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Algebra I – Semester 1 Final Review - 2015 Name___________________________ Foundations for Algebra Write the expression. 1) 5 more than x 2) n less than 2 Simplify 2 7 4) 5 10 5) 3) 4 more than twice a 3 9 4 10 6) 3 42 2 1 6 2 8) 23 (4 5) 3 7) 3.2 2.1 5.3 3.6 9) Evaluate 3x 2 2 y z if x=-3, y=-1, z = 4 10) Fred buys 10 computers for his child’s school for a total of $5000. Each additional computer after the first 10 costs $300. How much would Fred spend if he bought 25 computers? Use an expression to find this. Simplify 11) -62 12) 14) 15) 2a – 4b + 6c – c + 5b – (-4a) -3(x+3) –(5x-7) (-6)2 13) (-5)2-52 16) Classify the numbers using the following options: Real, Rational, Irrational, Natural, Whole, Integer a) 9 b) 3 4 c) 25 d) 2) 2 1 5 x 3 4 6 e) -2 3 Equations Solve 5 1) x 10 8 4) 4 – 6a + 4a = -1 -5(7 – 2a) 3) -2(x – 4) = 11 5) 12x – 3 + x = 5x – 4 + 8x 6) The museum charges $5 admission plus $2 for every hour spent in the building. Write an equation to represent this. How much would you spend if you were at the museum for 5 hours? 1 7) Solve for b: A bh 2 8) Solve for x: xyz = -5 9) Solve for y: ab 9 y 10) The length of a rectangle is 3cm less than 8 times the width. The perimeter is 30 cm. Find the length and width. 11) Find three consecutive even integers whose sum is 72. Solve for y: 12) 2x + 3y = 6 13) x – 2y = 10 14) Find four consecutive integers such that the sum of the second and twice the third is 101. 15) The sum of the angle measures of any triangle is 180⁰. Find the angle measures of a triangle if the second angle is three times the first and the third angle is 5 more than the first. Inequalities Solve and graph on a number line 1) d – 5 > -7 2 2) x 8 3 3) 2(7n – 1) < 3(5 – n) 4) Find all sets of two consecutive positive integers whose sum is no more than 5. 5) Mrs. Smith is taking herself and her 5 children to an amusement park. Tickets cost $20 per person. Her kids want some snacks when they get there. If Mrs. Smith has $254 to spend for the whole day, how many snacks can she buy? Snacks cost $5 each. 6) Write and solve the inequality: 2 less than 5 times a number is at least 19. Solve and graph on a number line 7) -4 < x + 6 < 10 8) 3 < s + 9 OR 1 > s – 4 9) x 7 10 12 10) 2 x 2 18 Functions 1) State the domain and range { (1, -1), (3, 5) (3, -2), (6, -1) } Domain: Range: Is it a function? 2) What is the vertical line test? Draw a sketch of a graph that would not be a function. 3) Write a function rule for: x 1 2 3 y 1 4 9 For the function, find the indicated values. 4) f ( x) 2 x 5 , find f(-3) 5) f (b) b2 9 , find f(-4) 6) What is the definition of a function (in your own words)? 7) Draw a graph that represents the following situation: A car accelerates and travels at a constant speed for a period of time. The car then slows to a stop. Linear Functions 1) Does something have to be linear in order to be a function? Put the following into standard form. 2) y = 4x + 3 3) 1 2 y 3x 2 3 Find the x and y intercepts. Graph. 4) -3x-2y = 12 Find the slope. 5) (3, -2) (5, 4) 6) (4, 5) (4, -10) Put the following into slope-intercept. Graph. 8) a) 2x – 3y = 9 b) y – 2x +5 = 0 7) (-7, 9) (-15, -5) Write the equation of the line in slope-intercept form with the given information. 1 9) slope = -4 y-int = 17 10) slope = through the point (5, -2) 4 11) Through the points (-6, 3) (9, 8) 12) Parallel to the line y = 1 x 9 through point (9, 1) 3 1 13) Perpendicular to the line y x 19 through the point (-2, 3) 5 14) Write an equation of the following in point-slope form: slope = -7 through the point (-1, 3) Systems of Equations 1) Solve the following by graphing: 2x – 5y = 20 and y 2 Solve the following by substitution. 2) y = ½ x – 3 and 2y – 3x = -2 3) 3x = 15 – 3y and 3y = 3x +1 Solve the following by elimination. 4) 5x + 6y = -11 and 3x + y = -4 5) 3x – 5y = 7 and 5x – 2y = -1 6) Tom bought 30 tickets to the symphony and spent $200. He bought a combination of regular tickets for $5 and premium tickets for $15. Write a system of equations. How many regular and premium tickets did Tom buy? Graph 7) y < 3x + 4 8) 3x - 2y < 6 9) x > 4 and y < -2 10) y < ½x + 1 x+y<3