MHCA Math Summer Packet 2015

Transcription

1 Directions: MHCA Math Summer Packet 2015 For students entering PreCalculus Honors You are to complete all the problems assigned in this packet by Friday, September 4 th. If you don t turn in your summer packet when it is due, you will be required to work on your summer packet in the library during your Club period time, every day until your summer packet is complete. You will also lose 10 points from your overall summer packet grade. The summer packet will count as your 1 st Marking Period Project. Failure to complete this on time or to take it seriously will drastically reduce your 1 st Marking Period Grade. Students in Honors class who don t turn in their packet on time WILL NOT be recommended for Honors the following year. You may use as much scrap paper as you want for this packet, but you will ONLY turn in the answer sheet for a grade. Any answers not written on the answer sheet will be assumed to have not been answered and you will lose the point for that problem. When you get your graded answer sheet back you can look back at your work to see where you made the mistake. If you can t find it, you are encouraged to see your teacher before school, during club or after school for help. All the material in this packet is what you learned in your math class this past year; so none of it should be new. You will be expected to know all the material in this packet for your PreCalculus Honors class this year. Your teacher WILL NOT reteach the material found in this packet; they will only review it with you at appropriate points in the class. If you do encounter questions where you are not sure how to solve, you should also watch videos from Khan Academy to help supplement your own notes from this year. In addition, a simple Google or YouTube search of the topic should yield numerous videos to help you out. If you have any questions regarding the completion of the MHCA Math Summer Packet please contact me at fmcmahon@maryhelp.org. Have a great summer and we look forward to seeing you at the start of the school year! Fred McMahon Mathematics Department Chair

2 Answer Sheet Week Week Week Week Week Week Week

3 Week # 1 Chapter 1 Equations and Inequalities Exercises 1. Evaluate (a y) y if a = 2 and y =. A 29 B 4 C 79 D 5 2. Evaluate a b if a = 2 and b = 6. A 20 B 16 C 20 D 6 180(n 2). The formula A = relates the measure A of an interior angle of a regular polygon to the n number of sides n. If an interior angle measures 120, find the number of sides. A 5 B 6 C 8 D Name the sets of numbers to which 28 belongs. A integers C integers, rationals B naturals, integers, reals D integers, rationals, reals 5. Simplify 1 (6x + ) 4(x 2). A 10x + 9 B 9x + 9 C 10x 1 D 10x 7 6. Name the property illustrated by 7 (9 + 1) = (9 + 1) 7. A Distributive Property C Associative Property of Multiplication B Commutative Property of Multiplication D Commutative Property of Addition For Questions 7 9, solve each equation y = 14 A x 5 = 12 B 5 C 5 D A {9} B {1} C {1, 9} D 9. (5x 1) = x + A 1 2 B 2 C 2 D 1 2

4 10. John is 12 years older than his sister. Six years from now, the sum of their ages will be 2. Find John s present age. A 10 B 18 C 4 D Two sides of a triangle are equal in length. The length of the third side is three meters less than the sum of the lengths of the other two sides. Find the length of the longest side of the triangle if its perimeter is 29 meters. A 8 m B 1 m C 55 m D 10 m 12. Solve the inequality. 2x 5 10 or 4x < 5 A x or x < 7 B 7 < x C all real numbers Identify the graph of the solution set of 8.5 > y. D A B C D 14. One number is two less than a second number. If you take one half of the first umber and increase it by the second number, the result is at least 41. Find the least possible value for the second number. A 0 B 28 C 82 D 15 Week # 2 Chapter 2- Linear Relations and Functions Exercises 1. Find the range of the relation {( 1, 4), (2, 5), (, 5)}. Then determine whether the relation is a function. A { 1, 2, }; function B { 1, 2, }; not a function C {4, 5}; function D {4, 5}; not a function 2. Find f(-1) if f(x) = x2 6x x+2. A 5 B 5 C 7 D 7

