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MTH 100 Practice Problems for Test 2 Decide whether the equation is conditional, an identity, or a contradiction. Give the solution set. 1) 20k + 3 = 5(4k - 1) 13) -3 -2 -18 -12 2) 2(3g + 34) - 6g - 68 = 0 14) 9 6 -20 3) 3(27t + 6) = 9(5t - 2) Solve the equation. 5x -5x + 7 3 4) + =6 2 3 -18 4 -6 Decide whether the relation is a function, and give the domain and range. 15) For the compound inequality, give the solution set in both interval and graph forms. 5) -12 < 3x - 6 and 8x - 4 < 12 10 y 5 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 -10 -5 5 x 5 x 6) x - 2 > 2 or x + 3 < 1 -5 -10 Solve the inequality and graph the solution set. 7) h + 9 ≤ 8 16) 10 -35 -30 -25 -20 -15 -10 -5 0 5 8) 9x - 5 ≥ 7 -14 -12 -10 -8 y 5 -6 -4 -2 0 2 4 6 8 10 12 -10 Find the slope and the y-intercept of the line. 9) 4x + 5y = 23 -5 -5 -10 Find an equation of the line passing through the two points. Write the equation in standard form. 10) (4, -2) and (0, 3) Solve the problem. 17) Find f(4) when f(x) = x2 - 4x + 2. Decide whether the relation is a function. 11) {(-1, 7), (1, -9), (4, -9), (7, -5), (10, -3)} 18) Find f(-4) when f(x) = 5x2 + 2x + 5. 19) Find f(k - 1) when f(x) = 2x2 - 4x - 4. 12) {(-4, 1), (-3, -6), (3, -8), (3, 4)} 20) Find f(x+h) when f(x) = 3x2 - 4x + 5. 1 Evaluate the function. 21) Find f(4). x 4 1 0 -1 -4 Apply the product rule for exponents, if possible. 33) x6 · x5 y = f(x) 64 4 0 4 64 34) (-3x5 y)(-4x9 y2 ) 35) y5 · y8 · y2 Evaluate the expression. 36) 8 0 Solve the system by substitution. 22) x = 22 + 5y 3x - 6y = 21 37) -100 23) 5x - 2y = -1 x + 4y = 35 38) (-13)0 Write the expression with only positive exponents. Assume all variables represent nonzero numbers. Simplify if necessary. 39) 5x-2 24) x + y = 9 x+y=5 25) x + y = 2 2x + 2y = 4 Evaluate the expression. 1 40) 8 -2 Solve the system by elimination. 26) 8x + 9y = 8 -2x + 2y = -2 41) 27) 5x - 2y = 3 -20x + 8y = -12 2 -3 7 Apply the quotient rule for exponents, if applicable, and write the result using only positive exponents. Assume all variables represent nonzero numbers. x17 42) x7 28) 2x - 3y = -2 6x - 9y = 6 29) -7x + 7y = 14 4x + 5y = 28 43) Tell how many solutions the system has. Do not actually solve. 30) 3x - 4y = -1 6x - 8y = -2 x-16 x-4 Simplify the expression. Write your answer with only positive exponents. Assume that all variables represent nonzero real numbers. 44) (x5 )-3 31) 3x - y = 8 x + 3y = 16 32) x - 7 = y y+ 2=x 45) 2 -3w3 4 x Simplify the expression so that no negative exponents appear in the final result. Assume all variables represent nonzero numbers. 46) m -9 m 5 m -1 Divide. 63) 20x10 - 10x7 5x4 47) (6x-4 )5 (x2 )-5 64) 30x9 - 24x6 -6x9 48) 3x4 y2 3 9xy2 65) -8x5 - 6x4 - 14x3 -2x4 49) 2x3 y-3 -5 x-4 y2 66) -40x7 + 15x5 - 15x3 -5x5 Find the product. 