Precalculus Unit 6 Practice

Transcription

1 Lesson 34-. What is the sum of ? A Precalculus Unit 6 Practice Model with mathematics. A cellphone compan offers three different models with two different plans. The prices in dollars are shown in the matri below. Basic Teting Smart Individual Famil Use matri subtraction to represent a price decrease of $. per item. Show our matrices. B C D. not possible. Use scalar multiplication to represent a price increase of.% decrease per item. Round to the nearest cent. Show our matrices. Make use of structure. Find each sum or difference. State if the operation is not possible Lesson What is the product? ? A B C D. not possible 0 College Board. All rights reserved. SpringBoard Precalculus, Unit 6 Practice

2 Make use of structure. Find each product. State if the operation is not possible ? Write a matri equation that calculates onl the amounts of each item of the Sanchez famil s purchase. Lesson ? Which of the following could be the determinant of the given matri? 9 3 A. 6 B. C. D. 4 Model with mathematics. A cellphone compan offers three different models with two different plans. The prices in dollars are shown in the matri below. Basic Teting Smart IndividualFamil Attend to precision. Determine the value(s) of so that the matri has an inverse. 3 Use appropriate tools strategicall. For Items 3, find the determinant and inverse of each matri. Use a graphing calculator when needed. 9. The Sanchez famil is buing one of each tpe of phone at the famil rate. Write a quantit matri that could be multiplied with the cost matri. Eplain College Board. All rights reserved. SpringBoard Precalculus, Unit 6 Practice

3 Write and simplif a matri sum to represent the translation of quadrilateral TUVW Lesson 3- Make use of structure. A quadrilateral in the coordinate plane has vertices T(, ), U(3, 7), V(4, 6), and W(3, ). The quadrilateral is translated units up and 3 units left. 8. Write and simplif a matri product to represent a reflection over the -ais of the translation in Item Which matri below could represent the translation of the quadrilateral? A B Write and simplif a matri product to represent a reflection over the -ais of the translation in Item 8. C D Construct viable arguments. Write the matri for reflecting an object across. Eplain. 3 0 College Board. All rights reserved. SpringBoard Precalculus, Unit 6 Practice

4 Lesson 3- Model with mathematics. A student is animating a triangle for a class project. The coordinates of the triangle are shown in the matri below Write and simplif a matri epression to represent the rotation of the translated triangle. 4. Finall, the triangle from Item 3 is dilated b a scale factor of. Write and simplif a matri epression to represent the dilation.. First the triangle must move so that the leftmost verte is on the origin. Write and simplif a matri epression to represent the translation.. Reason abstractl. Follow the above animation with a general point (a, b) that is not the origin. Describe what happens to that point throughout the animation.. Net, the triangle must rotate 90 degrees counterclockwise about the origin. Which of the following matrices could represent the rotation? A. B. C. D Lesson A triangle has vertices at (0, 0), (, 9), and (, 8). Which of the following determinants could be used to find the area of the triangle? A. 9 8 B. C. D College Board. All rights reserved. SpringBoard Precalculus, Unit 6 Practice

5 7. Use the determinant to find the area of the triangle in Item Reason quantitativel. Use the parallelogram from Item in Lesson 3-3. Suppose r, s, t 0., and u 3.. Use the determinant to find the area of the parallelogram. Lesson Which matri equation represents the sstem of 6 equations? A. B Make use of structure. Use the answer from Item in Lesson 3-3 to find the coordinates of the verte opposite the origin. C. D Refer to Item 7 in Lesson 3-3. Suppose r 6, s, t 4, u, v, and w. Find the area of the triangle. 3. Write a matri equation to represent the sstem. 7a b c 3a b c a 6b 33. Make use of structure. What sstem of equations does the matri equation represent? s t 3 0 College Board. All rights reserved. SpringBoard Precalculus, Unit 6 Practice

6 Model with mathematics. A teacher is tring to set up groups in his science class. Some groups can have 3 students and some can have 4. There are 8 groups in all for a class of Write a sstem of equations in two variables that can be used to find the number of groups with 3 students and the number of groups with 4 students. 38. Epress regularit in repeated reasoning. Use an inverse matri to solve the matri equation Write the sstem of equations as a matri equation. Model with mathematics. Mar is selling two tpes of coffees at the school café. On Monda she sells cups of coffee, one at $.0 per cup and the other at $ If Mar makes $4 on Monda, write a matri equation that she could use to figure how much of each tpe of coffee was sold. Lesson Which of the following inverse matrices could be used to solve 4 3 9? Use the matri equation in Item 39 to solve for the quantities sold on Monda. A. A 4 3 B. A 3 4 Lesson 36-3 C. A D. not possible Which of the following is indicated b the determinant of the given matri of a sstem of equations? A. The sstem has two unique solutions. B. The sstem has one unique solution. 37. What is the solution to 4 3 9? 9 C. The sstem has no solutions. D. The solution of the sstem cannot be determined. 6 0 College Board. All rights reserved. SpringBoard Precalculus, Unit 6 Practice

7 Use appropriate tools strategicall. For Items 4 43, use technolog to solve each matri equation z a b c d Lesson 37- Make use of structure. Eleven tablets are stacked in an oblique rectangular prism. One of the tablets measures 7 inches b 6 inches b. inches. 46. Which of the following is the volume of one of the tablets? A. 43. cubic inches B. 0.4 cubic inches C. 4 cubic inches D. 4. cubic inches 47. Find the volume of the entire stack of tablets. Make sense of problems. A workout group is doing eercise stations. The table below describes the number of eercises completed b each member. Member Rowing Medicine Ball Jump Rope Total Points Tina 34 Jacob 3 69 Mike Construct viable arguments. Diego sas that it is not possible to calculate the volume of an oblique rectangular prism because the slant height is not known. Is he correct or incorrect? Eplain. 44. Set up a matri equation that represents the given data. 49. What is the volume of an oblique clinder that has a height of 3 mm and a radius of 3.7 mm? Round to the nearest tenth. 4. Use the matri equation in Item 44 to solve for the point values of each activit. 0. What is the volume of an oblique cone that has a height of feet and diameter of feet? Round to the third decimal place. 7 0 College Board. All rights reserved. SpringBoard Precalculus, Unit 6 Practice

8 Lesson 37- Model with mathematics. A silo has a height of ards and a radius of 6. ards.. What is the approimate volume of the hemisphere on top of the silo? A. 60 cubic ards B. 0 cubic ards C. 740 cubic ards D. 000 cubic ards. What is the total volume of the silo? Round to the nearest whole number. 3. Reason abstractl. The farmer who owns the silo would like to build a second silo that is % larger in volume. How does this change in volume affect the scale factor for the radius? 7. Attend to precision. Find the eact limit of n lim n 4. 3n 8. Reason quantitativel. Use the table below to find the limit of the function as. Eplain Jennifer is looking at lim f( ) lim f( ) 4 and f( ) and finds that lim 4. Does the function have a limit at? Eplain. 4. Find the radius and height of the new silo. Round to the nearest hundredth. 60. Critique the reasoning of others. The table below shows the function values for particular values of.. Find the volume of the new silo. Round to the nearest whole number. Lesson What is the limit of lim? A. 0 B. C. D. f () ERROR Doug sas that the limit of the function does not eist at 3. Is Doug correct? Eplain. 8 0 College Board. All rights reserved. SpringBoard Precalculus, Unit 6 Practice