Algebra 2 Midterm Review 2024 PDF

Midterm Review 2024 Name Algebra 2 Period Date Simplify the algebraic expression. 1) -5(2x - 9) - 4x + 7 A) 14x + 52 B) -14x - 38...

Midterm Review 2024 Name Algebra 2 Period Date Simplify the algebraic expression. 1) -5(2x - 9) - 4x + 7 A) 14x + 52 B) -14x - 38 C) -14x + 52 D) 6x + 52 2) -5(3r + 4) + 10(9r + 9) A) -2r - 1 B) 75r + 4 C) -35r D) 75r + 70 Evaluate the algebraic expression for the given value or values of the variable(s). 3) 4x2 + 3y; x = 9 and y = 5 A) 127 B) 339 C) 1680 D) 1311 4) (x + 4y) 2 ; x = 3 and y = 4 A) 361 B) 49 C) 38 D) 19 Simplify the exponential expression. 2 5) (11x5 ) A) 11x10 B) 11x7 C) 121x10 D) 121x5 2 6) (-6x5 y6 ) A) -6x10y12 B) 36x10y12 C) 36x7 y8 D) -36x10y12 Simplify the exponential expression. Assume that variables represent nonzero real numbers. 7) (-4x4 y-5 )(2x-1 y) -8x3 -2x3 -8x5 A) -8x3 y6 B) C) D) y4 y4 y6 2 -8 x-4 y2 8) 2 -5 x-7 y4 8 1 x3 3x3 A) B) C) D) x y2 3 8x7 y2 8y2 y2 Simplify the radical expression. 9) 72 A) 12 B) 8 C) 2 6 D) 6 2 10) 325 A) 325 B) 25 13 C) 5 13 D) 65 Simplify each term. Then add or subtract terms whenever possible. 11) 8 3 - 6 12 A) -20 3 B) -4 3 C) 2 3 D) 4 3 1  12) -4 2 - 5 18 A) -11 2 B) -9 2 C) 19 2 D) -19 2 Simplify the radical expression. 3 13) -125 A) -5 B) -125 C) 5 D) not a real number 3 14) x7 3 3 3 3 A) x2 x B) x x2 C) x x D) x2 x2 Evaluate the expression using radicals. 15) 100 1/2 A) 20 B) 10 C) 5 D) 40 16) 644/3 A) 1024 B) 16,384 C) 4096 D) 256 Perform the indicated operations. Write the resulting polynomial in standard form. 17) (-3x5 - 5x2 + 5) + (7x5 + 9x2 + 5) A) 4x5 + 12x2 + 0 B) 4x5 + 4x2 + 0 C) 4x5 + 4x2 + 10 D) 18x7 18) (5x5 + 8x4 - 9x3 + 4) - (3x5 + 4x4 - 2x3 - 9) A) 2x5 + 12x4 - 11x3 - 5 B) 8x5 + 12x4 - 11x3 + 13 C) 2x5 + 4x4 - 7x3 + 13 D) 8x5 + 12x4 - 11x3 - 5 19) (x + 3)(8x2 + 4x + 7) A) 8x3 + 24x2 + 12x + 21 B) 96x4 + 8x3 + 84x2 + 21 C) 32x3 + 16x2 + 28x D) 8x3 + 28x2 + 19x + 21 20) (7x - 1)(x2 - 5x + 1) A) 7x3 + 36x2 - 12x + 1 B) 7x3 - 36x2 + 12x - 1 C) 7x3 - 34x2 + 2x - 1 D) 7x3 - 35x2 + 7x + 1 Factor out the greatest common factor. 21) 3x - 27 A) 3x(x - 9) B) 3(x - 27) C) 3x(-9) D) 3(x - 9) 22) 5x2 - 15x A) 5x(x - 3) B) 5(x2 - 3x) C) 5x(x - 3x) D) x(5x - 15) Factor by grouping. 23) x3 + 8x - 5x2 - 40 A) (x + 5)(x2 + 8) B) (x - 5)(x + 8) C) (x - 5)(x2 + 8) D) (x - 5)(x2 - 8) 2  24) 5x3 - 10x2 + 8x - 16 A) (x - 2)(5x2 - 8) B) (x - 2)(5x2 + 8) C) (x - 2)(5x + 8) D) (x + 2)(5x2 + 8) Factor the quadratic trinomial. 