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Do Now Solve the system by SUBSTITUTION y = 2x - 7 2x + y = 1 (2, -3)

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Presentation on theme: "Do Now Solve the system by SUBSTITUTION y = 2x - 7 2x + y = 1 (2, -3)"— Presentation transcript:

1 Do Now Solve the system by SUBSTITUTION y = 2x - 7 2x + y = 1 (2, -3)

2 Algebra 1 Released EOC Test Review

3 Objective SWBAT review concepts and questions from Algebra 1 Released EOC.

4 Problem 1

5

6 Based on the given data the y-intercept is 5 and the rate of change (slope) is 2/3, so based on the answer choices choice B would be correct.

7 Problem 2

8 Looking at the graph we Can generate the equation Y ≤ -2x + 5; however the Answer choices are written In words where they are in standard form 2x + y ≤ 5 and the only Answer choice that models This equation is Choice C.

9 Problem 3

10 Based on the difference of squares rule, factoring the expression you will get: (t+6)(t-6) Which is answer choice B.

11 Problem 4

12

13 Based on the equation we can find the vertex by using the equation x = -b/2a so substituting the values in we get: x = -(-8)/2(4) = 1. We then will substitute x into the equation f(x) = 4x 2 – 8x + 7. So f(1) = 4(1) 2 – 8(1) + 7 = 3. So our vertex is (1,3).Knowing this we can now eliminate choices B and C. We can now look at our y Intercept which is 7 and we then can eliminate choice A. So our answer is D.

14 Problem w + 2 w + 2 To find the area of the rectangle we use the Formula L∙W = (4+w+2)(w+2) = (w+6)(w + 2). Factoring this expression we get: N = w 2 + 8w+12 So choice D is our answer

15 Problem 6

16 Shawn walks at a speed of 5 feet per second BUT he begins walking 20 seconds earlier, so An equation to represent each boys walking speed is: Shawn: d = 5t (at 20 seconds Shawn walked 100 feet) Curtis: d = 6t So solving the system through substitution we get: 6t = 5t t t = 100 So they were walking for 100 seconds when they met BUT Shawn had a 20 second lead so Shawn was walking for 120 seconds

17 Problem 7

18 For this problem we need to set up a system of equations. Let x = candy bars and Let y = drinks. So 60x + 110y = x + 90y = 270 To solve this system multiply the first equation by 2 and solve by elimination. 120x + 220y = x + 90y = y = y = 2 y is the number of drinks so we need to substitute to find x. 120x + 90(2) = x = x = 90 x = 0.75 So the cost of the candy bars was $0.75.

19 Problem 8

20 Let n = the first positive integer, so the 3 consecutive numbers are: n, n+1, n+2 Since the product of the two smaller integers is 5 less than the largest integer we will set up our equation: n(n+1) = 5(n+2)-5 To find the smallest integer we need to solve for n. n 2 + n = 5n + 10 – 5 n 2 -4n -5 = 0 (n – 5)(n + 1) = 0 n = 5 and n = -1, but since n has to be a positive integer n = 5 only makes sense.

21 Problem 9

22 To see how long it takes the object to hit the ground we need to set our equation equal to zero. 0 = -5t t (t 2 - 4t - 12) = 0 t 2 – 4t – 12 = 0 (t – 6) (t + 2) = 0 t = 6 or t = -2 Time can not be negative so at 6 seconds the object will hit the ground.

23 Problem 10 Let x = Antonio’s Age Let y = Sarah’s Age 2x + 3y = 34 y = 5x Use Substitution to find Sarah’s age 2x + 3(5x) = 34 2x + 15x = 34 17x = 34 x = 2 y = 5(2) = 10 So Sarah’s age is 10

24 Problem 11

25 When finding the value of k we need to find the difference from the graph and f(x) = 2(2) x. The y-intercept of the graph is -3 and the y intercept of f(x) = 2(2) x is 2. So the difference between 2 and -3 is -5. So the value of k is -5.

26 Problem 12 Vv f(x) = 2x + 12 f(7) = 2(7) + 12 f(7) = 26 So it costs $26 dollars to rent 7 movies. Since Makayla has $10, she now needs $16 to rent 7 movies.

27 Problem 13

28 x X + 3X + 3 X + 6 Using the Pythagorean Theorem we get: x 2 + (x+3) 2 = (x+6)2 x 2 + x 2 +6x+9 = x 2 +12x+ 36 2x 2 +6x+9 = x 2 +12x+36 x 2 -6x -27 = 0 (x – 9)(x+3) =0 x = 9 or x = -3 So x must equal 9 because Measurement can be negative.

29 Problem 14

30 End of TurnPoints Katie’s Turns End of TurnPoints Jen’s Turns So at the end of turn 3 is when Katie’s points increase but the question said at the beginning of what turn, so at the beginning of the 4 th turn is when Katie will have more points.

