UNIT PARCC Assessment Readiness Name Class Date Selected Response. Kendrick is using a compass and straightedge to copy Q. The figure shows the portion of the construction that he has already completed. Where should Kendrick place the point of the compass to do the next step of the construction? Q A. point Q B. point R C. point X D. point Y R. Which lines can be proven parallel given the following diagram? X a b c 39º 40º 39º F. a ǁ b H. b ǁ c G. a ǁ c J. b ǁ d d Y 3. DEFG is a rhombus. You want to prove the property that a diagonal of a rhombus bisects a pair of opposite angles. To prove that DF bisects GDE, you first show that GDF EDF using the definition of rhombus, the Reflexive Property of Congruence, and the SSS Congruence Criterion. What other reasons are needed to complete the proof? G D A. Isosceles Triangle Theorem; SAS Congruence Criterion B. Definition of perpendicular; Triangle Sum Theorem F C. If a quadrilateral is a parallelogram, then opposite angles are congruent; definition of angle bisector D. Congruent Parts of Congruent Triangles are Congruent; definition of angle bisector 4. Which of the following is not preserved under a dilation? F. angle measure G. betweenness H. collinearity J. distance E Unit 87 PARCC Assessment Readiness
CONSTRUCTED RESPONSE. Use the definition of similarity in terms of similarity transformations to determine whether the two figures are similar. Explain your answer. A y 7. To find the distance AB across a pond, you locate points as follows. Starting at A and walking along a straight path, you walk 8 feet and put a marker at C. Then you walk 8 feet farther and put a marker at D. E 3 ft 3 ft C D 8 ft 8 ft 3 ft - B 0 - D E F C x Starting at B, you walk to C, measuring the distance you walked (3 feet). Then you walk 3 feet farther and put a marker at E. Finally, you measure the distance from D to E, as shown. Explain how to use this information to find AB. A B 6. You are proving that the AA Similarity Criterion follows from the definition of similarity in terms of similarity transformations. Given: R U and S V Prove: RST UVW R S U T You begin by applying a dilation to RST. What is the scale factor k of the dilation? Why do you choose this scale factor? V W 8 Find the value of x and justify each step, given that m JKL = 00. J M (6x + 8)º (x 4)º K L Unit 88 PARCC Assessment Readiness
UNIT PARCC Assessment Readiness Name Class Date Selected Response. Given that x is the measure of an acute angle, which of the following is equal to sin x? A. cos x B. cos(90 - x) C. sin(90 - x) D. tan x. Connor is building a skateboard ramp with the dimensions shown. Which expression can he use to find the height b of the ramp? F. sin 8 G. sin 8 H. cos 8 J. cos 8 3. In the right triangles shown below, M Q. This leads to the observation that MNP QRS by the AA Similarity Criterion. Therefore, corresponding sides are proportional, so RS NP = QR and algebra shows MN that RS QR = NP. This last proportion is the MN basis for defining which of the following? M b N P m a 8 R 4. The lengths of the two legs of a right triangle are inches and 4 inches. What is the length of the hypotenuse in simplest radical form? F. Ç 6 inches G. Ç 3 inches H. Ç inches J. Ç 0 inches. A square courtyard has a straight walkway from one corner to the opposite corner. If each wall of the courtyard is 0 feet long, what is the length of the walkway? A. 0 feet B. 0 feet C. 0 Ç feet D. 0 Ç 3 feet 6. The sides of an equilateral triangle are 40 inches long. What is the height of the triangle? F. 0 feet G. 80 feet H. 0 Ç 3 feet J. 40 Ç 3 feet Q S A. the cosine of M B. the cosine of P C. the sine of M D. the tangent of M Unit 3 PARCC Assessment Readiness