25) x2 + 5x - 24 A) (x - 8)(x + 1) B) (x + 8)(x - 3) C) (x - 8)(x + 3) D) prime 26) x2 - x - 72 A) (x + 9)(x - 8) B) (x + 8)(x - 9) C) (x + 1)(x - 17) D) prime 27) 3x2 - 14x + 16 A) (3x - 8)(3x + 2) B) (3x - 8)(x - 2) C) (3x + 2)(x - 8) D) 3(x - 8)(x - 2) 28) 7x2 + 32x + 15 A) (7x + 3)(x - 5) B) (7x + 5)(x - 3) C) (7x - 3)(x + 5) D) prime Factor the difference of two squares. 29) x2 - 100 A) (x + 10)2 B) (x - 10)2 C) (x + 10)(x - 10) D) prime 30) 4x2 - 81 A) (2x + 9)(2x - 9) B) (2x + 9)2 C) (2x - 9)2 D) prime Factor completely, or state that the polynomial is prime. 31) 2x2 - 16x - 18 A) 2(x + 1)(x - 9) B) 2(x2 - 8x - 9) C) (2x + 2)(x - 9) D) (x + 1)(2x - 18) 32) x2 + 4 A) (x + 2)2 B) (x - 2)2 C) (x + 2)(x - 2) D) prime Solve and check the linear equation. 33) 6x - (2x - 1) = 2 1 1 1 1 A) - B) C) - D) 4 4 8 8 34) 2x - 4 = -3 + 10x 1 12 A) - 8 B) - C) - D) 8 8 7 Solve the equation. x x 35) = + 8 2 5 80 A) {16} B) {10} C) {40} D) 3 3  x x 36) 20 - = 2 3 50 A) 50 B) C) {4} D) {24} 3 Solve the absolute value equation or indicate that the equation has no solution. 37) 3 x - 3 = 18 A) {3} B) {3, -9} C) {9, -3} D) ∅ 38) 8x - 5 - 1 = -7 1 11 11 1 1 A) - , - B) , C) - D) ∅ 8 8 8 8 8 Solve the system of equations (two linear functions). 39) y = 4x + 7 y = 9x + 6 39 1 1 39 A) {(1, 11)} B) , C) , D) ∅ 5 5 5 5 40) 2x + 7y = -10 2x + 2y = 20 A) {(16, -6)} B) {(-16, 2)} C) {(-6, 16)} D) {(-16, 7)} Find the slope of the line that goes through the given points. 41) (2, -3), (-7, 8) 9 11 11 A) - B) - C) - 1 D) 11 9 9 42) (-8, -9), (-8, -3) 3 3 A) B) C) Undefined D) 0 4 8 43) (6, -1), (2, -1) 1 1 A) B) - C) 0 D) Undefined 2 4 Use the given conditions to write an equation for the line in point -slope form. 44) Slope = 3, passing through (-7, 8) A) y + 8 = 3(x - 7) B) y - 8 = 3(x + 7) C) x - 8 = 3(y + 7) D) y = 3x + 29 45) Passing through (7, 3) and (5, 2) 1 1 1 1 A) y - 3 = (x - 5) or y - 2 = (x - 7) B) y - 3 = (x - 7) or y - 2 = (x - 5) 2 2 2 2 1 1 C) y + 3 = (x + 7) or y + 2 = (x + 5) D) y - 3 = 7(x + 7) or y - 2 = 5(x - 3) 2 2 4  46) Slope = 4, passing through (-8, 7) A) y + 7 = 4(x - 8) B) y - 7 = 4(x + 8) C) x - 7 = 4(y + 8) D) y = 4x + 39 47) Passing through (4, 5) and (6, 6) 1 1 A) y - 5 = 4(x + 4) or y - 6 = 6(x - 5) B) y - 5 = (x - 6) or y - 6 = (x - 4) 2 2 1 1 1 1 C) y - 5 = (x - 4) or y - 6 = (x - 6) D) y + 5 = (x + 4) or y + 6 = (x + 6) 2 2 2 2 Use the given conditions to write an equation for the line in slope -intercept form. 48) Slope = 3, passing through (3, 8) A) y - 8 = 3x - 3 B) y - 8 = x - 3 C) y = 3x - 1 D) y = 3x + 1 49) Slope = 2, passing through (-6, 3) A) y = 2x - 15 B) y - 3 = x + 6 C) y = 2x + 15 D) y - 3 = 2x + 6 50) Passing through (5, 3) and (4, 6) A) y - 3 = - 3(x - 5) B) y = - 3x + 18 C) y = mx + 18 D) y = 3x + 18 51) Passing through (1, -8) and (-7, 8) A) y = - 2x - 6 B) y = mx - 6 C) y = 2x - 6 D) y + 8 = - 2(x - 1) Determine the slope and the y -intercept of the graph of the equation. 