Honors Precalculus. For students ENTERING: *Each page number represents one week of work Page 1 = Week 1, Page 2 = Week 2, etc.

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Griselda Horton
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1 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:

3 *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 Solve: 2x Solve: (x 4) 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

4 1. Simplify: Simplify: ( 5i) (2 i). Simplify: x 2 x 20 x x 4 x 2 2x Simplify: k 2 6k k Solve: w 9w 0 x 2 y 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

5 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 Solve: 7x 5 y z 5 (calculator) 4x 4 y 4z Solve: x Solve: x 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

6 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 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 = 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 c)25x 2 16 y 2 100x 128y

7 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: Simplify: Solve: x 2 10x Solve: 8k 2 5k 2k Solve: x x 2 4x 4 0 (Hint: factor by grouping) 8. Solve: x 4 5x If f (x) x 2 find f 1 (x). x y Solve by graphing: y 2x 5

8 1. Simplify: Simplify: (x y) 1. Simplify: Rationalize the denominator: Simplify: 2x y 5 x 6 y 6. Solve: 8 y 2(2y 1) 7. Solve: (x 2)(x 5) 8 8. Factor: x Z varies jointly with x and y. If x = 2, when y =, z = 6, find z when x = 4 and y = Find the equation of the line containing the point (-2, 1) and perpendicular to y 2x 10. Leave answer in slopeintercept form. 6

9 1. Simplify: a 5 a 2 a a 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 Solve and graph: 1 8m Solve and graph: 2 y 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

10 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 Solve: 2x 5 y 10 x 2 y 6. Solve: 2x y 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 Graph: y

11 1. Solve: 5(2x 1) (x 4) x x 2 5x 2. Simplify: 2x x 2 5x 6. Simplify: Simplify: If P(x) (x 1)(x 1), find P(i). 5. Solve using quadratic formula: x 2 x Solve by completing the square: x 2 4x 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 Write the equation of the circle with center (2, -5) and radius Graph 1 x y

12 1. Simplify: x 2 18x Simplify: Simplify: x y x y 2x 2 y z 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

13 1. Find one positive and one negative angle that are coterminal with the angle Sketch the angle and find its reference angle Evaluate without a calculator: cot Evaluate without a calculator: tan 5. Evaluate without a calculator: sin Use Law of Sines to find the missing angle measures: A 120, a 5,b 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 Simplify: sin x

14 1. Find one positive and one negative angle that are coterminal with the angle Sketch the angle 5 and find its reference 6 angle.. Evaluate without a calculator: sec Change 2 from radians to degrees Evaluate without a calculator: cos Use Law of Cosines to find c. C 64, a,b 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 Find cosa bgiven that cos a 24 ; 25 a and sin b 12 ; b

15 Answers: Week 1 1) 4 2 2) 5 i ) ) 12x 4 24x 42x 5) 4 6) 22, 28 7) 1, 7 8) ) 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

16 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 ) ) 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, ), 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) ) 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

17 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) ) 2 9) x 2 2 y x 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) ) 6 7) 2 5i 8) 9) 75.6 g 10) V(1, 4); x = 1 15

18 Week 11 1) 11 ; 2) ; 20 ) -1 4) 5) 4 6) 14., ) ; 1 2 8) sin 9) 5, 6 6 Week 12 10) - cos x 1) ; ) ; ) 6 2 4) 40 5) 2 6) 8.1 7) y 2sin x 8) csc 2 9) 0,,, 7 10)

Statewide Framework Document for:

Statewide Framework Document for: 270301 Standards may be added to this document prior to submission, but may not be removed from the framework to meet state credit equivalency requirements. Performance