5 . Find f(a) if f(t) = 2t 2 t 2. A 2(t + a) 2 2t + a 2 C 2a 2 a 2 B 2(t + a) 2 2(t + a) 2 D 4a 2 2a 2 4. Which equation is linear? A x = 2 B y = x C y < 5x 2 D y 2 = 1 2 x + 5. Write y = 1 + 5x in standard form. A 5x y = 1 B 5x + y = 1 C y = 5 x 1 D x + 5y 1 = 0 6. Find the x-intercept of the graph of 4x 2y = 8. A 4 B 2 C 0 D 2 7. Find the slope of a line that passes through (2, 4) and (-7, 8). A 4 9 B 4 5 C 5 4 D What is the slope of a line that is parallel to the graph of 2x y = 6? A 2 B 2 C 2 D 2 9. The graph of the line through (2, ) that is perpendicular to the line with equation x = 1 also goes through which point? A (0, 1) B ( 2, ) C (2, 4) D (1, 4) 10. Write an equation in slope-intercept form for the line that passes through (0, 2) and is parallel to the line whose equation is x + 5y =. A y = x 2 B y = x 2 C y = x + 2 D y = x Identify the domain of y = x + 2. A all real numbers B {y y 0} C {x x 2} D {y y 2} 12. Which is not part of the definition of the piecewise function shown? A 2 if x 1 B x + 1 if 1 < x < 1 C -x + 1 if 1 x < 1 D 2x if x 1

6 1. The graph of the linear inequality y x 1 is the region? the graph of y = x 1. A above B below C on or above D on or below 14. Which inequality describes the situation when Bob has at least pets? A p > B p C > p D p Week # Chapter - systems of equations and Inequalities 1. The system of equations y = 2x and y = 4x has A exactly one solution. B no solution. C infinitely many solutions. D exactly two solutions. 2. Choose the correct description of the system of equations. 2x + y = 10 4x + 6y = 20 A consistent and independent B consistent and dependent C inconsistent D inconsistent and dependent. The first equation of the system is multiplied by 4. 2x + 5y = 16 By what number would you multiply the second 8x 4y = 10 equation to eliminate the y variable by adding? A 5 B 5 C 2 D 2 4. Which system of equations is graphed? A 2x + y = 2 C 2x + y = 2 x y = 4 x y = 4 B 2x + y = 2 D 2x + y = 2 x y = 4 x y = 4

7 5. Which system of inequalities is graphed? A 2x + y 5 B 2x y 5 x + 2y 9 x + 2y < 9 C 2x + y > 5 D 2x + y > 5 x 2y 9 x 2y 9 For Questions 6-8, use the system of inequalities y 1, y x 6, and x + 2y Find the coordinates of the vertices of the feasible region. A ( 6, 0), ( 2, 4), (6, 0) C ( 5, 1), ( 2, 4), (4, 1) B (0, 1), (0, ), (4, 1) D ( 5, 1), ( 2, 4), (0, ), (0, 1) 7. Find the maximum value of f(x, y) = 2x + y for the feasible region. A 0 B 11 C 9 D 8 8. Find the minimum value of f(x, y) = 2x + y for the feasible region. A 10 B 0 C 9 D 4 For Questions 9-10, use the matrices to find the following. P = [ ] Q = [0 ] R = [ ] S = [ 0 2] the first row of 5P 4Q A [15 6] B [15 4] C [19 9] D not possible 10. the determinant of P A 8 B 4 C 4 D Evaluate using diagonals A 8 B 94 C 42 D 114

8 12. Cramer s Rule is used to solve the system of equations 5f 9g = 10 and 4f + g = 6. Which determinant represents the numerator for f? A B 5 C 5 D Which product would be used to solve the matrix equation [ ] [m n ] = [2 ] by using inverse matrices? 6 A [ ] [2 6 ] B 1 [ ] [2 6 ] C 1 [ ] [2 ] D [ ] [2 6 ] 14. The 00 students at Holmes School work a total of 5000 hours each month. Each student in group A works 10 hours, each in group B works 15 hours, and each in group C works 20 hours each month. There are twice as many students in group B as in group A. Which equation would not be included in the system used to solve this problem? A A = 2B C A + B + C = 00 B 10A + 15B + 20C = 5000 D B = 2A Week # 4 Chapter 4 Quadratic Functions and Relations Exercises 1. Identify the y-intercept and the axis of symmetry for the graph of f(x) = x 2 + 6x A 2; x = 12 B 12; x = 1 C 2; x = 0 D 12; x = 1 2. Identify the quadratic function graphed at the right. A f(x) = x 2 4x B f(x) = x 2 + 4x C f(x) = x 2 4x D f(x) = (x + 4) 2

