Alg1CP Sem2 Review. Multiple Choice Identify the choice that best completes the statement or answers the question. 1. Simplify y 5 y 3.

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1 lg1p Sem2 Review Multiple hoice Identify the choice that best completes the statement or answers the question. 1. Simplify y 5 y 3. y 2 y 8 y 15 2y 8 2. Simplify (6x 3 )(x 2 ). 6x 5 6x 6 7x 5 7x 6 3. Simplify (b 4 ) 3. b 7 3b 4 b 12 3b 7 4. Simplify. ssume the denominator is not equal to zero. a 11 a 28 a rectangle has a length of 25x 3 and a width of 5x 2. Find the area in square units. 25x 6 25x 5 125x 6 125x 5 6. Simplify. ssume the denominator is not equal to zero. 7. Simplify. ssume the denominator is not equal to zero. m 7 n 5 m 3 n 8. Find the degree of the polynomial b 5 + 2b Which of the following polynomials shows the terms of x 2 + 5x 3 4 2x arranged so that the powers of x are in descending order? 5x 3 2x + x x + x 2 + 5x 3 5x 3 4 2x + x 2 5x 3 + x 2 2x Find (2a 5) (3a + 1). 5a + 6 a 4 a 6 a Find 3m 2 (2m 2 m). 5m 4 3m 3 6m 4 3m 2 5m 4 3m 6m 4 3m 3

2 12.Kiki and Jasmine are both saving money for the same amount of time to buy cars. The equations below represent the amount of money Kiki K and Jasmine J saves in m months. Which equation represents the total amount of money T both girls save? K = 2, m J = 1, m T = 4, m T = 2, m 13. Simplify 3(x 2 + 2x) x(x 1). 4x 2 + x 2x 2 + 7x 2x 2 + 3x 2x 2 + 5x 14. Solve 3(2n 6) = 4(n 3). 3 T = 1, m T = 3, m 4x Each side y of a square is increased by 5 units. Which expression represents the number of square units in the area of the new square? y y + 10 y y + 10 y y square can be changed into a rectangle by increasing the length of the square by 5 units and increasing the width by 3 units. Which expression represents the area of the rectangle in square units? x 2 + 8x + 15 x x + 8 2x Find (2n 3)(n + 4). 3n + 1 2n 2 + 5n 12 2n n n Find (x + 3)(2x 2 4x + 8). 2x x x x x x 2 4x x 3 + 2x 2 4x Find (3y 1) 2. 6y 2 6y + 1 9y 2 6y + 1 9y 2 3y + 1 9y 2 6y Factor the monomial 20a 2 b 2 completely a a b 2 10 a a b b a a b b 4 5 a a b b 22. Factor 12x 3 y completely. 2 3 x y x x x y 4 3 x 3 y 12 x x x y 23. Find the GF of 24a and 32b. 2 6ab 4ab Which binomial is a factor of 2n 2 32n? 2n 8 n + 16 n 16 n Factor xy + 3x 2x 2 completely. x(y + 3 2x) (2x 3y)(y + x) x(y + 3) + 2x y(x + 3x 2x 2 ) 19. Find (2x 5)(2x + 5). 4x 4x x 2 20x 25

3 26.Solve b(b + 17) 0. { 17, 0} {0, 17} {17} Factor each trinomial. 27. m m + 42 (m + 1)(m + 13) (m + 6)(m + 7) (m + 10)(m + 3) (m 6)(m 7) 28. The area of a rectangle is (y 2 8y + 15) square inches. Which expression represents a possible length for the rectangle? (y + 5) (y 2) (y 15) (y 3) 29. 3m m 5 (3m + 1)(m 5) (3m 1)(m + 5) (3m + 5)(m 1) (3m 5)(m + 1) 30. Which binomial is a factor of 4x 2 13x + 3? 2x 3 2x 1 4x 3 4x Solve 2x 2 5x 3 = 0. (2m 5)(2m 5) prime 33. x (x + 4)(x + 4) (x + 4)(x 4) (x 4)(x 4) prime 34. Solve 64y 2 = 25 by factoring. 35. Which trinomial is a perfect square trinomial? 3x 2 6x + 9 x x + 25 x 2 + 8x 16 x x The area of a circle is given by ( k 2 12 k + 36 ) square inches. What is the radius of the circle? k + 3 k + 4 k 6 k Solve x 2 16x + 64 = 0. {8} { 8, 8} {4} { 4} 38. Solve 2x x 18. { 3} {3} { 3, 3} { 9} Factor each polynomial, if possible. If the polynomial cannot be factored, choose prime m 2 25 (2m + 5)(2m + 5) (2m + 5)(2m 5)

