MATH 082 FINAL - PRACTICE TEST #1 Revised 06/23/09
Give all answers in simplest form.
- Simplify. Write all answers without negative or zero exponents.
2. Simplify the expression by combining like terms:
3. Solve for x: 18 – 4(2x – 3) + 5x = 41
4. Solve for x: x + = x –
5. Solve the inequality and graph the solution: -4x + 3 < 11
6. Solve for A if L = A + (M – 1)D. Given L = 29, M = 6, D = 5.
7. Solve for :
8. Graph the line whose slope is and is .
9. Find the slope of the line passing through the points (1, -2) and (-3, 10)
10. The slope of a line is 2 and one point on a line is (- 1, 3). Find the equation of the line
and write the answer in slope-intercept form.
11. Write the equation of the line that passes through the points (-3, 11) and (1, 3).
In problems 12 & 13, solve the system of equations.
12. 2x – y = 5
5x + 3y = 18
13. y = 3x + 2
4x – y = 0
14. Simplify (2xy3) 4
Math 082 Final - Practice Test #1 cont.
15. a). Write 350 in Scientific Notation
b). Convert to decimal notation.
c). Multiply. Give your answer in scientific notation form.
16. Multiply:
17. Multiply and simplify: (4x – 3y)(2x + 5y)
18. Simplify:
19. Factor completely: 2x3y– 6x2y+ 2xy
20. Factor completely: x2 + 4x – 21
21. Factor completely: x2 – 49
22. Solve for x by factoring:
23. Translate into an equation using one variable and solve: the sum of 5 times a number and nine is three less than the product of two and the number.
24. Solve by graphing:
25. I bought 3 notebooks and 5 folders for my classes and spent $25. My friend, Alex, bought 8 folders and 5 notebooks and spent $41. Set up a system of equations that models the situation and solve the system to find the cost of each notebook and folder.
PRACTICE TEST SOLUTIONS
1.
2.
= Distribute the -2
= combine like terms
3. 18 – 4(2x - 3) + 5x = 41 Distribute the -4
18 – 8x + 12 + 5x = 41 Combine like terms
-3x + 30 = 41 Subtract 30 from both sides of the equation
-3x = 11 Divide both sides of the equation by -3
x = -
4. x + = x – ;
Find the common denominator. Then multiply the common denominator by each term of the equation.
12 · + 12 · = 12 · + 12 ·
8x + 3 = 2x – 16 Subtract 2x from both sides of the equation
6x + 3 = -16 Subtract 3 from both sides
6x = -19 Divide both sides of the equation by 6
x =
5. -4x + 3 < 11 Subtract a 3 from both sides
-4x < 8 Divide both sides by -4 and flip the inequality symbol
x > -2
6. L = A + (M – 1)D L = 29, M = 6, D = 5
29 = A + (6 – 1) . 5 Substitute the given values
29 = A + 25 Subtract (6 – 1), then multiply by 5 (PEMDAS, Use correct order of operations,)
A = 4 Subtract 25 from both sides of the equation
7. Subtract from both sides
divide both sides by 3
Math 082 Final - Practice Test #1 cont.
8.
Graph the line by Plotting Points:
x / y0 / -3
4 / 0
Graph the line using the Slope and Y-intercept:
The slope of the line is ¾ and the y-intercept is –3. Plot the y-intercept (0, -3). Then use the slope to find other points on the line. Starting at (0, -3) rise 3 and run 4 (Move up 3 and right 4). Repeat this (Move up 3 and right 4) to find additional points on the line.
9. slope = = = = -3
10. ,
, since
Then, use the point (-1 , 3) in y = 2x + b to solve for b.
3 = (2)(-1) + b,
3 = - 2 + b, Add 2 to both sides of the equation
5 = b Equation: y = 2x + 5
11. First, calculate the slope. m = = = = -2
Then, use the point (1 , 3) in y = -2x + b to solve for b.
y = mx + b 3 = (-2)(1) + b 3 = - 2 + b
+ 2 + 2
5 = b Equation: y = -2x + 5
12. 2x – y = 5 6x – 3y = 15 Multiply by 3 2(3) – y = 5
5x + 3y = 18 5x + 3y = 18 Add down 6 – y = 5
11x = 33 Divide by 11 on both sides – y = -1
Solution: (3,1) x = 3 Substitute x = 3 into original equation to find y y = 1
Math 082 Final - Practice Test #1 cont.
13. y = 3x + 2 4x – (3x + 2) = 0 Substitute 3x + 2 for y y = 3(2)+2
4x – y = 0 4x – 3x – 2 = 0 Distribute the – y = 6+2
x – 2 = 0 Combine like terms y = 8
x = 2 Add 2 to both sides
Solution: (2,8) Substitute x = 2 into original equation to find x
14. (2xy3) 4 =16x4y12
15. a) 3 5 0 = 3.5 x 102
b)
c)
16.
17. (4x – 3y)(2x + 5y)= 8x2 + 20xy– 6xy –15y2 = 8x2 +14xy – 15y2
18.
19. Greatest Common Factor = 2xy
2x3y– 6x2y+ 2xy
=2xy(x2 – 3x + 1)
20. c = -21
x2 + 4x – 21 = x2 – 3x + 7x – 21
= x(x – 3) + 7(x – 3)
= (x – 3)(x + 7)
21. Factor a Difference of Two Squares:
x2 – 49 = (x)2 – (7)2
= (x + 7)(x – 7)
22. x2 – 3x – 28 = 0 Factor using the AC test (A = 1, B=-3, C=-28)
Set each factor equal to 0
x – 7 = 0 x + 4 = 0 Solve each equation
x = 7 x = -4
23. Let the number, translate the statement into a mathematical equation:
subtract 2x and 9 from both sides
Math 082 Final - Practice Test #1 cont.
24. Graph the lines the equations and , then find the intersection point between two lines.
solution:
25. Let x = the cost of one notebook
y = the cost of one folder
3x + 5y = 25 15x + 25y = 125 Multiply by 5 3x +5(2) = 25
5x + 8y = 41 -15x – 24y = -123 Multiply by -3 3x + 10 = 25
y = 2 Substitute into original equation 3x = 15
x = 5
The cost of one notebook = x = $5 and
The cost of one folder = y = $2
256