9 . Determine whether f(x) = 5x 2 10x + 6 has a maximum or a minimum value and find that value. A minimum; 1 B maximum; 11 C maximum; 1 D minimum; Solve x 2 x = 28 by factoring. A { 4, 7} B { 14, 2} C { 7, 4} D { 2, 14} 5. Which quadratic equation has roots 7 and 2? A 2x 2 11x 21 = 0 B x 2 19x 14 = 0 C x 2 + 2x + 14 = 0 D 2x x 21 = 0 6. Simplify (15 1i) ( i). A 16 0i B i C i D Simplify 1 + 2i 2 i. A i B i C 4 + 7i D i 8. To solve 4x 2 28x + 49 = 25 by using the Square Root Property, you would first rewrite the equation as. A (2x 7) 2 = 25 C (2x 7) 2 = ±5 B (2x 7) 2 = 5 D 4x 2 28x + 24 = 0 9. Find the value of c that makes x 2 + 5x + c a perfect square trinomial. A B 5 4 C 25 4 D Find the exact solutions to 2x 2 = 5x 1 by using the Quadratic Formula. A 5 ± 17 4 B 5 ± 17 4 C 5 ± 4 D 5 ± Use the value of the discriminant to determine the number and type of roots for the equation. x 2 x 12 = 0 A 2 complex roots C 2 real, rational roots B 1 real, rational root D 2 real, irrational roots

10 12. Identify the vertex, axis of symmetry, and direction of opening for y = 8(x + 2) 2. A ( 8, 2); x = 8 up B ( 2, 0); x = 2; down C (2, 0); x = 2; down D ( 2, 8); x = 2; down 1. Write an equation for the parabola whose vertex is at ( 5, 7) and passes through (, 1). A y = 1 11 (x + 5)2 + 7 B y = 2(x + 5) C y = 1 2 (x + 5)2 + 7 D y = 1 2 (x 5) Which quadratic inequality is graphed at the right? A y (x )(x + 1) C y (x + )(x 1) B y > (x )(x + 1) D y > (x + )(x 1) Week # 5 Chapter 5 - Polynomials and Polynomial Functions Exercises 1. Simplify (x 0 y 4 )(2x 2 y). A 24x 6 y 7 B 216x 6 y 5 C 24x 5 D 6x 6 y 5 2. Simplify 2x2 y 5 z 4 8x 6 yz. Assume that no variable equals 0. A y4 z 7 B y4 z 2 4x 4 6x 4 C y4 z D y4 z 7 4x 4 6x 4. John is simplifying the expression (x 6x)(2x + 5x 1). Which of the following shows the correct product? A 2x 6 7x 4 x 0x 2 + 6x B 2x 9 7x 4 11x 0x 2 + 6x C 2x 9 8x 0x 2 + 6x D 2x 6 + 5x 4 x 11x 2 6x

11 4. Simplify (5x 4) 2. A 25x 2 16 C 25x 2 40x + 16 B 25x 2 20x + 16 D 25x 2 18x Simplify (6x 16x x 5) (x 2). A 6x 2 12x + C 2x 2 4x x 2 1 x 2 B 2x 2 4x + 1 D x 2 + 8x x 2 9 x 2 6. Which represents the correct synthetic division of (x 2x + 5) (x 2)? A B C D 7. Factor 27x 1 completely. A (x 1)(9x 2 + x + 1) B (x 1)(9x 2 x 1) C (x 1) D (x 1)(9x 2 x + 1) 8. Find p( ) if p(x) = 4x 5x 2 + 7x 10. A 94 B 2 C 184 D State the number of real zeros for the function whose graph is shown. A 1 B C 4 D 2

12 10. Write the expression 9n 6 + 7n 6 in quadratic form, if possible. A 9(n ) + 7(n ) 6 B 9(n 2 ) + 7(n 2 ) 6 C 9(n ) 2 + 7(n ) 6 D not possible 11. Solve b 4 + 2b 2 24 = 0. A 2, 6, 6, 2 C 2, 2, i 6, i 6 B 6, 2, 2i, i 6 D 2i, 2i, 6, One factor of x + 2x 2 11x 12 is x + 4. Find the remaining factors. A x + 1, x + B x 1, x + C x + 1, x D x 1, x 1. Which describes the number and type of roots of the equation x + 121x = 0? A 1 real root, 2 imaginary roots C real roots B 2 real roots, 1 imaginary root D imaginary roots 14. State the possible number of imaginary zeros of g(x) = x 4 + x + 7x 2 6x 1. A or 1 B 2 or 0 C exactly 1 D exactly Week # 6 Chapter 6 Inverse and Radical Functions and Relations Exercises 1. Find (f g)(x) for f(x) = x 2 + 8x and g(x) = x + 5. A x 2 5x + 5 B x 2 + 5x + 5 C x 2 + 5x 5 D x x If f(x) = x 2, and g(x) = 2x 1, find [g f ](x). A 2x x 2 6x + B 4x 2 4x 2 C x 2 + 2x 4 D 2x 2 7