50) (4m 2 )(2m 2 ) 67) x2 + 7x + 12 x+4 68) x2 + 8x + 9 x+6 69) 5m 3 + 29m 2 - 39m + 21 5m 2 - 6m + 3 51) (-3x3 y4 )(-5x4 y2 ) 52) 9ax6 (-4ax5 - 10x4 - 9) 53) -3x5 (-3x6 - 12x4 ) 54) (3x + 10)(x + 1) Factor out the greatest common factor. Simplify the factors, if possible. 70) 12wx - 20wy - 16wz 55) (9a + 2b)(8a - 9b) 71) 3x(2x - 5) - 4(2x - 5) 56) (7p - 1)(49p2 + 7p + 1) 72) 5t2 - 10t - 25 57) (2x2 + 4x + 2)(x2 - 3x + 4) Factor by grouping. 58) (a - 10)(a + 10) 73) 4n + 4x - n 2 - nx 59) (7r - 9)(7r + 9) 74) y2 + 8y + 6y + 48 60) (10m - 9w)(10m + 9w) 75) 36r2 + 45ry - 4xr - 5xy 61) (7a - 5)2 Factor out the variable that is raised to the smaller exponent. 76) 7x-8 + x-2 62) (5x - 8y) 2 77) -5x-2 + x2 3 Factor the trinomial completely. 78) x2 - x - 30 79) -x2 - 2x + 15 80) x2 + 7xy - 120y2 81) s2 t2 - 5st + 31 82) 16x2 + 24x + 9 83) 12y2 + 17y + 6 84) 22m 2 + 133mn + 66n 2 85) -49x2 - 14x + 15 86) 7x2 - 21xy - 28y2 87) 9x2 - 39x - 30 88) 36x2 + 21xy + 3y2 89) 8x4 + 18x2 + 9 90) 10(p + 2)2 + 13(p + 2) + 4 4 Answer Key Testname: MTH 100 PRACTICE PROBLEMS FOR TEST 2 SPRING 2014 1) Contradiction; ∅ 2) Identity; {all real numbers} 3) Conditional; {-1} 16 4) 5 34) 12x14y3 35) y15 36) 1 37) -1 38) 1 5 39) x2 5) (-2, 2) -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 40) 64 343 41) 8 6) (-∞, -2) ∪ (4, ∞) -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 42) x10 1 43) x12 7 7) [-17, -1] -35 8) -∞, - -30 -25 -20 -15 -10 -5 0 5 10 15 2 4 ∪ ,∞ 9 3 -14 -12 -10 -8 9) Slope - -6 -4 -2 0 2 4 6 8 10 12 14 4 23 ; y-intercept 0, 5 5 10) 5x + 4y = 12 11) Function 12) Not a function 13) Function 14) Not a function 15) Not a function; domain: [-2, 6]; range: [-7, -3] 16) Function; domain: (-∞, ∞); range: (0, ∞) 17) 2 18) 77 19) 2k2 - 8k + 2 44) 1 x15 45) 81w12 x4 46) 1 m5 47) 65 x30 48) 3x11y4 y25 49) 32x35 50) 8m 4 51) 15x7 y6 52) -36a 2 x11 - 90ax10 - 81ax6 53) 9x11 + 36x9 20) 3(x+h)2 -4(x+h)+25= 3(x2 +2xh+h 2 )-4(x+h)+5= 54) 3x2 + 13x + 10 55) 72a 2 - 65ab - 18b2 3x2 + 6xh + 3h 2 - 4x - 4h + 5 21) 64 22) {(-3, -5)} 23) {(3, 8)} 24) ∅; 25) infinitely many solutions 26) {(1, 0)} 27) infinitely many solutions 28) ∅ 29) {(2, 4)} 30) Infinitely many 31) One solution 32) No solution 33) x11 56) 343p3 - 1 57) 2x4 - 2x3 - 2x2 + 10x + 8 58) a 2 - 100 59) 49r2 - 81 60) 100m 2 - 81w2 61) 49a 2 - 70a + 25 62) 25x2 - 80xy + 64y2 63) 4x6 - 2x3 64) -5 + 4 x3 65) 4x + 3 + 5 7 x Answer Key Testname: MTH 100 PRACTICE PROBLEMS FOR TEST 2 SPRING 2014 66) 8x2 - 3 + 3 x2 67) x + 3 68) x + 2 - 3 x+6 69) m + 7 70) 4w(3x - 5y - 4z) 71) (3x - 4)(2x - 5) 72) 5(t2 - 2t - 5) 73) (n + x)(4 - n) 74) (y + 8)(y + 6) 75) (4r + 5y)(9r - x) 76) x-8 (7 + x6 ) 77) x-2 (-5 + x4 ) 78) (x + 5)(x - 6) 79) -(x - 3)(x + 5) 80) (x + 15y)(x - 8y) 81) Prime 82) (4x + 3)(4x + 3) 83) (3y + 2)(4y + 3) 84) (2m + 11n)(11m + 6n) 85) -(7x + 5)(7x - 3) 86) 7(x + y)(x - 4y) 87) 3(3x + 2)(x - 5) 88) 3(3x + y)(4x + y) 89) (4x2 + 3)(2x2 + 3) 90) (5p + 14)(2p + 5) 6