2018 SUMMER ASSIGNMENT HONORS PRECALCULUS - For students ENTERING: Honors Precalculus *Each page number represents one week of work Page 1 = Week 1, Page 2 = Week 2, etc. Approved: L. Byre Updated: 05.05.18
*Each page number represents one week of work. Page 1 = Week 1, Page 2 = Week 2, etc. 1. Simplify: 2 2. Simplify: 2 i1 i 2. Simplify: 4 4. Simplify: 6x(2x 4x 2 7) 5. Solve: 1 (x 6) 2 x 14 5 15 6. Solve: 2x 6 50 7. Solve: (x 4) 2 9 8. Solve x 2 7x 11 0 (quadratic formula) 9. The school band is planning a carnival to raise money. They plan to sell 500 tickets. Adult tickets will be $4.50 and student tickets will be $2.50. They need to collect $1650 in ticket sales to meet their goal. How many adult and student tickets do they need to sell? 10. Tell whether the lines are or. Line 1: through (1, 5) and (-4, -5) Line 2: through (-1, -9) and (2, -) 1
1. Simplify: 81 125 2. Simplify: ( 5i) (2 i). Simplify: x 2 x 20 x x 4 x 2 2x 15 4. Simplify: k 2 6k k 2 6 5. Solve: w 9w 0 x 2 y 2 20 6. Solve: x y 2 7. Factor: x 5x 2 4x 20 (grouping) 8. Divide using synthetic division: (x 2x 2 8x 5) (x 1) 9. A financial planner wants to invest $8000, some in stocks earning 15% annually and the rest in bonds earning 6% annually. How much should be invested at each rate to get a return of $90 annually from the two investments? y 2x 10. Graph: 1 y x 2 2
1. Simplify: (p 5 )(5 p 2 ) (7 p )(2 p 4 ) 2. Simplify: x 2 17xy 20 y 2 x 2 xy 10 y 2. Simplify: 4 81x 6 y 8 4. Simplify: (5 i )(5 i ) 2x y z 20 5. Solve: 7x 5 y z 5 (calculator) 4x 4 y 4z 12 2 6. Solve: x 16 7. Solve: 1 2 7 2x 6 x 9 x 2 x 8. Solve: x 2 9 (x 1) 2 9. The sum of two numbers is 10. One number is 46 more than ½ the other number. What are the numbers? x 2 y2 10. Graph 1 9 16
1. Simplify: 4 4 x 2. Simplify: x x 2 6x 9 x 2 1 x. Simplify: 9(6 2) 7 2(8 6) 4. Solve: 9 x 27 5. Simplify: i(5 i) 6. If f (x) 2x 4 x 2x 4 find f (1). 7. Solve: 2 x 2 x 8. Solve for y: 4 x 10 y 5 9. Y varies directly as x. If x = 1 and y = 9, find y when x = 4. 10. Classify each conic section: a)x 2 y 10 0 b)16x 2 9 y 2 96 y 18 y 15 0 c)8x 2 8 y 2 64x 2 y 160 0 c)25x 2 16 y 2 100x 128y 44 0 4
1. Simplify: x 1 2(x 1) 4 2. Simplify: x 2 2x 5 x 2 1x 40 x 2 7x 12 x 2 12x 1 4. Simplify: 27 2. Simplify: 802 1 16 2 5. Solve: x 2 10x 21 0 6. Solve: 8k 2 5k 2k 2 4 7. Solve: x x 2 4x 4 0 (Hint: factor by grouping) 8. Solve: x 4 5x 2 4 0 9. If f (x) x 2 find f 1 (x). x y 9 10. Solve by graphing: y 2x 5
1. Simplify: 125 2. Simplify: (x y) 1. Simplify: 64 2 4. Rationalize the denominator: 1 49 5. Simplify: 2x y 5 x 6 y 6. Solve: 8 y 2(2y 1) 7. Solve: (x 2)(x 5) 8 8. Factor: x 27 9. Z varies jointly with x and y. If x = 2, when y =, z = 6, find z when x = 4 and y = 7. 10. Find the equation of the line containing the point (-2, 1) and perpendicular to y 2x 10. Leave answer in slopeintercept form. 6
1. Simplify: a 5 a 2 a a 2 25 2. Simplify: (x 2 y ) 2 ( 1 x 5 y z 2 ) using 6 positive exponents.. Simplify: 125x 6 y 4 4. Simplify: x 1 1 x x 5. Simplify: 8x 1 4 x 2 x 6 x 2 6. Find the slope and y-intercept of the line 5x y 12 7. Solve and graph: 1 8m 7 2 8. Solve and graph: 2 y 5 1 9. Find the probability of drawing a jack and then a from a standard deck (without replacement). 10. Is each relation a function? a) b) c) d) 7
1. Simplify: (4 i) 2 2. Simplify: 5 i. Given the points (-4, -2) and (1, -5), find the distance between them and the coordinate of the midpoint of the line segment joining the two. 4. Simplify: (5x 2 y) 2 xy 2 x 8 y 16 5. Solve: 2x 5 y 10 x 2 y 6. Solve: 2x y 12 7. Factor: a 2 x 12a 2 x 2 20a 2 x 8. For what values of x is x undefined? x 2 9. The width, length, and diagonal of a rectangle are consecutive even integers. Find the numbers. x 2 2 10. Graph: y 1 25 8
