Math Placement Exam Practice Problems Georgia State University

Part 1 Part 1 Simplify (2a^3b)^-3 (2^-3 a^(3 -3) * b^-3) 2^-3 a^-9b^-3 1/8a^9b^3 Simplify (-4x^2y^-3)^-2 y^6/16x^4 Simplify Radical 1/64 Radical 1/Radical 64 1/8 ^3 Radical -27 -3 Complex numbers: Complex numbers Find x and y such that the following is correct: 3x + 5yi= 15 + 5i 3x + 5yc= 15 + 5c 3x=15 and 5yc=5c x=5 and y=1 Find x and y such that the following is correct: 10x -4yi = 20 + 1/2i 10x - 4yc = 20 + 1/2x x=2 and y=-1/8 Simplify Radical 27 - 18 Radical 27 - 18 Radical 9 3 Simplify Radical -1/25 i/5 Complex Numbers and Exponents Complex Numbers of Exponents Simplify i^15 i^15 (i^3)^5 -i^5 -(i^3 * i^2) -(i * -1) -i Simplify i^47 -i Solving Quadratic Equations by Factoring Solving Quadratic Equations by Factoring Solve for x in 3x^2 + 8x + 4 = 0 3x^2 + 8x + 4 = 0 (3x + 2)(x+2)= 0 3x + 2 = 0 of x + 2= 0 x= -2/3 or x= -2 Solve for x in x^2 + 4 = 0 x= +/- 2 Solving Quadratic Equations that are irreducible Solving Quadratic Equations that are irreducible Solve for x in x^2 + 7x + 3 = 0 x^2 + 7x + 3 = 0 x= -7+/- Radical 49 -4(1)(3)/2*1 x= -7 +/- Radical 37 /2 Solve for x in 2x^2 + 10x -1 = 0 2x^2 + 10x -1 = 0 x=b-10 +/- Radical 108 / 4 Solving and graph in Equalities Solving and graph in Equalities Solve and graph 2-4x > 10 2-4x> 10 -4x >8 x < -2 Solve for x and graph the solution on number line for x^2 -2 >/eqaul to 1 x^2 -2 >/ equal to 1 x >/equal to radical 3 or x </ equal to - radical 3 Solve the following equations for x and y 3x +2y =5 7x - y = 1 3x + 2y = 5 7x - y =1 3x + 2y = 5 2(7x - y =1) 3x + 2y = 5 14x -2y= 2 17x= 7 x= 7/17 Plug in for x 3(7/17) + 2y = 5 21/17 + 2y = 5 2y = 5 - 21/17 2y= 78/17 y= 39/17 Solve the following equations for w and z: w + 2z = 10 4w + z = 5 w + 2z = 10 4w + z = 5 w + 2z = 10 -2(4w + z = 5) w + 2z= 10 -8w -2z = -10 -7w= -0 w= 0 0 + 2z = 10 2z= 10 z= 5 Graph the function f(x) = x^2 + 2 and identify x and y intercepts x=0 f(x)= x^2 + 2 y= x^2 + 2 y= 0^2 + 2 y= 0 +2 y= 2 y-intercept = (0, 2) When y = 0 f(x) = 0 never occured Graph the function f(x) = 3x-9 and identify x and y intercepts f(x) = 3x - 9 f(0) = 3(0) -9 Set y=0 0= 3x - 9 9=3x x=3 (3, 0) y intercept Set x=0 y=3(0) -9 y=-9 (0.-9) x-intercept Solve for x in 0.3x+ 0.2 = 0.5 x=1 Solve for x in 0.5x + 0.4 = 1.2 x=1.6 Solve for x in x+3/x-9 =0 x+3/x-9 =0 Numerator must be zero (x-9)(x-3)/x-9 0 * (x-9) x+ 3 = 3 x=-3