3 - A.REI.C.6, F.BF.A.1a, F.BF.A.1b 15 CR 7 A.REI.C.6, A.CED.A.3,

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1 SEMESTER EXAMS SEMESTER # Question Type Unit Common Core State DOK Key Standard(s) Level 1 MC 7 A.REI.C.6 D MC 7 A.REI.C.6 B 3 MC 7 A.SSE.A. C 4 MC 7 A.REI.C.6 1 D 5 MC 7 F.BF.A.1a D 6 MC 7 A.REI.C.6 B 7 MC 7 A.REI.C.6 1 B 8 CR 7 A.REI.C.5, A.REI.C CR 7 A.CED.A., A.REI.D CR 7 A.REI.C.6-11 MC 7 A.REI.C.6 D 1 MC 7 A.REI.C.6 D 13 MC 7 A.CED.A.3 A 14 ER 7 N.Q.A., A.CED.A.3, 3 - A.REI.C.6, F.BF.A.1a, F.BF.A.1b 15 CR 7 A.REI.C.6, A.CED.A.3, - A.REI.D.1 16 MC 7 A.CED.A.3, A.REI.D.1 1 C 17 MC 8 N.RN.A. 1 D 18 MC 8 F.IF.7e C 19 MC 8 F.BF.3, F.IF.4 1 B 0 MTF 8 F.IF.4 1 A 1 MTF 8 F.IF.4 1 B MTF 8 F.IF.4 1 A 3 MC 8 F.IF.7e D 4 MTF 8 F.LE.5 1 A 5 MTF 8 F.LE.5 1 B 6 MC 8 F.BF.3 C 7 MC 8 F.IF.6 B 8 MTF 8 F.IF.8b 1 A 9 MTF 8 A.SSE.3c 1 A 30 MTF 8 A.SSE.3c 1 B 31 MC 8 F.LE.1 D 3 MC 8 F.LE. 1 A 33 FR 8 N.RN.A.1, N.RE.A CR 8 A.SSE MC 8 F.BF.1a A 36 MC 8 F.BF. B 37 TF 8 N.RN.3 1 B 38 TF 8 N.RN.3 1 A 39 CR 8 N.RN TF 8 N.RN.3 1 B 41 CR 8 N.RN.3 4 CR 8 N.RN., N.RN MC 8 N.RN. 1 B 44 MC 8 N.RN. 1 C 45 MC 8 N.RN. 1 A

2 SEMESTER EXAMS SEMESTER 46 MC 8 N.RN. 1 D 47 MC 8 N.RN. 1 B 48 MC 8 N.RN. 1 A 49 MC 8 N.RN. 1 A 50 MC 8 N.RN. 1 C 51 MC 8 N.RN.A. 1 C 5 MC 8 N.RN.A.1 1 B 53 MC 11 A.REI.4b C 54 TF 11 A.SSE. 1 A 55 TF 11 A.SSE. 1 A 56 MC 11 A.CED.4 C 57 MC 11 A.REI.4b D 58 MC 11 A.REI.4b 1 A 59 MC 11 A.REI.4b A 60 CR 11 A.REI.4b 61 MC 11 A.CED.1 D 6 MC 9 A.APR.1 1 A 63 MC 9 A.APR.1 A 64 MC 9 A.APR.1 1 D 65 TF 9 A.APR.1 1 A 66 TF 9 A.APR.1 1 B 67 TF 9 A.APR.1 1 A 68 CR 9 A.APR.1 69 MC 9 A.APR.1 1 D 70 MC 9 A.SSE. 1 C 71 MC 9 A.SSE.3 D 7 MC 9 A.APR.1 1 C 73 MC 9 A.APR.1 1 B 74 CR 9 A.APR.1 75 CR 9 A.APR.1 76 MC 9 A.SSE. 1 B 77 TF 9 A.SSE. 1 A 78 TF 9 A.SSE. 1 A 79 TF 9 A.SSE. 1 B 80 MC 9 A.SSE.3a B 81 MC 9 A.SSE.3a A 8 MC 9 A.SSE.3a C 83 MC 9 A.SSE.3a A 84 MC 9 A.SSE.3a A 85 MC 9 A.SSE.3a A 86 MC 9 A.SSE.3a D 87 MC 9 A.SSE.3b 1 D 88 TF 11 A.SSE.3a B 89 TF 11 A.SSE.3a A 90 TF 11 A.SSE.3a B 91 MC 9 A.SSE.3a 1 A 9 MC 11 A.SSE.3a D 93 MC 11 A.SSE.3a 1 A 94 MC 11 A.REI.4b 1 B 95 MC 11 A.REI.4b B