7. ABC and PQR are similar right triangles, with right angles at B and Q. Which of the following represents the ratio of PQ to QR? A. the sine of C B. the cosine of C C. the tangent of C D. the tangent of A 9. From a point on the ground feet in front of the building, the angle of elevation to the top of the building is 76. How tall is the building? Round the answer to the nearest foot. CONSTRUCTED RESPONSE 8. You paddle a kayak due north at the rate of. mi/h. The river has a mi/h current that flows due east. You want to find the kayak s actual speed and direction. a. In the space below, sketch and label vectors that represent the situation. 76 ft b. Find the kayak s actual speed and direction. 0. To avoid a large, shallow reef, a ship set a course from point A and traveled miles east to point B. The ship then turned and traveled miles south to point C. If the ship could have traveled in a straight line from point A to point C, how many less miles would the ship have traveled? Round your answer to the nearest tenth of a mile. Unit 4 PARCC Assessment Readiness
UNIT 3 PARCC Assessment Readiness Name Class Date Selected Response. A wire frame in the shape of the cube is used to support a pyramid-shaped basket, as shown. The vertex of the pyramid lies in the same plane as a face of the cube. To the nearest tenth, what is the volume of the pyramid-shaped basket? 4. PR and QR are tangents to circle C. Which expression represents m C? R y P C Q 8 cm 0 cm.3 ft F. 0.7 f t 3 H.. f t 3 G..7 f t 3 J..3 f t 3. A food manufacturer sells yogurt in coneshaped cups with the dimensions shown. To the nearest tenth, how many fluid ounces of yogurt does the cup hold? (Hint: c m 3 0.034 fl oz) A. 0.6 fl oz C. 7. fl oz B..7 fl oz D..8 fl oz 3. You want to design a cylindrical container for oatmeal that has a volume of 90 in. 3 You also want the height of the container to be 3. times the radius. To the nearest tenth, what should the radius of the container be? F..0 in. H. 3.0 in. G..9 in. J. 3. in. A. (y) C. (90 - y) B. (80 - y) D. ( y ). In circle O, ABC is an inscribed angle and AC is a diameter. Which of the following must be true? F. ABC is an acute angle. G. ABC is a right angle. H. AB is a radius. J. AC BC 6. What is the radian measure of the angle whose degree measure is 0? A. π C. π 0 9 B. π D. π 8 9 7. JK is a tangent to circle C. What is m KL? C F. H. 6 G. 0 J. 30 K L J Unit 3 87 PARCC Assessment Readiness
CONSTRUCTED RESPONSE 8. In order to develop and justify the formula for the volume of a cone, you begin with a given cone that has radius r and height h. You consider pyramids with regular polygonal bases that are inscribed in the cone. 9. A spherical gas tank has the dimensions shown. When filled with butane, it provides 468,766 BTU. How many BTUs does one cubic foot of butane yield? Round to the nearest BTU. 6. ft You show that when the inscribed pyramid has a base that is a regular n-gon, the volume of the pyramid is given by the following expression. n ) cos ( 80 n ) 3 r hn sin ( 80 Describe the remaining steps of the argument. 0. Write an expression in terms of m that you can use to find the area of sector AOB. ft O m A B. Using the figure below, Andrea discovers that the length of the arc intercepted by the 60 angle is proportional to the radius. What is the constant of proportionality for the relationship? Show your reasoning. O 60 3 Unit 3 88 PARCC Assessment Readiness
UNIT 4 PARCC Assessment Readiness Name Class Date Selected Response. What is the definition of a complex number? A. A number of the form a + bi where a and b are real B. A number of the form a + bi where a = 0 and b is real C. A number of the form a + bi where a is real and b = 0 D. A number of the form a + bi where a = 0, b is real, and b 0. What is the simplified form of the product (-4 + i)(3-9i)? F. 6-4i H. 6 + 4i G. -30-4i J. -6 + 4i 3. What is the conjugate of - 3i? A. - - 3i C. 3 + i B. + 3i D. 3 - i. What is - - i? A. + i C. Ç B. D. 0 6. Solve the equation x + 8 = 0. F. x = 3 ± i H. x = ±3i G. x = ±3 J. x = ±3 + i 7. Find the zeros of the function f(x) = x + 6x + 8. A. x = 3i or -3i C. x = -3 + 3i B. x = -3 + 3i D. x = -6 + 3i or -3-3i or -6-3i 8. Find the complex conjugate of 3i + 4. F. -4-3i H. 4 + 3i G. -4 + 3i J. 4-3i 4. What is the simplified form of the quotient - 4i - + i? F. - + 7 i 3 H. 3 + 3i G. - 6 + 7 i J. + 9 i Unit 4 309 PARCC Assessment Readiness
