately 16.97 miles approximately 8.60 blocks VI) Commutative, Associative and Distributive Properties A) i) distributive property
ii) associative property of * iii) distributive property iv) commutative property of * v) commutative property of + vi) associative property of + PROOF Reasons 2) distributive property 3) Commutative Property of + 4) Associative Property of + 5) Commutative Property of + 6) Associative Property of +