MAT 1033MIDTERM PRACTICE TESTNAME ____________________________INSTRUCTOR M.BEYLINFind all real square roots of the number.1)1691)Find the square root. Assume that all variables represent positive real numbers.2)4492)3)49x183)4)-5294)Find the cube root.5)3125x65)6)-3-125x18 y366)Simplify. Assume that all variables represent any real number.7)64x27)8)(x - 2)28)1Use radical notation to write the expression. Simplify if possible.9)3x1/59)10)(-8x15)1/310)11)(-8)4/311)12)(3x + 6)3/812)Write with positive exponents. Simplify if possible.13)16-5/413)14)47x-3/714)Use the properties of exponents to simplify the expression. Write with positive exponents.15)z-2/5 · z3/515)16)y5/9(y2/9 - 8y3/9)16)17)x4/7 · x1/5x3/417)2Use rational exponents to simplify the following.18)8y10z2018)Use rational exponents to write as a single radical expression.19)5x · 3x219)Use the product rule to multiply. Assume all variables represent positive real numbers.20)3x3 · 3x520)Use the quotient rule to divide and simplify.21)84621)Simplify. Assume all variables represent positive real numbers.22)32k7q822)Add or subtract. Assume all variables represent positive real numbers.23)3 8 + 3 200 - 6 1823)24)3x2 + 6 108x2 - 4 108x224)25)69 + 150425)3Multiply, and then simplify if possible. Assume all variables represent positive real numbers.26)( 2 + 6)( 2 - 6)26)27)(7 13 + 8)(9 13 + 9)27)28)( 14 - 98)( 7 + 2)28)Rationalize the denominator. Assume all variables represent positive real numbers.29)1441129)30)43p30)31)379x231)32)7 - 107 + 1032)33)2 + 72 - 733)Solve.34)5q + 6 = 634)35)p2 - 3p + 36 = p + 335)36)Find the length of the unknown side of the triangle.12 km16 km36)437)A balloon is secured to rope that is staked to the ground. A breeze blows the balloon sothat the rope is taut while the balloon is directly above a flag pole that is 50 feet from wherethe rope is staked down. Find the altitude of the balloon if the rope is 110 feet long.37)Write in terms of i.38)-1638)39)-18839)Write the number as a product of a real number and i. Simplify the radical expression.40)-4940)41)-12841)Add or subtract as indicated. Write your answer in the form a + bi.42)(4 + 8i) - (-9 + i)42)43)[(3 + 9i) - (2 + 4i)] - (3 - 10i)43)Graph the equation.44)3x - y = -3x-10-5 5 10y105-5-10x-10-5 5 10y105-5-1044)545)y = - 14xx-10-5 5 10y105-5-10x-10-5 5 10y105-5-1045)Determine the slope and the y-intercept. Then graph the equation.46)2x - 5y = -30x-10-5 5y105-5-10x-10-5 5y105-5-1046)47)x + y = 5x-10-5 5 10y105-5-10x-10-5 5 10y105-5-1047)Write the equation of the line in slope-intercept form given the slope and the coordinates of the y-intercept.48)m = 0; (0, 2)48)6Write the equation of the line in slope-intercept form given the y-intercept and one other point.49)(-4, 2), (0, -3)49)Write the equation of a line in slope-intercept form with the given slope passing through the given point.50)m = 34; (0, 2)50)Write the equation of a line connecting the given points in slope-intercept form.51)(-1, 10), (-1, -2)51)52)(-8, 1), (2, 4)52)53)(9, -2), (4, 2)53)Write the equation of a line through the given points in the form Ax + By = C, where A, B, and C are integers and A > 0.54)(4, 4), (-3, 6)54)55)(-6, 3), (-7, 3)55)7Write the equation of a line that passes through the given point and is parallel to the given line. Write the equation inslope-intercept form and in the form of Ax + By = C, where A, B, and C are integers and A > 0.56)(4, 5); x + y = 1456)Write the equation of a line that passes through the given point and is perpendicular to the given line. Write the equationin slope-intercept form and in the form of Ax + By = C, where A, B, and C are integers and A > 0.57)(-9, -2); 2x - 5y = 757)Solve the system of equations using substitution. Note that the system may be inconsistent or consistent with dependentequations.58)x - 5y = 25-2x - 4y = 2058)59)x + y = 42x + 2y = 859)Solve the system of equations using the elimination method.60)7x + 9y = 36-4x - 3y = -1260)8Graph the solution of the system.61)3x - 2y ≤ 6 x - 1 ≥ 0x-55y5-5x-55y5-561)62)x + 2y ≥ 2 x - y ≤ 0x-55y5-5x-55y5-562)9Answer KeyTestname: 1033 EXAMMID REVIEW1)13, -132)273)7x94)not a real number5)5x26)5x6 y127)8 x8) x - 29)35x10)-2x511)1612)8(3x + 6)313)13214)4x3/7715)z1/516)y7/9 - 8y8/917)x3/14018)y5/4z5/219)15x1320)3x421)1422)4k3q4 2k23)18 224)13x 325)17 6626)-427)891 + 135 1328)7 2 + 2 7 - 7 14 - 1429)12 111130)4 3p3p31)321x3x32)59 - 14 103910Answer KeyTestname: 1033 EXAMMID REVIEW33)11 + 4 7-334){6}35){3}36)20 km37)40 6 ft38)4i39)2i 4740)7i41)8i 242)13 + 7i43)-2 + 15i44)x-10-5 5 10y105-5-10x-10-5 5 10y105-5-1045)x-10-5 5 10y105-5-10x-10-5 5 10y105-5-1011Answer KeyTestname: 1033 EXAMMID REVIEW46)m = 25; y-intercept: 0, 6x-10-5 5y105-5-10x-10-5 5y105-5-1047)m = -1; y-intercept: (0, 5)x-10-5 5 10y105-5-10x-10-5 5 10y105-5-1048)y = 249)y = - 54x - 350)y = 34x + 251)x = -152)y = 310x + 17553)y = - 45x + 26554)2x + 7y = 3655)y = 356)y = -x + 9x + y = 957)y = - 52x - 4925x + 2y = -4958)(0, -5)59)All ordered pairs along x + y = 460)(0, 4)12Answer KeyTestname: 1033 EXAMMID