52) 6x - 7y - 42 = 0 6 7 6 A) m = - ; (0, 6) B) m = 6; (0, 42) C) m = ; (0, 7) D) m = ; (0, -6) 7 6 7 53) -x + 3y - 27 = 0 1 1 A) m = - ; (0, 9) B) m = 3; (0, -27) C) m = ; (0, 9) D) m = -1; (0, 27) 3 3 5 Graph the line whose equation is given. 3 54) y = - x + 1 4 y 6 5 4 3 2 1 -6 -5 -4 -3 -2 -1 -1 1 2 3 4 5 6 x -2 -3 -4 -5 -6 A) B) y y 6 6 5 5 4 4 3 3 2 2 1 1 -6 -5 -4 -3 -2 -1 -1 1 2 3 4 5 6 x -6 -5 -4 -3 -2 -1 -1 1 2 3 4 5 6 x -2 -2 -3 -3 -4 -4 -5 -5 -6 -6 C) D) y y 6 6 5 5 4 4 3 3 2 2 1 1 -6 -5 -4 -3 -2 -1 -1 1 2 3 4 5 6 x -6 -5 -4 -3 -2 -1 -1 1 2 3 4 5 6 x -2 -2 -3 -3 -4 -4 -5 -5 -6 -6 6 Find an equation for the line with the given properties. 55) The solid line L contains the point (-2, 4) and is perpendicular to the dotted line whose equation is y = 2x. Give the equation of line L in slope-intercept form. y 5 -5 5 x -5 1 1 1 A) y = - x+3 B) y - 4 = 2(x + 2) C) y = x+3 D) y - 4 = - (x + 2) 2 2 2 56) The solid line L contains the point (3, 2) and is parallel to the dotted line whose equation is y = 2x. Give the equation for the line L in slope-intercept form. y 5 -5 5 x -5 A) y = 2x - 4 B) y - 2 = 2(x - 3) C) y = 2x + b D) y = 2x - 1 Express the interval in set-builder notation and graph the interval on a number line. 57) (-1, 4] -10-9 -8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8 9 10 A) {x -1 < x < 4} B) {x -1 ≤ x ≤ 4} -10-9 -8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8 9 10 -10-9 -8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8 9 10 C) {x -1 < x ≤ 4} D) {x x ≤ 4} -10-9 -8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8 9 10 -10-9 -8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8 9 10 7  7 58) - ∞, 2 -10-9 -8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8 9 10 7 A) {x 2 ≤ x ≤ 7} B) x x > 2 -10-9 -8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8 9 10 -10-9 -8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8 9 10 7 7 C) x x ≤ D) x x < 2 2 -10-9 -8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8 9 10 -10-9 -8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8 9 10 59) [3, ∞) -10-9 -8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8 9 10 A) {x x ≥ 3} B) {x x ≥ 3} -10-9 -8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8 9 10 -10-9 -8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8 9 10 C) {x x > 3} D) {x x > 3} -10-9 -8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8 9 10 -10-9 -8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8 9 10 Use the graph to determine the functionʹs domain and range. 