Rational Numbers, Irrational Numbers, Whole Numbers, Integers, Natural Numbers

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1 College Readiness Math Semester Eam Review Write the set using interval notation and graph the inequality on the number line. 1) { -6 < < 9} Use the order of operations to simplify the epression. 4 (8 + 2) ) 4 (6-1) Simplify the epression. 3) 7a - 4a - a - 13 List all the elements of set B that are of the indicated type. 4) B = {12, 8, -13, 0, 0 1, 16} Rational Numbers, Irrational Numbers, Whole Numbers, Integers, Natural Numbers Evaluate the epression for a = -, b = 16 and c = 7. ) b + 40 a Write the set by listing its elements. 6) {a a is an even integer greater than 4} Translate the verbal phrase into a mathematical epression. Use to represent the unknown number. 7) The product of 6 and 1 less than a number Solve the equation. 8) r + 6 = r ) 0.07y + 0.1(000 - y) = 0.47y 10) 13(8c - 2) = 6c - 2 Solve the problem. 11) Janet drove 272 km, and the trip took 4 hr. At what average rate was Janet traveling? Provide an appropriate response. 12) 2-7 = 3 Is this a linear equation? Decide if the statement is true or false. 13) -8 is a solution of = 40. Solve the equation for the specified variable. Use the distributive property to factor as necessary. 14) -9s + 8p = tp - 8 for p 1

2 Solve the formula for the specified variable. 1) S = 2πrh + 2πr2 for h Solve the equation. 16) 31s + 2 = -4s Find the slope of the line and sketch the graph. 17) 2 + 3y = y Decide whether the pair of lines is parallel, perpendicular, or neither. 18) 3-4y = 4 and 8 + 6y = -6 Decide whether the relation is a function. 19) {(-4, 1), (-3, -6), (3, -8), (3, 4)} Find the - and y-intercepts. Then graph the equation. 20) 12y - 4 = y Find the midpoint of the segment with the given endpoints. 21) (8, 2) and (7, 7) Find the slope of the line through the pair of points. 22) (7, -8) and (, 2) 2

3 Find the equation in slope-intercept form of the line satisfying the conditions. 23) m = 2, passes through (, -4) Find an equation of the line passing through the two points. Write the equation in standard form. 24) (2, -9) and (0, 4) Find an equation of the line satisfying the conditions. Write the equation in slope-intercept form. 2) Through (-6, ); parallel to -7 + y = 7 Solve the system of equations. 26) 7 + 7y + z = 1 + 8y + 8z = y + 9z = 9 Solve the system by substitution. If the system is inconsistent or has dependent equations, say so. 27) = y -6-8y = -38 Solve the system by elimination. If the system is inconsistent or has dependent equations, say so. 28) - + 6y = y = -7 Identify the polynomial as a monomial, binomial, trinomial, or none of these. Also give the degree. 29) 18c6-4c + 3c4 Write the polynomial in descending powers of the variable. Give the coefficient of the highest degree. 30) Identify the polynomial as a monomial, binomial, trinomial, or none of these. Also give the degree. 31) 142 Apply the product rule for eponents, if possible. 32) (8y)(-7-2y-4) Apply the quotient rule for eponents, if applicable, and write the result using only positive eponents. Assume all variables represent nonzero numbers. 33) 7 13 Add or subtract as indicated. 34) ( ) + ( ) Simplify the epression. Write your answer with only positive eponents. Assume that all variables represent nonzero real numbers. -3w7 4 3) 3

4 Simplify the epression so that no negative eponents appear in the final result. Assume all variables represent nonzero numbers. 36) (3-) 4 (2) -4 Divide. 37) Add or subtract as indicated. 38) ( ) - ( ) Find the product. 39) (9y - 7)(81y2 + 63y + 49) 40) (4 + 12)( + 2) Write the epression with only positive eponents. Assume all variables represent nonzero numbers. Simplify if necessary. 41) (3p)-3 Find the product. 42) (r - )2 Divide. 43) Find the product. 44) (10r - 3)(10r + 3) Divide. 4) 4y 4 + 6y3 + 3y - 1 2y2 + 1 Add or subtract as indicated. Write the answer in lowest terms. 46) 3 r + 9 r )

5 48) Perform the indicated operation and epress in lowest terms. 49) z 2 + 9z + 20 z2 + 11z + 28 z2 + z z2 + 4z ) 4p - 4 p 8p2 p - Solve the equation. 1) = ) 6-6 = ) = Factor by grouping. 4) 20r2 + 1ry - 4r - 3y ) 3a a2 - a Factor the trinomial completely. 6) Factor out the greatest common factor. Simplify the factors, if possible. 7) ( - 4)( + 7) + ( - 4)( + 3) 8) 9w - 1wy - 12wz Factor the trinomial completely. 9) 1z2 + 4z - 4

