Summer Packet Honors PreCalculus

Transcription

1 Summer Packet Honors PreCalculus Honors Pre-Calculus is a demanding course that relies heavily upon a student s algebra, geometry, and trigonometry skills. You are epected to know these topics before entering Honors Pre-Calc. You should be able to do 95% of this packet without a calculator! DUE: 1 st day of school PRE-REQUISITES TEST: Friday, September 7, 018 The first major assessment of the year will cover the following pre-requisite topics: Linear functions (graphing, finding intercepts, writing equations, slope, parallel vs. perpendicular, etc.) Solving systems of linear and non-linear equations Quadratic functions (graphing, verte vs. general form, solving equations, etc.) Functions (notation, domain and range, operations on functions, composition of functions, testing for functions, evaluating functions, finding intercepts, graphing, parent functions etc.) Dividing polynomials Factoring polynomials Rules of eponents Rules of radicals Comple numbers Right triangle trigonometry Pythagorean theorem Special right triangles Circles (graphing, finding the center and radius, standard form, etc.) Unit circle trigonometry Law of Sines and Law of Cosines Transforming Sine and Cosine Functions Solving eponential and logarithmic equations Each of these topics has been covered in your previous math classes and is considered pre-requisite material for this course. Eample problems for each topic are included in the summer packet. Solutions to the packet will be provided upon returning to school. Etra review for each topic can also be found in your tet book. 1

2 1. Find the - and y- intercepts. Graph the function 4y 8 X: Y:. Are the points solutions to 4y 8? Justify. a) (3, 4) b) (-, 6) 3. Find the slope of each line and graph. a) y 4 m = b) m = 4. If the point ( 3, 1 ) lies on the graph of the equation + ky = 11, find the value of k. 5. A line has equation y 5. Find the slope of a line that is a) parallel b) perpendicular

3 6. Put 79y 18 into slope intercept form and graph. 7. Find an equation in Standard Form of the line with intercept 5 and y-intercept Find an equation in Slope-Intercept Form of the line that goes through (8, 3) and (, -1). 9. Find an equation in Standard Form of the line through (1, -4) that is perpendicular to the line y Find an equation in Standard Form for the perpendicular bisector of the segment joining (0, 3) and (-4, 5). 11. Use substitution to find all points of intersection of the graphs of y and 6 5y 16. 3

4 1. Use elimination to find all points of intersection of the graphs of 3 y 10 and 5y Find all points of intersection of the system of y and 4 y 6 by graphing. 14. Solve each system of equations. y0 a) b) 4 y 0 y 3 0 y Without putting the parabola in verte form, identify the verte. Is the verte a maimum or minimum? a) f() = b) y =

5 16. Find the intercepts, zeros, ais of symmetry and verte of the graph of y Graph the parabola. 17. Change into verte form: a) f ( ) 6 8 b) 1 f 4 ( ) Simplify. 1 a) b) 3 i (6 7 i) 5 4i c) d) 1 i 16 4 i 5

6 19. Solve the quadratic. Solutions may be real or comple. a) 0 b) Factor each epression. a) y y b) 4 b 81 c) d) 3 8m 15 e) 3 3 y y 5y y f) 6n 11n g) 8 8 h) 15a b 10ab i) c 98 j) 8a a 6 6

7 1. Divide a) Use synthetic division. b) Use long division Find the - and y-intercepts of the graph of the equation. a) y 4 b) y 10 4 c) y 5 d) y 1 3. Find the domain and range of each: a) y = 3 9 b) y c) y 6 7 7

8 4. Let f() = + + 1, g() = + and h() = 4. Find: a) (g h)() b) (g()) c) f( ) d) ( f g)( ) e) f ( b) f) ( f g)( ) h g g) 5. Determine whether the relation determines a function. a) A person and their birthday f) b) 5y10 c) y 16 d) y 75 e) y 4 8

9 6. Evaluate each. a) Given f ( ) 3, find (5) f. b) Given 1 f ( ), find (3) f. 7. Simplify each a) ( 34 a 7 b 3 d a 4 b 5 c 6) 4 b) y y 1 1 Change the following equations into the form ( h) ( y k) r. Graph the functions y y 40 0 Equation Center Radius 9

10 9. 4y 4 4y Equation Center Radius 30. Find the equation of a circle. a) with center (, -3) and point (5, 1) b)with endpoints of the diameter at (-4,0) and (-4, -6) 31. In right triangle ABC, with angle B being the right angle, a) If AB = 16 and m A = 53, find BC b) If AB = 36 and AC = 47, find m A 10

11 3. In right triangle ABC, with angle B being the right angle, a) If AB = 16 and m A = 53, find BC b) If AB = 36 and AC = 47, find m A 33. Solve for the unknown sides. a) b) 45⁰ 8 in. 15cm. 60⁰ 34. Find the unknowns. a) Find BC. b) Find m C 0 c) Find AB. d) Given ABC withb 34, b = 15cm, and c 0cm., solve the triangle. 11

12 35. Convert each angle from radians to degrees. 7 a) 3 b) Convert each angle from degrees to radians in terms of pi. a) 370 b) Find a positive and negative co-terminal angle for each. a) -500 b) Find the reference angle for each. a) 700 b) Find the eact value for each trig function without a calculator. a) sin 5 b) cos( 30 ) 5 c) tan10 d) sin e) cos ( ) f) tan 4 6 g) sin 70 h) tan( ) 1

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14 4. Solve each equation a) (3) 5 b) 5log( ) 11 c) d) log 5 log log ( 1) e) 4 3(5 ) 15 f) 6 6 log log ( 1) log 0 g) h) Rewrite as a single log 1 log log4 log4 14

15 44. Graph, name and state the domain and range of each of these functions. Each graph should have a minimum of four points. f f f f f f