13 . State the domain and range of the function graphed at the right. A D = {x x > 4}, R = {y y > 0} B D = {x x 4}, R = {y y 0} C D = {x x 4}, R = {y y 0} D D = {x x > 4}, R = {y y < 0} 4. Find the inverse of f(x) = + 5x. A f 1 (x) = 5 + x B f 1 (x) = x 5 C f 1 (x) = + 5x 5 Df 1 (x) = x 5. Determine which pair of functions are not inverse functions. A g(x) = 2x + 9 B g(x) = x 1 C g(x) = x 6 D g(x) = x + 4 h(x) = 1 x 9 h(x) = x + 1 h(x) = 1 x 4 x + 2 h(x) = 2 6. Which inequality is graphed at the right? A y x B y < x + C y x D y > x + 7. Simplify 25p 4 t 2. A 5 p 2 t B 5p 2 t C ±5p 2 t D 5p 2 t 8. Simplify 256t 4. A 4t 4t B 16t t C ±4t 4t D 4t 4t 9. Simplify A B C D

14 5 10. Simplify 2 A B 10 5 C 10 5 D Simplify the expression t 4. 1 t5 A t 2 B t C t D t Solve x A x 0 B 2 x 10 C x 10 D x 2 1. When inflation causes the price of an item to increase, the new cost C and the original cost c are related by the formula C = c(1 + r) n, where r is the rate of inflation per year as a decimal and n is the number of years. What would be the price of a $000 item after six months of 6% inflation? A $ B $794.7 C $ D $50, Find the area of a circle whose radius is x 4z 5 inches. Use.14 for π. A x 2z 10 in 2 B 9.42x 2z 10 in 2 C x 9 4z 10 in 2 D 28.26x 9 4z 25 in 2 Week # 7 Chapter 7 Exponential and Logarithmic Functions and Relations Exercises 1. Find the domain and range of the function y = 1 2 (2)x. A D = {all real numbers} C D = {x x > 0} R = {y y > 0} R = {y y > 0} B D = {all real numbers} D D = {x x > 0} R = {y y < 0} R = {all real numbers} 2. Which function represents exponential growth? A y = 1 20 (5 2 )x B y = 16(0.4) x C y = 20( 1 8 )x D y = 8x. Solve 4 2x + 7 = 2 x + A 2 B 1 C 1 D 2 4. Solve ( 1 81 )t = 24 t 2 A 9 2 B 10 9 C 2 9 D 9 10

15 5. Solve 64 x < 2 x + 2. A {x x > 10} B {x x < 10} C {x x > 10} D {x x < 10} 6. Write the equation log = 4 in exponential form. 5 A = 24 B = 81 C ( 4 5 )81 = 24 D ( 4 5 )24 = Evaluate 9 log A log 9 54 B 54 C 6 D Solve log1 x = 1. 8 A 8 B 8 C 0 D Solve log 2 (7x ) log 2 (x + 12). A {x x 5 2 } B {x x 5 2 } C{x x 2 } D {x x 5 2 } 10. Solve log a + log (a 8) = 2. A 8 B 5 C 9 D 1, Solve 9 2n = 40 4n 7. Round to the nearest ten-thousandth. A B C D Use common logarithms to approximate log 9 72 to four decimal places. A B C D Suppose you deposit $1000 in an account paying 4% annual interest, compounded continuously. Use A = pe rt to find the balance after 10 years. A $ B $ C $ D $ Solve ln(x + 2) =. A B C D Solve e 9x 6. A {x x } B {x x } C {x x } D{x x }

16 16. At a wholesale food distribution center, the price of sugar has increased 6.% annually since Suppose sugar cost $0.4 per pound in 1980 and this growth continues. What will a pound of sugar cost in 2017? Use y = a(1 + r) t and round to the nearest cent. A $4.12 B $1.21 C $2.42 D $.0