60) y 6 5 4 3 2 1 -6 -5 -4 -3 -2 -1 1 2 3 4 5 6 x -1 -2 -3 -4 -5 -6 A) domain: (- ∞, -5) or (-5, ∞) B) domain: (- ∞, ∞) range: (- ∞, -2) or (-2, ∞) range: (- ∞, ∞) C) domain: (- ∞, ∞) D) domain: [-5, ∞) range: [-2, ∞) range: [-2, ∞) 8  61) y 6 5 4 3 2 1 -6 -5 -4 -3 -2 -1 1 2 3 4 5 6 x -1 -2 -3 -4 -5 -6 A) domain: (- ∞, -3] B) domain: (- ∞, -3) or (-3, ∞) range: (- ∞, 2] range: (- ∞, 2) or (2, ∞) C) domain: (- ∞, ∞) D) domain: (- ∞, ∞) range: (- ∞, ∞) range: (- ∞, 2] Identify the intervals where the function is changing as requested. 62) Increasing 5 y 4 3 2 1 -10 -8 -6 -4 -2 2 4 6 8 10 x -1 -2 -3 -4 -5 A) (3, 6) B) (-2, 0) C) (-2, ∞) D) (3, ∞) 9  63) Decreasing y 5 4 3 2 1 -10 -8 -6 -4 -2 2 4 6 8 10 x -1 -2 -3 -4 -5 A) (0, 3) B) (0, -2) C) (- ∞, -2) D) (- ∞, 3) Use the shape of the graph to name the function. 64) y x A) Standard cubic function B) Standard quadratic function C) Square root function D) Constant function 65) y x A) Absolute value function B) Standard cubic function C) Constant function D) Identity function 10 Begin by graphing the standard quadratic function f(x) = x 2. Then use transformations of this graph to graph the given function. 66) h(x) = (x - 5)2 + 7 10 y 8 6 4 2 -10 -8 -6 -4 -2 2 4 6 8 10 x -2 -4 -6 -8 -10 A) B) y y 10 10 8 8 6 6 4 4 2 2 -10 -8 -6 -4 -2-2 2 4 6 8 10 x -10 -8 -6 -4 -2-2 2 4 6 8 10 x -4 -4 -6 -6 -8 -8 -10 -10 C) D) y y 10 10 8 8 6 6 4 4 2 2 -10 -8 -6 -4 -2-2 2 4 6 8 10 x -10 -8 -6 -4 -2-2 2 4 6 8 10 x -4 -4 -6 -6 -8 -8 -10 -10 11 67) h(x) = -(x + 7)2 - 2 y 10 8 6 4 2 -10 -8 -6 -4 -2 2 4 6 8 10 x -2 -4 -6 -8 -10 A) B) y y 10 10 8 8 6 6 4 4 2 2 -10 -8 -6 -4 -2-2 2 4 6 8 10 x -10 -8 -6 -4 -2-2 2 4 6 8 10 x -4 -4 -6 -6 -8 -8 -10 -10 C) D) 10 y 10 y 8 8 6 6 4 4 2 2 -10 -8 -6 -4 -2 2 4 6 8 10 x -10 -8 -6 -4 -2 2 4 6 8 10 x -2 -2 -4 -4 -6 -6 -8 -8 -10 -10 12  1 68) g(x) = - (x - 5)2 + 3 3 y 10 8 6 4 2 -10 -8 -6 -4 -2 2 4 6 8 10 x -2 -4 -6 -8 -10 A) B) y y 10 10 8 8 6 6 4 4 2 2 -10 -8 -6 -4 -2-2 2 4 6 8 10 x -10 -8 -6 -4 -2-2 2 4 6 8 10 x -4 -4 -6 -6 -8 -8 -10 -10 C) D) y y 10 10 8 8 6 6 4 4 2 2 -10 -8 -6 -4 -2-2 2 4 6 8 10 x -10 -8 -6 -4 -2-2 2 4 6 8 10 x -4 -4 -6 -6 -8 -8 -10 -10 Find the product and write the result in standard form. 69) -3i(5i - 4) A) 12i - 15i2 B) 15 + 12i C) 12i + 15i2 D) -15 + 12i 70) (8 + 2i)(3 - 7i) A) 38 + 50i B) -14i2 - 50i + 24 C) 10 + 62i D) 38 - 50i Rationalize the denominator and simply the complex number. 