UNIT 1 EQUATIONS, INEQUALITIES, FUNCTIONS
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1 UNIT 1 EQUATIONS, INEQUALITIES, FUNCTIONS Act 1 Act 2 A rental car company charges $50.00 per day, plus $0.05 per mile driven. Write a function to model the story. How far did Angie drive if she rented the car for a day and ended up paying $70.50? Graph the system of inequalities y <x+2 x 4 y> -2 for x 2x-1 = 7 Act Act 4 the system of equations graphically y=-2x+7 y= x-8 Write the function that creates the following graph Solution: (, ) the system of equations algebraically x+2y = 16 2x-y = - Graph the Piecewise Function xx, xx < 0 ff(xx) = xx + 2, xx 0 Solution: (, )
2 Act 5 Act 6 f(x) = x+5 g(x) = (x-2) 2 h(x)= x-4 Evaluate f(-6)= 2x+ Find f -1 (x) (f+h)(-)= f(g(4))= Unit 2 QUADRATIC FUNCTIONS Act 7 x 2-64 x 2 +6x+9 x 2-9x+14 6x 2 +11x-10 by ing x 2 +5x-6=0 Act 8 What does i represent? Circle the correct answer i 29 = i, 1, -1, -i Act 9 2(x+) 2-6=12 (8+4i) (2+i) (2-4i)(+2i) Find the quotient in a+bi form 2 + ii 5 2ii by completing the square x 2 +10x = 8 Find the discriminant of 2x 2 +x+2 =0 by the quadratic formula 4x 2-12x+9=0 What does it tell you about the nature of the solutions? There are (circle): 2 Real, Rational solutions 2 Real, Irrational solutions 1 Real (double root) solution 2 Complex solutions
3 Act 11 and 12 Write the function that will produce the following graph in vertex form State the vertex, x-intercepts (if any) and y-intercept of **NO CALCULATOR f(x) = x 2-2x-15 Vertex: ( ) X Intercepts: (, ) (, ) Y Intercept (, ) Act 1 the system of equations (Calculator OK) y=x 2-4 y=x+2 (, ) (, ) Unit POLYNOMIALS Act 14 Rewrite the polynomial in standard form. State the degree and the leading coefficient 4x 2 +7x 5 -x +2 Degree: Describe the end behavior of f(x) =x 4 -x 2-2 As x->, y-> As x->-, y-> Leading Coefficient: Act 15 Add (x 2 +5x-)- (2x 2-2x+2) Multiply (x-)(x 2 +2x+1) Divide using long or synthetic division ( x 5 x 4 + 6x 2x 2 + x 8) ( x 1) A. B. C. D. x 2x + 4x + 2x+ x x + 6x 8x 7 x x + 6x + 6x+ 7 x x + 6x + 4x+ 5 x 1 4 2
4 (real of g(x)=x 4-16 ALGEBRA 2 FINAL EXAM Version A [Box answers, Attach all work] Name: Per: Act 16 Act 17 Expand using the binomial theorem Find the zeroes and complex) (x+) 4 The zeroes are: Act 17 Write the function for a third degree polynomial with zeros of -1, 2, and. What are the zeroes of x +2x 2-9x-18 *hint- factorable by grouping Zeroes: Unit 4 SERIES, EXPONENTIAL AND LOGARITHMIC FUNCTIONS Act 19 Act 20 A sequence is 7,11,15,19,2. Write the explicit rule for the sequence Find the 100 th term of the sequence 40,20,10,5. to find the nth term What is the sum of the first 100 terms? The sum is: Act 21 Sketch 2 x -4 clearly NO CALCULATOR An= Evaluate 4 (2) nn 1 nn=1 The sum is: Act 22 Express log w= k in exponential form w A) = k C) w = k k B) = w D) k = w Simplify log 10,000 Simplify log Rewrite as a logarithmic equation 2 x =2 What is the exact value of ln(e)? (A) 2 (B) e (C) 10 (D) 1
5 Act 2 Act 24 What is the domain and range of ln(x-2) 2 x- = 128 Domain: Range: Simplify () log 550-log 52 Evaluate log 100 to the nearest hundredth to the nearest hundredth e x =20 log (x+2)= to the nearest hundredth ln(x-2)= Unit 5 RADICAL AND RATIONAL FUNCTIONS Act 25 Write the equation of a function g(x) that represents the parent function xx reflected on the x-axis, stretched vertically by 2, and shifted three steps right g(x)= What are the domain an range of f(x) = xx + 2 xx 2 + = 7 xx 1 = 2 domain: range: Act 27 Act 28 It costs $100 to make a silk screen for a t-shirt, plus an additional $4.00 per shirt Sketch f(x) = 1 xx 4 Write a rational function to find the average cost per t-shirt where x is the number of t-shirts What is the least one can charge per shirt if they make 100 t-shirts and still make a profit?
6 Act 29 Multiply and simplify xx 2 4 xx 2 5xx xx + 4 Divide and Simplify xx 2 + 4xx + 4 5xx + 20 xx Add to make a single rational expression 2 xx xx Act = xx+2 xx What is the horizontal asymptote of 2xx+2 xx HA: y=. State answer in interval notation (xx+2)(xx ) > 0 (xx+4) Unit 6 TRIGONOMETRY Act 1 Act 2 Convert 120ᶛ to radians List one positive and one negative angle coterminal to 50ᶛ Convert 4ππ 5 radians to degrees No Calc sin(60ᶛ) = tan( ππ ) = 4 If the hour hand of a clock is 4 inches long, how many inches does the tip travel from 1:00 to 5:00 to the nearest tenth of an inch? cos(-180ᶛ)= Sin( 11ππ 4 ) Act Act 4 Given sin(θ) = and θ is in QII, what is cos θ? cos(2x)+1 5 State the function s (assume graphed in radians) Use identities to simplify to a single trig function tan(θ)csc(θ) Amplitude: Period: Range: Act 5 A windmill s blades are feet long. The center of the wheel is 12 feet off the ground and the windmill completes one counter clockwise rotation every 4 seconds. Write a sinusoidal function modeling the vertical position of the tip of the blade, with a starting height at the center of the wheel.
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