Find the slope of the line that goes through the given points. 1) (-9, -68) and (8, 51) 1)

Transcription

1 Math 125 Semester Review Problems Name Find the slope of the line that goes through the given points. 1) (-9, -68) and (8, 51) 1) Solve the inequality. Graph the solution set, and state the solution set in interval notation. 2) x < 2 2) Solve the system of equations using elimination. 3) 7x + 2y = -18 2x + 2y = 12 3) Solve the absolute value equation. 4) 7x = 6 4) 1

2 Determine whether the relation represents a function. If it is a function, state the domain and range. 5) 5) Alice Brad Carl snake cat dog Graph the linear function. 6) G(x) = x 6) Find the zero of the linear function. 7) G(x) = -5x ) 2

3 Solve the problem. 8) One number is 3 less than a second number. Twice the second number is 13 more than 3 times the first. Find the two numbers. 8) Solve the compound inequality. Express the solution using interval notation. Graph the solution set. 9) 9x - 6 < 3x or -3x -9 9) Find an equation of the line with the given slope and containing the given point. Express your answer in slope-intercept form. 10) m = 2, (-5, 7) 10) Simplify the polynomial by adding or subtracting, as indicated. Express your answer as a single polynomial in standard form. 11) (3x7 + 15x4-4) - (-12x4 + 9x7-9) 11) Find the product. 12) (8x5y)(-10x7y4) 12) 3

4 13) 9y(5y2-2y) 13) Find the product of the polynomials. 14) (p + q)(p2 - pq + q2) 14) Find the product of the two binomials. 15) (-3x - 7)(x + 5) 15) Find the special product. 16) (x - 13)2 16) Divide and simplify. 17) 24x 7-12x3-4x7 17) 4

5 Divide using long division. 18) -10x 3-17x2 + 7x x ) Factor out the greatest common factor. Be sure that the coefficient of the term of highest degree is positive. 19) 45x4 + 40x2 19) Factor the polynomial completely. If the polynomial cannot be factored, say it is prime. 20) a2-2a ) 21) x2 + x ) 22) 4x2 + 5x ) 5

6 Factor the difference of two squares completely. 23) x ) Factor completely, or state that the trinomial is prime. 24) x2 + 8xy + 16y2 24) Factor the polynomial completely. 25) x4-2x ) Add or subtract, as indicated, and simplify the result. 9 26) 10x + 7 5x2 26) 27) x x x2 + 5x ) 6

7 Simplify the complex rational expression 28) 28) 1-9 x x - 81 x 29) 16t2-64s2 st 4 s - 8 t 29) Solve the rational inequality. 30) x - 7 x + 3 > 0 30) Solve the proportion problem. 31) The ratio of the weight of an object on Earth to an object on Planet X is 2 to 11. If a person weighs 190 pounds on Earth, find his weight on Planet X. (Round your answer to the nearest whole number, if necessary.) 31) 7

8 Solve the work problem. 32) A painter can finish painting a house in 5 hours. Her assistant takes 7 hours to finish the same job. How long would it take them to complete the job if they were working together? (Round your answer to the nearest tenth, if necessary.) 32) Divide. 33) 5 8-6i 33) Multiply, and then simplify if possible. Assume all variables represent positive real numbers. 34) ( ) 2 34) Use the square root property to solve the equation. 35) (2x - 3)2 = 49 35) Use the quadratic formula to solve the equation. 36) -2x2-3x - 7 = 0 36) 8

9 Solve the equation by completing the square. 37) x2 + 10x + 14 = 0 37) 38) x2 + 18x = ) Complete the square for the binomial. Then factor the resulting perfect square trinomial. 39) x2-18x 39) Solve the equation. 40) y2-2y + 66 = y ) Add or subtract. 41) (4 + 3i) - (-3 + i) 41) 9

10 Use the product rule to multiply. Assume all variables represent positive real numbers. 42) ) Add or subtract. Assume all variables represent positive real numbers. 43) ) Write the expression as a complex number in the form a + bi ) 5 44) Rationalize the denominator and simplify. Assume that all variables represent positive real numbers. 3 45) 45) 2-4 Solve the problem. 46) If f(5) = 11, what is f-1(11)? 46) 10