31 Problem 15

32 Alex: 1 mi Sally: 3520 yd 15 min 24 min A: 1 mi ∙ 60 min1 mi = 1760 yd 15 min 1 hr2 mi = 3520 yd A: 4 miS: 2 mi = 1mi 1 hr 24 min 12 min S: 1 mi ∙ 60 min 12 min 1 hr 5 mi 1 hr So Sally walked 1mi/hr faster than Alex.

33 Problem 16 Calc ACTIVE

34 Problem 16 = 8 1/3 ∙x 2/3 ∙y 3/3 ∙z 4/3 2x 2/3 yz 4/3 So answer choice B is the correct answer

35 Problem 17

36 School Buys: 50x, where x is the candy bars Cost $30 a box to buy School Sells: 50x, where x is the candy bars Want to make $10 profit so they need to make $40. So to find out ho much each candy bar should cost we set up an equation: 50x = 40 x = 40/50 = 0.80 So each candy bar should cost $0.80 which is choice C.

37 Problem 18

38 E = mc 2 To solve for m we divide both sides by c 2 and get m = _E_ Which is choice D c 2

39 Problem 19

40 This is a quadratic function and the question is asking for the least which is the minimum value of this function. To find the minimum value we need to find the x value of the vertex, because x equals the number of years since Vertex formula: x = -b =-(-458.3) = a 2(20.8) So 11 years since 1964 is = 1975 So the year of 1975 is when the car value was at its least. So answer choice C is correct.

41 Problem 20

42 Based on Exponents Property, we will multiply our exponents and get x -1 which simplifies further to 1_. So choice B is correct. x

43 Problem 21

44 0.07 – 0.04 = – 0.07 = – 0.14 = – 0.25 = 0.24 So the average rate of change is: = Or you can find the average rate of change (slope) of (8,0.04) and (12, 0.49) 0.49 – 0.04 = 0.45 = – 8 4

45 Problem 22

46 We know the y intercept of f(x) is 5 so we need to find the y intercept of g(x) and find the difference. The rate of change of g(x) is ½ so to find the y intercept we need to find what g(x) equals when x = 0. So the table at the right shows the extension of the table where x = 0. We now see that the y intercept of g(x) is 5.5. So the difference is 5.5 – 5.0, which is 0.5 and Choice C, is the best answer.

47 Problem 23

48 y =.10x + 10 z = 0.20x So y – z is.10x + 10 – 0.20x = -0.10x + 10 Which is choice B.

49 Problem 24

50 Method one is neither constant or exponential but Method 2 is exponential because the rate of change is a product.

51 Problem 25

52 The slope of the line is 1/3. To find the slope of the 2 nd function we need To use the x and y intercepts to find the slope. x intercept: 4/3  (4/3, 0) y intercept: -2  ( 0, -2) So using the slope formula: y2 – y1 x2 – x1 We get: -2 – 0_ = _-2 _ = -2 ∙-3/4 = 3/2 0 – 4/3 -4/3 3/2 > 1/3 so answer choice B is correct.

53 Problem 26

54 The Slope is decreasing, so we can eliminate choices A and B = _18_ = _1.8_ 10,000 1,000 So answer choice D is correct.

55 Problem 27

56 K is the midpoint: (2+6, 4+8) = (4,6) 2 2 Equation of line JL: J(2,4) and L(6,8) Find the slope: 8-4/6-2 = 1 y = mx + b 4 = 1(2) + b 2 = b Equation of JL is: y = x + 2 The line perpendicular to JL Because it is perpendicular the slope of this line must be the opposite reciprocal of JL. So the opposite reciprocal of 1 is -1. Since the midpoint of K is on the line we can use the point (4,6) to find our line. y = mx + b 6 = -1(4) +b 6 = -4 + b 10 = b So our equation is y = -x + 10 which is answer choice A.

57 Do Now! In you composition Notebook Discuss your experience in Algebra 1 this year, and what would you like to see different in Geometry, Be honest!!

58 Problem 28

59 We need to use the distance formula: √(x 2 -x 1 ) 2 + (y 2 -y 1 ) 2 √(1- -1) 2 + (3- -1) 2 √(4+16) = √20 ≈ 4.47 √(1-2) 2 + (3- -3) 2 √(1+36) = √37 ≈ 6.08 √(-1-2) 2 + (-1- -3) 2 √(9+4) = √13 ≈ = Perimeter ≈14.16 Which is answer choice B.

60 Problem 29

61 Without DelawareWith Delaware Mean: downMean: 28.1 Range: 53upRange: 57

62 Problem 29 Without DelawareWith Delaware IQR: 44upIQR: 46.5 IQR: Q3 – Q1: The median of 1 st and 2 nd half 6, 9, 11, 12, 46, 54, 54, 59 Q1: 6, 9, 11, 12 The median is 9+11/2 = 10 Q3: 46, 54, 54, 59 The median 54+54/2 = 54 So Q3 – Q1 = 54 – 11 = 44

63 Problem 29 Without DelawareWith Delaware Standard Deviation To find SD subtract each value from the mean and then square that value. You then find the mean of those values and find the square root of the mean.