4 39.-Find two different integers such that the square of the integer is 12 less than seven times the integer. 3 and 4 3 and 4 4 and 3 3 and GEOMETRY The length of a rectangle is 5 centimeters more than the width. The area of the rectangle is 36 square centimeters. What is the length? 1, 3 1, 1 3, 1 1, One root of the quadratic equation whose related function is graphed lies between which consecutive integers? 4 cm 9 cm 14 cm 26 cm 41. Which equation corresponds to the graph shown? y = x y = x 2 1 y = x 2 1 y = x What is the equation of the axis of symmetry of the graph of y = x 2 + 6x 7? x = 6 x = 3 x = 3 x = Find the coordinates of the vertex of the graph of y = 4 x 2. Identify the vertex as a maximum or a minimum. (2, 0); maximum (0, 4); minimum (0, 4); maximum (2, 0); minimum 1 and 2 2 and 3 0 and 1 0 and Solve k 2 + 4k + 4 = 25 by taking the square root of each side. 5, 5 5 3, 7 7, Which value of c makes y 2 + 8y + c a perfect square? Which equation is equivalent to x 2 + 2x 3 = 0? (x + 1) 2 = 2 (x 1) 2 = 4 (x 1) 2 = 2 (x + 1) 2 = What are the roots of the quadratic equation whose related function is graphed below?

5 49.Solve the equation 2x 2 + 3x 5 = 0 by using the Quadratic Formula. 5, 1 1, State the value of the discriminant for y = x 2 8x etermine the number of real roots of n 2 5n 6 = 0. 1 real root 2 real roots infinitely many real roots no real roots 52. Which function is quadratic? y = x(3x + 2) x 5y = 9 y = 5 x 2 y = x 3 + 2x Which equation corresponds to the graph shown? TOURNMENTS chess tournament starts with 16 people competing. The exponential function describes how many people are remaining in the tournament after x rounds. How many people are left in the tournament after 2 rounds? Which set of data displays exponential behavior? y = 2 x + 2 y = 2 x What is the y-intercept on the graph shown? 57. Which equation represents exponential decay? y = 0.5(1.2) x y = 10(1.1) x y = 100(0.9) x y = 0.1x 2 Simplify each expression.

6 Solve Solve. 2, , Find the length of the hypotenuse of a right triangle if a = 3 and b = etermine which side measures form a right triangle. 4, 5, 6 3, 4, 5 5, 11, 12 4, 8, Find the distance between the points at (1, 3) and (9, 9) What is the length of a diagonal of a rectangle with a length of 8 meters and a width of 6 meters? 10 m 14 m 48 m 100 m 69. etermine which side measures form a right triangle. 10, 24, 28 13, 17, 21 5, 12, If y varies inversely as x and y = 18 when x = 2, find y when x = State the excluded value(s) of. 2 2, 2 2, 4 4

7 72. Simplify. 90m 3 n 3 6mn 73. Find. 77. Find (x 2 5x 14) (x + 2). x 7 5x 7 x + 7 x 2 6x Express 3600 minutes in days. 150 days 60 days 79. Find. 74. Find. 75. Find. 80. Find. 81. Find. 76. Find (a 2 + 4a 5) (5a). a 2 + 3a

8 82. Find. 83. Write as a rational expression Find. 300 km/hr 12 km/hr 300 m/hr 12 m/hr 88. basketball team uses red or white jerseys and red or white shorts. Which tree diagram shows the possible uniforms the team can wear? 15a 84. Simplify. 85. Solve store sells shirts with 3 designs and 4 colors. How many different shirts are possible if there is only 1 design and 1 color per shirt? Which value is an extraneous solution of 0 4?

9 The table shows the attendance of 300 ninth graders over the past month. Number of Number of bsences Students or more Find the probability that a randomly-chosen ninth grader will be absent 2 days next month. 91. Find the probability that a randomly-chosen ninth grader will be absent fewer than 2 days next month.