3 SEMESTER EXAMS SEMESTER 96 MC 11 A.REI.4b A 97 MC 9 A.SSE.3a D 98 MC 11 A.REI.4a A 99 MC 11 A.REI.4a B 100 CR 11 A.REI.4b 101 MC 11 A.CED.1 B 10 TF 11 A.REI.4b A 103 MC 11 A.REI.4b A 104 MC 11 A.REI.4b B 105 MC 11 A.REI.4b D 106 CR 11 A.SSE.3a 107 CR 11 A.APR.1, A.SSE MC 11 A.REI.11 B 109 CR 11 A.REI.4b, A.REI.3b, F.IF.8a 110 TF 11 A.REI.4b B 111 MC 11 A.REI.4b D 11 MC 11 A.REI.4b C 113 MC 11 A.REI.4b C 114 MC 11 A.REI.4b C 115 TF 11 A.CED.1 A 116 TF 11 A.CED.1 B 117 CR 11 A.CED CR 11 A.REI.4b, F.IF.8a 119 CR A.CED.1, A.APR.1, A.REI.4b, 11 N.Q.1 10 CR F.BF.1, A.REI.4b, N.Q.1, N.Q., 11 N.Q.3 11 TF 11 F.IF.4 1 A 1 TF 11 F.IF.4 1 B 13 TF 11 F.IF.5 1 B 14 MC 11 F.IF.5 D 15 TF 11 F.IF.8a 1 A 16 TF 11 F.IF.8a 1 A 17 TF 11 F.IF.8a 1 B 18 MC 11 F.BF.4a 1 D 19 CR 11 F.BF.1b, A.REI.4b, N.Q MC 10 A.REI.4b A 131 MC 10 F.IF.4 A 13 MC 10 F.IF.5 1 A 133 MC 10 F.IF.7a 1 B 134 MC 10 F.IF.7a C 135 MC 10 F.IF.7a B 136 MC 10 F.IF.7a C 137 TF 10 F.IF.8a 1 A 138 TF 10 F.IF.8a 1 B 139 MC 10 F.IF.8a 1 B 140 MC 10 F.IF.9 B 141 CR 10 F.IF.7a, F.IF.8a, F.IF.4 14 MC 10 F.IF.8a B 143 TF 10 F.IF.8a A

4 SEMESTER EXAMS SEMESTER 144 TF 10 F.BF.3 B 145 MC 10 F.IF.9 A 146 MC 10 A.SSE.3b 1 B 147 MC 10 F.IF.8a 1 A 148 CR 10 F.IF.7a, F.IF.8a, F.IF CR 10 F.BF.1a, F.IF.8a 150 MC 10 A.SSE.1 C 151 MC 10 A.SSE.1 B 15 MC 10 F.IF.6 1 D 153 MC 10 F.IF.7a A 154 TF 10 F.BF.3 A 155 TF 10 F.BF.3 A 156 CR 10 A.SSE.3, A.REI.4b, F.IF.7a, A.REI MC 11 A.REI.7 C 158 TF 11 A.REI.11 A 159 TF 11 A.REI.11 B 160 MC 11 A.REI.11 C 161 MC 1 F.BF.B.4a C 16 MC 1 F.IF.C.7b C 163 CR 1 F.IF.C.7b MC 1 F.IF.C.7b B 165 MC 1 F.IF.C.7b B 166 MC 1 F.IF.C.7b B 167 MC 1 F.IF.C.7b C

5 SEMESTER EXAMS SEMESTER 8. This question assesses the student s ability to find the solution to a system of linear equations and explain why replacing one equation in a system with the sum of that equation and multiple of the other produces a system with the same solutions. (a) (10, 5) Students may use any method (graphing by hand, graphing using technology, substitution, elimination, guess-and-check, etc.) to get this answer. (b) When the ordered pair (10, 5) is substituted into each equation, a true statement results. Since the left side of each equation equals the right side of each equation, then the sum of the left sides ( 4x + 11y) must equal the sum of the right sides (35). The ordered pair (10, 5) must also satisfy this equation. 9. This question assesses the student s ability to identify solutions of a linear equation in two variables, create a system of inequalities with a given solution, and create a system of inequalities with no solution. (a) Answers will vary. (b) Answers will vary, but one point identified in part (a) must satisfy the equation and one must not. (c) y = x is the only acceptable answer