64 Problem 29 Without Delaware Mean: ( ) 2 = ( ) 2 = (12 – ) 2 = (11 – ) 2 = (9 – ) 2 = (54 – ) 2 = (46 – ) 2 = The mean of these values are Standard Deviation is: √ ≈ You will do the same for With Delaware.

65 Problem 30

66 Total Number The difference between Juniors and Seniors is 0.27 – 0.24 is But the college surveyed 3,500 students so we must multiply 0.03 by 3,500 which is 105 students.

67 Problem 31

68 AgeFictionNonfictionTotal Total We need to change the Relative frequency values to Actual numbers based on the 200 members in the club. So answer choice D is correct.

69 Problem 32

70 Finding the Linear Regression Model from the Calculator. (STAT  Edit(enter data) STAT  Calc  4(linReg)  Enter) We get y = 0.8x = 8/10x = 4/5x. So our slope is 4/5 which is 4 miles every 5 minutes which is answer choice D.

71 Problem 33

72 A = ½ h (b 1 + b 2 ) h = 4, b 1 = x – 3, b 2 = x+7 A = ½ 4 (x – 3) + (x + 7) A = ½ 4 (2x + 4) A = ½ 8x + 16 A = 4x + 8 So Choice B is correct.

73 Problem 34

74 Model for this scenario: Let pens = x Let pencils = y 100≤x≤240 70≤y≤170 x + y < 300 Total Profit: 1.25x+0.75y We will then make a table from this equation

75 Problem 34 Graphing all 3 inequalities on graphing calculator we get this graph:

76 Problem 34 Total Profit: 1.25x+0.75y Not possible because 70≤y≤170 And 69 is less than 70.

77 Problem 35

78 Model for Scenario: 4lbs almonds = 22 Almonds = 22/4 = 5.5 per pound Cashews = (5.50) Cashews = 8.80 per pound Combined = 8.8C+5.5(4) = 6.50 (c+4) 8.8c+5.5(4) = 6.0(c+4) =8.8c + 22 = 6.50c c = 4 C = 4/ 2.3 ≈ 1.74 total mixture is = 5.74 And the Cashew % is 1.74/5.74 ≈ 30% which is choice C

79 Problem 36

80 f(x) = g(x) 10x+5 = 7.5x x + 5 = x = 20 x = 8 Which is choice C

81 Problem 37

82 0.05x y = 0.65 (Since 0.65 is odd x must be odd also.) So our domain(x values) are 1, 3, 5, 7, 9, 11, 13 which is Choice D.

83 Problem 38

84 V(x) = (1.009) 2/3x = 107,000( /3 ) x = 107,000( ) x = 107,000( ) x  ≈ 0.60% Which is choice C.

85 Problem 39

86 When n = 0, C = 10.5 C(n) = n C(n) = 12 – n C(n) = n – 1.5 C(n) = (n – 1) Which is choice A.

87 Problem 40

88 Graph the inequalities 1.75x y ≤ 10 2x + 1y ≤ 12 0≤x≤5 0≤y≤8

89 Problem 40 Let x = Chocolate Chip Cookies Let y = Peanut Butter Cookies To maximize: 4x+2y So at 5 batches of CC and 1 batch of PB is when its at its Max. So answer choice A is correct. Choc Chip Peanut Butter Profit (4x+2y) 5 batches =8.75 flours + 10 eggs 1 batch 1.25 flour 1 egg 5(4)+1(2 ) = $22 4 batches = 7 flour + 8 eggs 2 batches 2.5 flour 2 eggs 4(4) + 2(2) = $20 3 batches =4.25 flour + 6 eggs 4 batches 5 flour 4 eggs 3(4) + 4(2) = $20

90 Problem 41

91 Year (NEXT)Trees (NOW) The sequence is being multiplied by 4 so our equation is NEXT = NOW ∙ 4 Which is choice A.

92 Problem 42

93 Model for Scenario: m = = 174 = 6 29 – 0 29 y = 6x + 4 t(n) = 6n + 4 Which is answer choice C. YearTrees 04 (y-intercept) 29178

94 Problem 43

95 This a rectangle that is not A square because all sides are Not equal so answer choice C

96 Problem 44

97 The midpoint is (10,2) So answer choice D is correct

98 Problem 45

99 Answer choice B is correct.

100 Problem 46

101 The volume is So answer choice A is correct

102 Problem 47

103 Because the SD And IQR decreased Choice C is correct

104 Problem 48

105

106 Problem 49

107

108 Problem 50 Most useful signifies the mean is the best.

109 Gooooood LUCK TRY your best Take your time Get some Rest And DON’T worry!


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