1. Solve: 5(2x 1) (x 4) x x 2 5x 2. Simplify: 2x x 2 5x 6. Simplify: 20 15 4. Simplify: If P(x) (x 1)(x 1), find P(i). 5. Solve using quadratic formula: x 2 x 8 0 6. Solve by completing the square: x 2 4x 8 0 7. Write the equation of the line in standard form that passes through (-, ) and (2, -7). 8. Find the center and radius of the circle: x 2 y 2 2x 4y 4 0 9. Write the equation of the circle with center (2, -5) and radius 7. 10. Graph 1 x y 0 2 4 9
1. Simplify: x 2 18x 81 2. Simplify: 54 2 6. Simplify: x y x y 2x 2 y z 0 2 4. Simplify: 4 1 xyz 5. Solve: x x 9 6. Solve: 1 x 2 (Hint-Quad Formula) 2x 7. What is the conjugate of 2 5i? 8. If f (x) x 2 2 and g(x) 2x 1, find f (g(1)). 9. The mass of a metal disc varies directly as the thickness and jointly as the square of the radius. A disc 2 cm thick with radius 5 cm has a mass of 840g. Find the mass of a disc of the same metal that has radius cm and 0.5 cm thickness. 10. Given y x 2 2x 5, find the vertex, the axis of symmetry, and graph. b Hint: x 2a 10
1. Find one positive and one negative angle that are coterminal with the angle 5. 2. Sketch the angle and find its reference angle. 160.. Evaluate without a calculator: cot 15 4. Evaluate without a calculator: tan 5. Evaluate without a calculator: sin 2 1 2 6. Use Law of Sines to find the missing angle measures: A 120, a 5,b 10. 7. What are the amplitude and period of the function: y sin 4 x. 8. Simplify: sin tan 2 9. Solve over 0 x 2 : 2sin 2 x 5sin x 0 10. Simplify: sin x 7 2 11
1. Find one positive and one negative angle that are coterminal with the angle 1. 5 2. Sketch the angle 5 and find its reference 6 angle.. Evaluate without a calculator: sec 210 4. Change 2 from radians to degrees. 9 5. Evaluate without a calculator: cos 1 1 2 6. Use Law of Cosines to find c. C 64, a,b 9. 7. Write an equation of the graph of y 2sin x translated up and right units. 8. Simplify: sin 2 cos 2 cot 2 9. Solve over 0 x 2 : 2 sin x cos x sin x 0 10. Find cosa bgiven that cos a 24 ; 25 a and sin b 12 ; b. 2 1 2 12
Answers: Week 1 1) 4 2 2) 5 i ) 16 9 4) 12x 4 24x 42x 5) 4 6) 22, 28 7) 1, 7 8) 7 5 2 9) 200 adult, 00 students 10) parallel Week 2 5 1) 25 2) 5 6i ) x x 4) k k 6 5), 0, 6) 2, 4,4, 2 7) x 5 x 2 x 2 8) x 2 x 9 4 x 1 9) $5000 stocks $000 bonds 10) Week 1) 29 p 7 2) x 4 y x 2 y 4) 28 ) xy2 x 5), 4, 2 6) 64 7) 6 8) 4 9) 56 and 74 10) 1
Week 4 1) 4 4x 2x 1 2) 4x 9 x 2 6x 9 ) 181 5) 1 5i 6) 8 7) 4) 2 8) y 2 x 25 10 9) -108 10) Parabola, Hyperbola, Circle, Ellipse Week 5 x 2 5 1) 4(x 1) 2) x(x 7) (x )(x 8) ) 5 4) 54 5) 7, 9) f 1 (x) 1 x 2 6) 1, 4 2 10), 6 7) 1, 2i 8) 1, 2 Week 6 1) -5 2) x x 2 y xy 2 y ) 2 4) 7 7 2x 6) y : y 2 7), 6 8) (x )(x 2 x 9) 5) y 2 9) 28 10) y x 2 2 Week 7 a 1) a 5 4x 1 5) x x 2 9) 4 66 2) 24 y x 11 z 6 ) 5x y 2 5 4) 9 2 6) 5; (0, -12) 7) m : 1 m 2 8) y : 2 y 10) yes, no, no, no 14
Week 8 1) 7 24i 2) 1 i 7 4) 75x 5 y 4 ) 4 ; 2 2 2, 2 5) 0, 2 6) 5, 22,, 6 7) a 2 x(x 10)(x 2) 8) 2 9) 6, 8, 10 10) Week 9 7 1) 1 41 5) 2 9) x 2 2 y 5 2 49 5x 4 ) 10 4) -2 2) 2(x 2) 6) 2 2i 10) 7) 2x y 8) C(1, -2); r = Week 10 1) x 9 2) 7i 6 ) x 2 xy y 2 4) x 6 z 2 64 y 4 5) 1 2 22 6) 6 7) 2 5i 8) 9) 75.6 g 10) V(1, 4); x = 1 15
Week 11 1) 11 ; 2) ; 20 ) -1 4) 5) 4 6) 14., 45.7 7) ; 1 2 8) sin 9) 5, 6 6 Week 12 10) - cos x 1) ; 7 5 5 2) ; ) 6 2 4) 40 5) 2 6) 8.1 7) y 2sin x 8) csc 2 9) 0,,, 7 10) 6 4 4 25 16