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Review Advanced Algebra/Trigonometry Honors Name ______________________ Basic Things You Absolutely Need to Know: Remember? Special Triangles Domain, Range, Roots Domain: x-values x 0 x 4 Range: y-values y 3 y Roots: where the function crosses the x-axis (“zeros”) Simplifying Fractions Ratios Adding/Subtracting: Find the LCM of the denominators… 2 1 2 3 1 5 6 5 11 5 3 5 3 3 5 15 15 15 3 2 3 20 60 60 15 4 = now simplify 2 = 5 9 5 9 45 15 3 45 Dividing: Multiply the numerator by the reciprocal of the denominator Multiplying: Multiply across and simplify… 2 1 12 16 12 15 3 4 35 9 1 now make ones… 2 1 or 2 5 15 5 15 5 16 5 44 4 4 **When multiplying or dividing, change mixed numbers into improper fractions. Proportions Cross-multiply!! 5x 1 7 now cross-multiply 10 x 2 28 simplify 10x 30 x 3 4 2 Fractions with Radicals When a single radical is in the denominator 3 2 3 2 7 3 14 7 7 7 7 multiply the top and bottom by the radical. When a sum/difference of a radical is in the denominator, multiply the top and bottom by the conjugate 3 x 7 3 3x 3 7 2 x 7 x 7 x 7 x 7 C. Hunsberger Page 1 of 11 Review Advanced Algebra/Trigonometry Honors Name ______________________ Practice Special Triangles Simplify: Fill in the missing angles and sides: 1. x 4 7 11 2x 2. 7 5y 3 30° 8 3. 2 3 5 4. 4 x 5 5. 6 x 1 7 3 6. 7 x 1 2x 3 4 5 Functions Factor Completely 1. 9 x 2 49 Domain __________________ 2. 2 x 2 10 x 28 Range ___________________ Root(s) ___________________ C. Hunsberger 3. 2 xy 5 y 6 x2 15x Page 2 of 11 Review Advanced Algebra/Trigonometry Honors Name ______________________ More Practice!! C. Hunsberger Page 3 of 11 Review Advanced Algebra/Trigonometry Honors Name ______________________ More Practice!! C. Hunsberger Page 4 of 11 Review Advanced Algebra/Trigonometry Honors Name ______________________ Factoring: C. Hunsberger Page 5 of 11 Review Advanced Algebra/Trigonometry Honors C. Hunsberger Name ______________________ Page 6 of 11 Review Advanced Algebra/Trigonometry Honors C. Hunsberger Name ______________________ Page 7 of 11 Review Advanced Algebra/Trigonometry Honors Name ______________________ Remember… linear functions? Lines, slope, intercepts, slope-intercept form, pointslope form, standard form, x-axis, y-axis, origin, quadrants, distance and mid-point formulas, perpendicular, parallel, etc. Take a look at the following problems. Try to do the problems you know, and begin those you are unclear about. When you have looked through all of the problems and worked through them, complete a K-W-L chart on linear functions. Ask yourself what you already KNOW about linear functions and what you WANT to know; at the end of the first unit, we will fill in what you have LEARNED. 1. Let A = (-4, 7) and and B = (4, -5). a. Find the length of segment AB. (4 4) 2 (7 5) 2 (8) 2 (12)2 64 144 208 16 13 4 13 b. Find the coordinates of the midpoint of segment AB. 4 4 7 5 , 2 2 0,1 2. Find the value of a if it is known that the point (-3, 7) lies on the line 2𝑥 + 𝑎𝑦 = 26. 2( 3) a (7) 26 6 7 a 26 7 a 32 32 a 7 3. Solve the system of equations 3𝑥 − 2𝑦 = 3 and 5𝑥 + 4𝑦 = 16 for the variables. What does your solution mean in reference to the graph of the system? 6x 4 y 6 3(2) 2 y 3 2(3x 2 y 3) 5 x 4 y 16 6 2y 3 11x 22 x2 2 y 3 y 3 3 2, 2 2 The solution is the intersection points of the two lines. 4. Find the slope and the y-intercept of the line 3𝑥 + 2𝑦 = −1. 3 x 2 y 1 3 1 Slope: Y-intercept: 2 y 3 x 1 3 1 y x 2 2 C. Hunsberger 2 2 Page 8 of 11 Review Advanced Algebra/Trigonometry Honors Name ______________________ 5. Tell which of the following equations have parallel line graphs and which have perpendicular line graphs. a. 3𝑥 − 2𝑦 = 12 3x 2 y 12 2 y 3 x 12 3 y x6 2 3 b. 𝑦 = 2 𝑥 + 1 y 3 x 1 2 c. 4𝑥 + 6𝑦 + 20 = 0 4 x 6 y 20 6 y 4 x 20 2 10 y x 3 3 a b, a c , bc 6. Write an equation of the line through the points (6, -2) and (3, 7). Slope: 7 2 9 3 36 3 7 3(3) b 7 9 b 16 b y 3x 16 7. Write an equation of the line through the point (2, 5) and parallel to the line 4𝑥 − 3𝑦 = −50. 4 (2) b 3 4 x 3 y 50 8 4 7 y x 5 b 3 y 4 x 50 3 3 3 4 50 7 y x b 3 3 3 8. Write an equation of the line with x-intercept 2 and y-intercept -3. 5 (2, 0) (0, 3) C. Hunsberger 3 m(0) b 3 b 0 m(2) 3 3 2m 3 m 2 y 3 x 3 2 Page 9 of 11 Review Advanced Algebra/Trigonometry Honors Name ______________________ 9. Write an equation of the vertical line through the point (5, 1). x=5 10. a. Writing: Describe the steps for finding an equation of the median from vertex A in triangle ABC. 1. Get midpoint of segment BC 2. Use point A and midpoint, and plug them in for x and y to solve for the slope and y-intercept of the line. 3. Put it into slope-intercept form. b. Write an equation of the median from A if A(2,1), B(4, 8), and C(8,-2) are the vertices of triangle ABC. Midpoint of BC: (6,3) Use (2, 1) and (6,3) 2 1 m=4=2 1 3 (6) b 2 3 3b 0b y 1 x 2 11. Twyla buys a 10-ride pass so that she can use public transportation to go to and from work. The pass costs $15 and is worth $0 after the tenth ride. a. Give an equation of the linear function that models the value of the pass as a function of the number of rides completed. 0 m(10) 15 15 10m 3 m 2 1.5 m y 1.5 x 15 b. Use the equation to find the value of the pass after the sixth ride. y 1.5(6) 15 y6 C. Hunsberger So, the pass has $6.00 left on it after six rides. Page 10 of 11 Review Advanced Algebra/Trigonometry Honors Name ______________________ Linear Functions K C. Hunsberger NOW W ant to know What I L earned Page 11 of 11