2 71) 3+i 3 1 3 1 3 1 3 1 A) + i B) - i C) - i D) + i 5 5 4 4 5 5 4 4 13  7 + 3i 72) 3 - 7i A) -1 B) 1 C) -i D) i Solve the equation by factoring. 73) x2 = x + 20 A) {-4, -5} B) {4, 5} C) {-4, 5} D) {1, 20} 74) 6x2 + 23x + 20 = 0 5 4 5 4 5 1 5 4 A) ,- B) , C) - ,- D) - ,- 2 3 2 3 6 5 2 3 75) 12x2 - 7x = 0 7 7 7 7 A) {0} B) 0, C) ,- D) - ,0 12 12 12 12 Solve the equation by the square root property. 76) 4x2 = 44 A) {-11, 11} B) {- 11, 11} C) {22} D) {12} 77) 6x2 + 4 = 58 A) {29} B) {-4, 4} C) {-3, 3} D) {3} Determine the constant that should be added to the binomial so that it becomes a perfect square trinomial. Then write and factor the trinomial. 78) x2 + 4x A) 16; x2 + 4x + 16 = (x + 4)2 B) 4; x2 + 4x + 4 = (x + 2)2 C) 4; x2 + 4x + 4 = (x + 16)2 D) 2; x2 + 4x + 2 = (x + 4)2 79) x2 - 12x A) 144; x2 - 12x + 144 = (x - 12) 2 B) -36; x2 - 12x - 36 = (x - 6) 2 C) 36; x2 - 12x + 36 = (x - 6) 2 D) -144; x2 - 12x - 144 = (x - 12) 2 Solve the equation by completing the square. 80) x2 - 14x + 13 = 0 A) {1, 13} B) {- 13, 13} C) {1, 12} D) {-13, -1} 81) x2 + 8x - 3 = 0 A) {-4 - 19 , -4 + 19} B) {-1 - 19 , -1 + 19} C) {-4 - 1 19 , -4 + 1 19} D) {4 + 19} 82) x2 + 8x + 25 = 0 A) {-4 ± 3i} B) {-4 + 3i} C) {-4 ± 9i} D) {-7, -1} 14 Solve the equation using the quadratic formula. 83) x2 + 3x + 1 = 0 3- 5 3+ 5 A) , 2 2 -3 - 13 -3 + 13 B) , 2 2 -3 - 5 -3 + 5 C) , 6 6 -10 - 15 -10 + 15 D) , 2 2 -3 - 5 -3 + 5 E) , 2 2 Compute the discriminant. Then determine the number and type of solutions for the given equation. 84) x2 + 6x - 7 = 0 A) -8; two complex imaginary solutions B) 0; one real solution C) 64; two unequal real solutions 85) x2 + 8x + 16 = 0 A) 0; one real solution B) -64; two complex imaginary solutions C) 64; two unequal real solutions 86) 4x2 = -5x - 3 A) 0; one real solution B) -23; two complex imaginary solutions C) 73; two unequal real solutions Solve the equation using the quadratic formula. 87) 2x2 + 10x + 5 = 0 -5 - 15 -5 + 15 -5 - 15 -5 + 15 -5 - 35 -5 + 35 A) , B) , C) , 2 2 4 4 2 2 88) x2 - 10x + 50 = 0 A) {5 - 5i, 5 + 5i} B) {5 - 25i, 5 + 25i} C) {0, 10} D) {5 + 5i} 89) 8x2 + 1 = 3x -3 ± i 23 3 ± i 23 -3 ± 23 3 ± 23 A) B) C) D) 16 16 16 16 Solve the system of equations (quadratic and linear function). 90) -2x - y = -52 y = x2 + 4 A) {(6, 32), (-8, 60)} B) {(-6, 40), (-8, 68)} C) {(-6, 40), (8, 68)} D) {(6, 40), (-8, 68)} 15 91) x + y = 4 y = x2 - 8x + 16 A) {(-3, 7), (-4, 8)} B) {(3, 7), (4, 0)} C) {(3, 1), (4, 0)} D) {(4, 0)} 92) y = (x + 5)2 + 1 2x - y + 10 = 0 A) {(-4, 2)} B) {(-5, 0)} C) {(-4, 2), (4, 18)} D) {(0, 10), (0, 26)} 16