11 Use the properties of logarithms to find the exact value of the expression. Do not use a calculator. 47) log ) Change the logarithmic expression to an equivalent expression involving an exponent. 1 48) log = -2 48) 4 16 Use the properties of logarithms to find the exact value of the expression. Do not use a calculator. 49) log log ) 50) 10log 15 - log 3 50) Solve the equation. Give an approximate solution to four decimal places. 51) 2x + 6 = 8 51) 11

12 52) 10 2x = 43 52) Find the distance d(p1, P2) between the points P1and P2. 53) P1 = (2, -7); P2 = (4, -3) 53) Solve the equation. 54) log (3x - 5) - log 9x = 3 54) Solve the equation. Give an exact solution. 55) e(x + 8) = 3 55) Write the first four terms of the sequence. 56) {n - 4} 56) 57) 1 5 n 57) 12

13 58) n 58) 59) (-1)n + 1 n ) The given pattern continues. Write down the nth term of the sequence suggested by the pattern. 60) 6, 18, 30, 42, 54,... 60) 61) 1 1, 1 4, 1 9, 1 16, 1,... 61) 25 62) -3, 9, -27, 81,... 62) 13

14 Write out the sum. Do not evaluate. 63) 5 k = 1 k + 1 k ) Determine whether the sequence is arithmetic. If the sequence is arithmetic, determine the first term a and common difference d. 64) 4, 12, 36, 108, 972,... 64) 65) 2, -1, -4, -7, -10,... 65) An arithmetic sequence is given. Find the common difference and write out the first four terms. 66) {7n + 3} 66) Find a formula for the nth term of the arithmetic sequence whose first term a and common difference d are given. 67) a = -1, d = 2 67) 14

15 68) a = -8; d = ) Write a formula for the nth term of the arithmetic sequence. Use the formula to find the 20th term of the sequence. 69) 1, 4, 7, 10, 13,... 69) Write a formula for the nth term of the arithmetic sequence. Use the formula to find the indicated term of the sequence. 70) a = 4, d = -2; Find a13. 70) Find the first term and the common difference of the arithmetic sequence described. Give a formula for the nth term of the sequence. 71) 3rd term is 26; 8th term is 71 71) Use the partial sum formula to find the partial sum of the given arithmetic sequence. 72) Find the sum of the first eight terms of the arithmetic sequence: -7, -18, -29, ) 15

16 73) Find the sum of the first 43 terms of the arithmetic sequence {3n + 8}. 73) Find the common ratio for the geometric sequence. 74) 1, 1 2, 1 4, 1 8, 1 16,... 74) 75) 2, -0.2, 0.02, ,... 75) Write the first four terms of the geometric sequence whose first term and common ratio are given. 76) a = 8; r = ) The general term of a sequence is given. Determine whether the given sequence is arithmetic, geometric, or neither. If the sequence is arithmetic, find the common difference; if it is geometric, find the common ratio. 77) {5n - 2} 77) 16

17 78) {2n} 78) 79) {3n2-2} 79) 80) 1 7, 1 9, 1 11, 1 13,... 80) Find the fifth term and the nth term of the geometric sequence whose initial term, a, and common ratio, r, are given. 81) a = 3; r = 4 81) Find the indicated term of the sequence. 82) The fifth term of the geometric sequence 6, -12, 24,... 82) Use the formula for the nth term of a geometric sequence to find the indicated term of the sequence with the given first term, a, and common ratio, r. 83) Find a11 when a = 4, r = 2. 83) 17

18 Write a formula for the nth term of the geometric sequence. 84) 4, -12, 36, -108, 324,... 84) Solve the problem. 85) A particular substance decays in such a way that it loses half its weight each day. How much of the substance is left after 10 days if it starts out at 128 grams? 85) Find the indicated sum. Use the formula for the sum of the first n terms of a geometric sequence. 86) 5 n = 1 3 4n 86) 87) 5 n = n 87) Evaluate the expression. 10! 88) 8! 2! 88) 18

19 89) 8! 3! 5! 89) Evaluate the given binomial coefficient ) 5 90) Expand the expression using the Binomial Theorem. 91) (4x - 2)4 91) 92) (x - 5)5 92) 93) (x - 9y)5 93) 19