6 SEMESTER EXAMS SEMESTER 10. This question assesses the student s ability to build linear functions based on a contextual description, graph linear functions, identify solution to a system of linear equations, and evaluate a function in context. (a) $3 Cn $10,000 n doll $7 I n n doll (b) (c) $3 $7 $10,000 n n doll doll $4 $10,000 n doll $10,000 n $4 doll 500 dolls n (d) I1500 C1500 $10,500 $14,500 $3,000, so if the company only produced and sold 1500 dolls, they would lose $3,000.

7 Total Cost ALGEBRA I SEMESTER EXAMS SEMESTER 14. This question assesses the student s ability to create linear functions, solve systems of linear equations, and combine linear functions in context. (a) The costs for each game and allowance/savings over the specified periods are: Game months 5 months 7 months m months played Space Pilot $75 $75 $75 S(m) = $75 Puzzles of Gold $5 + $10()= $5 + $10(5) = $5 + $10(7) = P(m) = $5 + $10m $45 $75 $95 World of Cars $5() = $50 $5(5) = $15 $5(7) = $175 W(m) = $5m Least Cost? Puzzles of Gold Space Pilot Space Pilot & Puzzles of Gold Allowance/Savings A(m) = $50 + $15(m 1) or A(m) = $35 + $15m (b,c) A graph would be best to answer this part, but students may use a table or solve inequalities to justify their answer. $400 $350 $300 $50 $00 $150 $100 Allowance, A(m) Space Pilot, S(m) Puzzles of Gold, P(m) World of Cars, W(m) P(m) + S(m) $50 $ Months Played (m) Juan can afford Puzzles of Gold for the next year (and beyond) because he has enough saved to buy it and because the monthly fee is less than his allowance. Juan can afford World of Cars right away, but on the 3 rd month he will not have enough money to pay the subscription fee, since the monthly fee is greater than his allowance and he will have exhausted his savings. Juan cannot afford Space Pilot until he receives his allowance at the end of the nd month, but can afford it for as long as he wants after that because he will have saved enough money to purchase it and there is no monthly fee. Other arguments are also acceptable, such as Juan could afford World of Cars for one year (costing $300) if he saved his allowance for 18 months. (d) Because the cost of World of Cars exceeds Juan s finances after months, consider the other two games only. The combined cost of Puzzles of Gold and Space Pilot is P(m) + S(m) = $5 + $10m + $75 = $100 + $10m. Since his savings are less than the combined game prices ($50 < $100), he cannot afford them both now. However, since his allowance grows faster than the total subscription fees ($15 > $10), he will be able to eventually afford both,

8 SEMESTER EXAMS SEMESTER when A(m) P(m) + S(m), or $35 + $15m $100 + $10m. Solving, m 13. Juan must wait 13 months to afford both at the same time. Other arguments are acceptable, such as buying Puzzles of Gold now and buying another later, for example. In that case, Juan s finances would be A(m) P(m) = $10 + $5m. He would still need 13 months to save enough to buy Space Pilot for $ This question assesses the student s ability to solve application problems using systems of linear inequalities (linear programming) and interpret linear equations and inequalities in context. (a) The vertices are (0, 0), (600, 0), (0, 500), and the intersection of 1 L500 S and 4 L800 S or (360, 30). 3 (b) Income is maximized at $1,680 when 360 small and 30 large frogs are produced. Vertex Small (x $) Large (x $3) Income (0, 0) 0 0 $0 (c) It takes 1 sheet of paper to make a small frog and (600, 0) $1,00 (0, 500) $1,500 one sheet of paper to make a large frog. In this equation, (360, 30) $1,680 1 S represents the number of sheets of paper used to make small frogs and L represents the number of sheets of paper needed to make large frogs, the total of which may not exceed the 500 sheets of paper the club has.

9 SEMESTER EXAMS SEMESTER 33. This question assesses the student s ability to solve equations using properties of integer and rational exponents, and create equivalent expressions using properties of exponents. (a) x = 4 (b) n = 6 (c) t = This question assesses the student s ability to construct algebraic expressions for sequences from physical patterns and show algebraic expressions are equivalent. (a) Mark is correct because each figure is a square of n n dots plus one additional dot, or n Sofia is correct because each figure is a rectangle of n (n + 1) minus a rectangle of 1 (n 1), or nn1 n (b) Using Sofia s expression, n n1 n1 n nn1 n 1 which is Mark s expression.