CONSTRUCTED RESPONSE 9. Graph the complex number 4 + i. 4 3 --4-3 -- - 0 - -3-4 - imaginary 3 real 4. Consider the equation x - 4x + = 0. a. Without solving the equation, tell whether it has real or imaginary solutions. Explain how you know. b. What are the solutions of the equation? 0. Graph the complex number - + i. 4 3 --4-3 -- - 0 - -3-4 - imaginary 3 real 4 c. Evaluate x - 4x + for each solution. Show your results each time you perform an operation (squaring, multiplying, subtracting, and adding). What can you conclude?. Find (-3 + 6i) + (-4 - i) by graphing on the complex plane. 0 8 6 4-0-8-6 -4- - 0-4 -6-8 -0 imaginary 4 6 real 8 0 Unit 4 30 PARCC Assessment Readiness
UNIT PARCC Assessment Readiness Name Class Date Selected Response. The graph of which function is a reflection and vertical stretch of the parent quadratic function? A. f (x) = 3 x C. f (x) = -3 x B. f (x) = 0.3 x D. f (x) = -0.3 x. Which of the following describes the graph of f (x) = - x as a transformation of the graph of the parent quadratic function? F. reflection across the x-axis and vertical stretch by a factor of G. reflection across the y-axis and vertical shrink by a factor of H. translation units left J. translation units down 3. What is the minimum value of f (x) = x + 0x + 0? A. - C. B. - D. 4. Jon has rewritten the expression x 3-0 x + 7x - 8 in order to factor it. Which is a reasonable next step for Jon to perform? F. Use the Commutative Property to rewrite the terms in a different order. G. Factor from the second and fourth terms. H. Group the first two terms and factor out the greatest common factor, x. J. Factor x from each of the four terms.. What is the factored form of n -n + 6? A. (n - 6)(n + ) B. (n + 6)(n - ) C. (n + )(n + 3) D. (n - )(n - 3) 6. What is the factored form of 3 c + c - 4? F. (3c - )(c + ) G. (3c + )(c + ) H. (3c + 4)(c - ) J. (3c - )(c + 4) 7. Which of the following polynomials have a common binomial factor? A. ( x + 4) and ( x + 4x + 4) B. ( x + 4) and ( x - 4x + 4) C. ( x - 4) and ( x + 4x - 4) D. ( x - 4) and ( x + 4x + 4) 8. Which expression is not equivalent to the polynomial 6 x 3 + x - 9x? F. 3( x 3 + x - 3x) G. 3x( x + x - 3) H. 3x(x + 3)(x - ) J. 3x(x - )(x + 3) Unit 38 PARCC Assessment Readiness
CONSTRUCTED RESPONSE 9. Amanda is adding a border to a rectangular quilt with a length of 4 feet and a width of 3 feet. The border has a width of x feet. Write a quadratic function f (x) in standard form for the area of the border in square feet. What is f (0.) and what does it represent?. Complete the diagram and the equation that represent the binomial multiplication shown by the algebra tiles. x + x x x x x x 0. The function f (x) = - 6x + 40x models the height in feet of a football x seconds after it is kicked from the ground. a. Graph the function. (x + ) ( + ) =. Show how to factor the polynomial 0 a b - 0ab - b + 6ab completely. 0 b. What does the origin of the graph represent? c. What is a reasonable domain of the function? Explain. 3. The area of a square room (in square feet) is given by the polynomial 6 x + 40x +. The length of each wall can be written in the form cx + d, where c and d are whole numbers. a. Show how to write an expression in terms of x for the perimeter of the room. b. Find the perimeter when x = feet. d. What is the maximum of the function, and what does it represent in this situation? Unit 386 PARCC Assessment Readiness
UNIT 6 PARCC Assessment Readiness Name Class Date Selected Response. Tyrell s teacher asks him to prove or disprove that the triangle with vertices A(, ), B(, ), and C(6, 4) is an isosceles triangle. Which of the following should he do? A. Disprove the statement by using the distance formula to show that AB, BC, and AC all have different lengths. B. Prove the statement by using the distance formula to show that AB = BC. C. Prove the statement by using the distance formula to show that AB = AC. D. Prove the statement by using the distance formula to show that BC = AC. 4. Three friends are planning to visit each other. To optimize travel time, they want the meeting place to be equidistant from the three different cities they live in. The cities are located at A(-6, -), B(, 6), and C(, -8). What are the coordinates where the meeting should take place? F. (-7.,.) H. (-4.3, -4.3) G. (-7, -9.) J. (-4, -6). Position a right triangle with leg lengths r and s + 4 in the coordinate plane and give the coordinates of each vertex. A. (0, r). What is the equation in standard form for the parabola with focus F(0, -6,) and directrix y = 6? F. y = 4 x G. x = 4 y H. x = - 4 y J. y = - 4 x 3. What is an equation in standard form for the parabola shown? X = - 4 3 - -4-3 - - - - -3-4 - y F(, 0) 3 4 x B. C. (0, 0) (s + 4, 0) (r, 0) (0, 0) (0, s + 4) (0, s + 4) A. y = - 8 C. x = 8 B. y = 8 D. x = - 8 (0, 0) D. Both a. and c. (r, 0) Unit 6 4 PARCC Assessment Readiness
