MATH 1000KC
FINAL EXAM REVIEW
Determine whether the pair of equations represents parallel lines, perpendicular lines or neither.
1) 4x - 12y = -15
6x + 16y = -15
Factor completely.
2) x2 + 5x - 66
3) 64x2 - 81
4) 8y2 + 36y - 20
5) x3 + 5x2 - 2x - 10
Write an equivalent expression by factoring out the greatest common factor.
6) 6m 7 + 8m 5 - 20m 3
Evaluate using a calculator.
7) 3(m - 3n) ÷ m, for m = 1.5 and n = 5.8
(Round to the nearest thousandth.)
Solve the problem.
r
8) The wavelength w, in meters per cycle, of a musical note is given by w = , where r is the speed of the sound in
f
meters per second and f is the frequency in cycles per second. The speed of sound in air is 344 m/sec. What is
the wavelength of a note whose frequency in air is 25 cycles per second? Round to the nearest tenth of a meter
per cycle.
Perform the indicated operations.
9) (2r2 - 6) - (8r2 - 3) + (-3r2 - 2)
Solve the equation.
10) 5x + 6(-2x - 7) = -46 - 3x
11) 4x - (2x - 1) = 2
12) 5x + 3 + 3x = 9x + 2 - x
13)
11
9 5
x+ = x
14
7 7
14)
7
1
1 5
x + x = 7x + + x
6
6
3 6
Solve the inequality.
15) -25r + 10 -5(4r - 5)
Express the radical in simplified form.
16) 72
Multiply.
17) (2x - 7)(x - 4)
18) (8m + 1)2
Solve the system of equations using substitution or elimination. State the value of x.
19) 9x + 7y = 45
5x - 2y = 25
Simplify. Write the answer using positive exponents only.
-4
20) 4x8 y-7
21)
5
5x3 y-5
4y-3
22) (w5 z)2 (w3 z 8 )
Find an equation of the line containing the given pair of points. Write your final answer in slope-intercept form.
23) (4, -2) and (0, 3)
Find the coordinates of the labeled points.
24)
Solve the problem.
25) Sammy paid $535.27, including 8% tax, for an LCD computer monitor. How much did the computer monitor
itself cost? Round to the nearest penny, if necessary.
26) An inclined walkway leading to a new building is to rise 14 inches for each horizontal distance of 288 inches.
Write this slope as a grade. (Round to the nearest tenth of a percent if necessary.)
Is the following correspondence a function?
27)
28)
Graph the equation.
29) -4x - 8y = 8
30) y =
1
x-2
2
Find an equation of the line having the specified slope and containing the indicated point. Write your answer in
slope-intercept form.
31) m = -8; (-6, 6)
Solve the problem.
32) A rectangular Persian carpet has a perimeter of 236 inches. The length of the carpet is 20 inches more than the
width. What is the length of the carpet?
33) There were 390 people at a play. The admission price was $9.00 for adults and $4.00 for children. The admission
receipts were $2560. How many adults and children attended?
Solve the problem.
34) In a school survey, students showed these preferences for instructional materials. Answer the question.
About how many students would you expect to prefer radio materials in a school of 300 students?
Solve using the five-step problem-solving process.
35) A triangular lake-front lot has a perimeter of 2200 feet. One side is 300 feet longer than the shortest side, while
the third side is 400 feet longer than the shortest side. Find the lengths of all three sides.
Find the intercepts for the equation.
36) -6x - 18y = 36
Find the slope and the y-intercept of the line.
37) -4x + 5y = 5
Convert to decimal notation.
38) 8.55 × 103
39) 8.788 × 10-6
Convert to scientific notation.
40) 0.000389
Find the slope of the line containing the given pair of points.
41) (1, -2) and (9, 8)
Decide whether or not the ordered pair is a solution to the equation.
42) 2x + 3y = 25; (5, 5)
Find the domain of f(x).
-8
43) f(x) =
x+1
Solve the formula for the indicated letter.
44) d = rt for r
45) S = 4 r2 , for r2
(surface area of a sphere with radius r)
Find the function value.
46) Find f(-4) when f(x) = x2 + 4x - 7.
Solve the problem.
47) The total sales made by a salesperson was $25,000 after 3 months and $68,000 after 23 months. Find a linear
equation that relates the total sales, y, to the number of months, x.
Graph.
48) 2x - y = 4
Determine whether the graph is the graph of a function.
49)
50)
Answer Key
Testname: 1000KC FINAL-REVIEW
1) Neither
2) (x - 6)(x+11)
3) (8x + 9)(8x - 9)
4) 4(2y - 1)(y + 5)
5) (x + 5)(x2 - 2)
6) 2m 3 (3m 4 + 4m 2 - 10)
7) -31.8
8) 13.8 meters per cycle
9) - 9r2 - 5
10) 1
1
11)
2
12) No solution
13) -18
2
14) 39
15) [-3, )
16) 6 2
17) 2x2 - 15x + 28
18) 64m 2 + 16m + 1
19) x = 5
y28
20)
256x32
21)
3125 x15
1024 y10
22) w13z 10
5
23) y = - x + 3
4
24) G(7, -5); H(-4, -2)
25) $495.62
26) 4.9%
27) Yes
28) No
29)
Answer Key
Testname: 1000KC FINAL-REVIEW
30)
31) y = -8x - 42
32) 69 in.
33) 200 adults and 190 children
34) About 15 students
35) 500 ft, 800 ft, 900 ft
36) (0, -2), (-6, 0)
37)
4
; (0, 1)
5
38) 8550
39) 0.000008788
40) 3.89 × 10-4
41)
5
4
42) Yes
43) {x x is a real number and x
d
44) r =
t
45) r2 =
S
4
46) -7
47) y = 2150x+18550
48)
49) No
50) Yes
-1}