10 SEMESTER EXAMS SEMESTER 39. This question assesses the student s understanding of the properties of real number system and its subsets, specifically rational and irrational numbers. (a) An irrational number is a real number that cannot be expressed as the ratio of two integers. (b) We know is rational and 3 is irrational. Assume 3 n, where n is a rational number. Then 3n. Since n and are both rational, and the rational numbers are closed under subtraction, n is also rational. That means 3 is rational. But that contradicts what was given, that 3 is irrational. Thus, 3 must be irrational. 41. This question assesses the student s understanding of the properties of real number system and its subsets, specifically rational and irrational numbers. (a) Both addends are ratios of integers, as is the sum. 4 4 (b) Radicals are rational if they are perfect squares. Only one factor is rational; the product is 1 irrational. (c) Both factors are irrational, but the product is rational. 4. This question assesses the student s understanding of the properties of real number system and its subsets, specifically rational and irrational numbers. (a) (b) (c) Let a be a rational number and b be an irrational number. Assume a + b, where n is a rational number. Then b n a. Since n and a are both rational, and the rational numbers are closed under subtraction, n a is also rational. That means b is rational. But that contradicts what was given, that b is irrational. Thus, a + b must be irrational. 60. This question assesses the student s ability to use solve a quadratic equation. (a) x 80 x 8 x 8 or x (b) x 4 0 x 4 x x x0 or x4 (c) x 3 x x 6 5 x 6 5

11 SEMESTER EXAMS SEMESTER 68. This question assesses the student s understanding that polynomials are similar to systems of numbers. (a) A polynomial is a monomial or sum of monomials. A monomial is a number, a variable, or the product of a number and one or more variables raised to whole number powers. x 3 x4 x x 7 (b) (c) The product of two polynomials is the sum of all products of all monomials between the two polynomials. The coefficients of the monomials are real numbers, and since multiplication is closed for real numbers, any coefficients must also be real numbers. Since variables in monomials must be whole number powers, which are closed under addition, and when multiplying monomials the resulting exponents are the sums of the exponents in the factors, the product must have whole number powers. When like terms are added, since real numbers are closed under addition, the resulting coefficients must also be real numbers. Hence, all terms in the resulting expression meet the definition of a monomial, and the sum of them is therefore a polynomial. 74. This question assesses the student s ability to do arithmetic with polynomials. x x x x 1.x 0.6x 0.3x x.5x x 0.3x x.5x x 0.6x x.5x 1.3.9x 1.9x.6 so a =.9, b = 1.9, and c = This question assesses the student s ability to do arithmetic with polynomials. x f x g x x 3 x 3x (a) f x h x x 3 3x x4 3x x 7 (b) x 5x (c) f x gx x 100. This question assesses the student s ability to use solve a quadratic equation. x 10x 5 81 x 5 81 x 5 9 x 59 or x 59 x14 or x 4

12 SEMESTER EXAMS SEMESTER 106. This question assesses the student s understanding of quadratic equations and the number of solutions they may have under certain circumstances. If the quadratic has a factor of x 3, then it has a zero at 3 x. It is NOT possible for the quadratic to have no real zeros since we know it already has one. To have only one real zero, the other factor must be the same, so the expression is x 3. To have two real zeros, the other factor can be any linear expression, for example x 3x This question assesses the student s ability to find equivalent forms of expressions. f x a x h k a x hx h k ax ahx ah k ah x ah k ax ax bx c So, b ah, c ah k 109. This question assesses the student s ability to complete the square and apply the quadratic formula to a quadratic function. (a) (b) f x x x 9 x x1 9 1 x x 34 Because the discriminant is negative, there are no real zeros for this quadratic.

13 SEMESTER EXAMS SEMESTER 117. This question assesses the student s ability to use polynomial arithmetic and solve equations in applied situation. h b (a) Given that b = h and A = 5 1 A bh 1 5 hh 5 h 5 h The negative value is extraneous here, so the base has length 10 m and the height is 5 m. (b) Any similar triangle has a base twice the length of the height, so 1 A bh 1 A hh A h The area can be any positive number (in square feet) that is a perfect square, since h is an integer. For example, if h = 4 feet, then A = 16 square feet.