6 60) y - 24y2 Factor the polynomial completely. 61) ) 36y4-49 Find all solutions by factoring. 63) 3m2-10m = 0 Solve the equation. 64) = 0 Factor by grouping. 6) 36r2 + 4ry - 4r - y Factor the trinomial completely. 66) ) Factor out the greatest common factor. Simplify the factors, if possible. 68) ( - 8)( + 3) + ( - 8)( + 3) Factor the polynomial. 69) y + 81y2 Factor the trinomial completely. 70) 6z2 + z ) y - 40y2 Factor the polynomial completely. 72) ) Find all solutions by factoring. 74) 7m2-9m = 0 Solve the equation. 7) = 0 6

7 Find the vertical asymptotes and then state the domain. 4 76) f() = ) f() = Epress the rational epression in lowest terms. 78) 27m p2 9m10p 79) y 2 + 7y + 12 y2 + 8y + 1 Perform the indicated operation and epress in lowest terms. 80) 4p - 4 4p2 p p - 81) k k + 40 k2 + 14k + 48 k2 + 6k k2 + 9k ) z 2 + z + 6 z2 + 7z + 10 z2 + 3z z2-2z ) Add or subtract as indicated. Write the answer in lowest terms. 84) 3 r + 6 r - 2 8) Simplify the comple fraction. 86) )

8 Without actually solving the equation, identify the vertical asymptotes and state the domain ) = 0 Solve the equation. 89) = ) = ) = ) = Solve the problem. 93) If m varies directly as p, and m = 24 when p = 3, find m when p is 6. 94) If varies inversely as y2, and = 3 when y = 8, find when y = 4. 9) The intensity of a radio signal from the radio station varies inversely as the square of the distance from the station. Suppose the the intensity is 8000 units at a distance of 2 miles. What will the intensity be at a distance of 11 miles? Round your answer to the nearest unit. 8

9 Answer Key Testname: SEMESTER EXAM REVIEW SHEET 1) (-6, 9) 2) 17 3) 2a ) 12, -13, 0, 0 1, 16 ) -4 6) {6, 8, 10,...} 7) 6( - 1) 8) {-4} 9) {1000} 12 10) 49 11) 68 km/hr 12) No 13) True 14) p = 9s - 8 or p = -9s t t - 8 1) h = S - 2πr 2 2πr 16) ) Slope: y ) Perpendicular 19) Not a function 9

10 Answer Key Testname: SEMESTER EXAM REVIEW SHEET 20) (2, 0); 0, y ) 1 2, ) - 23) y = ) y = 8 2) y = ) {(0, 0, 1)} 27) {(1, 4)} 28) {(1, 9)} 29) Trinomial; ) ) Monomial; 2 32) 1214y3 33) ) ) 81w ) ) ) ) 729y ) ) 27p3 42) r2-10r )

11 Answer Key Testname: SEMESTER EXAM REVIEW SHEET 44) 100r2-9 4) 2y2 + 3y ) 12r - 6 r(r - 2) 47) 48) 3( + 21) ( - 4)( + 4)( + 1) 49) z - 3 z 0) 32p 1) {-7, 6} 2) {10,-12} 17 3) 6 4) (4r + 3y)(r - ) ) (a + )(3 - a) 6) (3 + 2)(2 + 3) 7) 2( - 4)( + ) 8) 3w(3 - y - 4z) 9) (3z + 2)(z - 2) 60) 3( - 2y)( + 4y) 61) ( + 2)( - 2) 62) (6y2 + 7)(6y2-7) 10 63) 3, 0 64) -6, , 0 6) (4r + y)(9r - ) 66) (4 + 3)(3 + 2) 67) ( + 9)( - 10) 68) 2( - 8)( + 3) 69) (7-9y)2 70) (2z + 3)(3z - 2) 71) 2( - 4y)( + y) 72) (6 + )(6 - ) 73) Prime 9 74) 7, 0 7) -6, , 0 76) -7 77) -3, 9 11

12 Answer Key Testname: SEMESTER EXAM REVIEW SHEET 78) 3p m 79) y + 4 y + 80) 16p 81) k k ) z - 7 z 83) ) 8) 86) 87) 12 9r - 6 r(r - 2) ( - 4)( + 4)( + 1) ( + ) 3 88) 1, -3 89) {-9, 8} 90) 91) {3} 92) {-11} 93) 48 94) 12 9) 264 units 12

Solve the equation for the specified variable. Use the distributive property to factor as necessary. 2) -9s + 8p = tp - 8 for p

College Readiness Math Final Eam Review Sheet Solve the equation. 1) r + 6 = r + 8 3 6 Solve the equation for the specified variable. Use the distributive propert to factor as necessar. 2) -9s + 8p = tp