CONSTRUCTED RESPONSE 6. Prove or disprove that the point (, Ç ) lies on the circle that is centered at the origin and contains the point (0, -3). - 0 y x 8. Prove that the angle inscribed in a semicircle below is a right angle. P 4 3 - -4-3 - - - 0 - -3-4 - y 3 Q R 4 x - 9. Find the point(s) of intersection of the line x - y = -6 and the circle x + y = 8 by solving the system of equations. 7. What is the equation of the parabola with focus (4, -) and directrix x =? Without graphing, tell the direction in which the parabola opens. How do you know? Unit 6 46 PARCC Assessment Readiness
UNIT 7 PARCC Assessment Readiness Name Class Date Selected Response. You spin a spinner with 0 equal sections that are numbered through 0. Event A is rolling an odd number. Event B is rolling a number greater than. What is P (A B)? A. C. 8 B. D. 4. There are 9 players on a basketball team. For a team photo, 4 of the players are seated on a row of chairs and players stand behind them. In how many different ways can 4 players be arranged on the row of chairs? F. 4 H. 80 G. 6 J. 304 3. There are peaches and 4 nectarines in a bowl. You randomly choose pieces of fruit to pack in your lunch. What is the probability that you choose peaches? A. C. 36 B. D. 8 9 4. You shuffle the cards shown below and choose one at random. What is the probability that you choose a gray card or an even number? 4 7 9 0 3 6 8 9 F. 0 H. 6 G. 3 44 J. The two-way table provides data about 40 randomly chosen people who visit a movie theater. Use the table for Items and 6. Purchases a snack Purchases no snack Discount Admission Regular Admission TOTAL 4 7 96 36 08 44 TOTAL 60 80 40. Consider the following events. Event A: Pays for a regular admission. Event B: Purchases a snack. Which is the best description of the two events? A. complementary events B. dependent events C. independent events D. mutually exclusive events 6. What is the probability that a visitor to the movie theater purchases a snack given that the visitor pays for a discount admission? F. 0. H. 0.4 G. 0. J. 0.7 7. A bag contains 8 yellow marbles and 4 blue marbles. You choose a marble, put it aside, and then choose another marble. What is the probability that you choose two yellow marbles? A. 7 C. 4 8 9 B. 4 D. 33 3 Unit 7 463 PARCC Assessment Readiness
8. Events A and B are independent events. Which of the following must be true? F. P (A and B) = P(A) P(B) G. P (A and B) = P(A) + P(B) H. P (A) = P(B) J. P ( B A ) = P ( A B ) 9. Which expression can you use to calculate the conditional probability of event A given that event B has occurred? A. P (A) + P(B) - P(A and B) B. P (B) P(A B) P (A and B) C. P(B) D. P(A) P(B). Two students, Naomi and Kayla, play a game using the rules shown below. The winner of the game gets a box of 80 fruit chews. Game Rules One student repeatedly tosses a coin. When the coin lands heads up, Naomi gets a point. When the coin lands tails up, Kayla gets a point. The first student to reach 8 points wins the game and gets the fruit chews. The game gets interrupted when Naomi has 7 points and Kayla has points. How should the 80 fruit chews be divided between the students given that the game was interrupted at this moment? Explain why your answer provides a fair way to divide the fruit chews. CONSTRUCTED RESPONSE 0. It is known that % of all mice in a laboratory have a genetic mutation. A test for the mutation correctly identifies mice that have the mutation 98% of the time. The test correctly identifies mice that do not have the mutation 96% of the time. A lab assistant tests a mouse and finds that the mouse tests positive for the mutation. The lab assistant decides that the mouse must have the mutation. Is this a good decision? Explain. Unit 7 464 PARCC Assessment Readiness