14 SEMESTER EXAMS SEMESTER 118. This question assesses the student s ability to use polynomial arithmetic and solve equations in applied situation. 3s 10s Graphing d and d = 150: 40 When d = 150 feet, s = 40 mph. Distances less than 150 feet correspond to speeds less than 40 mph. So, the fastest speed a car can be moving so braking distance does not exceed 150 feet is 40 miles per hour This question assesses the student s ability to create equations, apply polynomial arithmetic, solve quadratic equations, and use units in applied situations. (a) Perimeter = x + x x x = 6x + 3 feet. (b) Area = (x)(x) + (3)(x) = x + 3x square feet. (c) The volume of sand is 40 cubic feet. The sand is 3 inches deep which is ¼ of a foot. So, the volume of the 1 x 3 x 40 4 x 3x160 pit is x 3x x x 4 x 8. A graphical solution is also shown. (d) The dimensions of the pit are about 8. feet by feet. x feet The fence will be on the perimeter, so 6(8.) feet are needed. 3 feet x feet V 1 V x 3 x 4 x

15 SEMESTER EXAMS SEMESTER 10. This question assesses the student s ability to create quadratic functions and use them in applied situations, and use units to make sense of problems. (a) Let S equal the number of bushels the farmer can grow at a rate of bushels/km. So, on a x km by x km plot a farmer can grow S 10000x bushels. (b) Let E equal the earnings made at p dollars/bushel.. dollars E Sp x bushels p px dollars bushel (c) bushels dollars E dollars km x bushel dollars dollars x km 6.4 km x x 6.4 km x.5 km So the field is.5 km square. 19. This question assesses the student s ability to find solutions to quadratic functions and slopes of linear functions in the context of a system of a quadratic and a linear function. (a) We are told the height of the cylinder is 7 times its radius, so the lateral surface can be written as A r 7r 14r. L The surface area of the capsule is the cylinder s lateral area plus the surface area of two hemispheres. C r r r r (b) 11 r.3 cm r.3 cm 11.3 cm r 11 r cm To two significant figures, r 0.6 cm.

16 SEMESTER EXAMS SEMESTER 141. This question assesses the student s ability to find solutions to graph quadratic functions and describe characteristics of the function. (a) There is a y-intercept when x= 0; y The y-intercept is at (0, 1). The x-intercepts occur when y = 0; 0 x x1 4 1 x 1 x. 4 3 x x Since the x-intercepts at,0 and,0 or approximately (0.37, 0) and ( 1.37, 0). (b) The axis of symmetry is at (c) The x-coordinate of the vertex is at b 1 x a b 1 x. The y-coordinate is a y The vertex is at,. (d) (e) The domain is all real numbers, the range is 3 f x.

17 SEMESTER EXAMS SEMESTER This question assesses the student s ability to derive the equation of a quadratic from a graph, find its zeros, and compute the rate of change between two points. (a) The vertex of the quadratic is at (1, 5), so the equation is of the form is a solution, so a 4 a a (b) Its x-intercepts are where x. Thus, the equation of the parabola is x x 1 5 x 1 5. y a x1 5. The y-intercept at (0, 4) y x1 5. (c) The average rate of change of the function between (0, 4) and (1, 5) is This question assesses the student s ability to define and sketch quadratic functions with certain characteristics. Answers will vary. (a) f should be of the form, or equivalent to, (b) g should be of the form, or equivalent to, f x a x k where a > 0 and k > 0. g x ax bx 3 where a < 0. (c) h should be of the form, or equivalent to, hx axx r where ar 4. f(x) g(x) h(x) g x x 3 f x x 1 x x h x 6x x x

18 SEMESTER EXAMS SEMESTER 156. This question assesses the student s ability to factor, solve, and graph a quadratic function; and solve a system of a quadratic and a linear function. (a) x 4x16 x4x x 4x 4 0 (b) x x 4 0 x 4 or x (c) The key points are the x-intercepts at ( 4, 0) and (, 0), the y- intercept at (0, 16), and the vertex at ( 1, 18). (d) x 8 x 4x 16 0 x 6x8 x x x1 and x 4 The solution to the system is (1, 10) and ( 4, 0) This question assesses the student s ability to find solutions to graph quadratic functions and describe characteristics of the function.