Expert: Scott A Wilson - 2/7/2012

Question
1. Evaluate (3x + 6) ÷ [y3(x + 2)] if x = 2 and y = 1.
A) 9/4
B) 3
C) 15/12
D) 26

2. Simplify the following expression:
1/8(16x+24)+2(y-3)-1/9(27y-18x)
A) 4x – y
B)–y – 3
C) 4x – y – 3
D)–16x – y + 21

3. Identify the solution to the following equation:
3x+14=1/3(12x+3)
A) x = –11
B) x = 13
C) x = 11/9
D) x = 13/14

4. The sum of twice a number and four is twelve. Find the number.
A) 2
B) 3
C) 4
D) 5

5. Identify the solution to the equation 2 |3x – 5| = 8.
A) x = 3 or x = –3
B) x = 3 or x = 1/3
C) x = 13/6 or x = –13/6
D) x = 13/6 or x = –1/2

6. Identify the solution to the following inequality:
-1/2(x+3)>x-3
A) x < 1
B) x > 1
C) x < 3
D) x > 3

7. Identify the solution to the inequality |5 – 3x| + 3 ≤ 7.
A) x ≥ 3 or x ≤ 1/3
B) 1/3 ≤ x ≤ 3
C) x ≥ 1/3
D) no solution

8. Identify the domain of the relation {(1, 3), (1, 4), (3, 8), (4, 7)}.
A) {3, 4, 8, 7}
B) {1, 3, 4}
C) {1, 3, 1, 4, 3, 8, 4, 7}
D) {1, 3, 4, 7, 4, 8}

9. Identify the standard form of the equation 1/3 x = 7/3 y + 2.
A) y = 7/3 x + 2
B) y = 1/7 x – 6/7
C) 1/3 x + 7/3 y = 2
D) 1x – 7y = 6

10. Find the slope, y–intercept, and x–intercept of the line whose equation is 2x – 3y = 12.
A) m = 2/3, x–intercept = 6, y–intercept = –4
B) m = 12, x–intercept = 2 , y–intercept = –3
C) m = 2, x–intercept = 2/3, y–intercept = 12
D) m = –3, x–intercept = 2, y–intercept = 12

11. Identify the slope-intercept form of the line with slope –3 that passes through the point (–1, 12).
A) y = –1x + 12
B) y = –1x + 9
C) y = –3x + 12
D) y = –3x + 9

12. Use the table below to find a prediction equation to show how altitude (in thousands of feet) relates to rainfall (in inches).

ALTITUDE:  0    2    4    6    12
RAINFALL:  3    4    5    6    9

A) y = 2x + 1
B) y = 3x – 1
C) y = 1/2 x + 3
D) y = 1/3 x – 3

Answer
1. Evaluate (3x + 6) ÷ [y3(x + 2)] if x = 2 and y = 1.
Note the expression is 3(x+2)/(y³(x+2)); y is 1, so y³ is 1; to evaluate, put in 2 for x.

2. Simplify the following expression: (16x+24)/8 + [2(y-3)-1]/[(27y-18x)/9]
Note 16x+24 is the same as 2x+3.
Note that at the end, (27y-18x)/9 = 3y-2x.
Note that 2(y-3)-1 converts to 2y-7.
This doesn't come out even ...

3. Identify the solution to the following equation: 3x+14=(12x+3)/3
Divide each term on the right by 3, giving 3x + 14 = 4x + 1.
Subtract 3x from both sides, subtract 1 from both sides.

4. The sum of twice a number and four is twelve. Find the number.
Solve 2x + 4 = 12 by subtracting 4 from both sides, then dividing both sides by 4.

5. Identify the solution to the equation 2 |3x – 5| = 8.
Solve 6x - 10 - 9 for x>5/3  or  -2x + 10 = 9 for x<5/3.

6. Identify the solution to the following inequality: -1/2(x+3)>x-3
Multiply both sides by -2, changing the > to a <.
Subtract 3 from both sides, and there's the answer.

7. Identify the solution to the inequality |5 – 3x| + 3 ≤ 7.
Solve 5 - 3x + 4 <= 7 for x<5/3  or  -5 + 3x  +  3 <= 7 for x>5/3.

8. Identify the domain of the relation {(1, 3), (1, 4), (3, 8), (4, 7)}.
The domain is the possible values of x.

9. Identify the standard form of the equation 1/3 x = 7/3 y + 2.
Reverse the equation to 7y/3 + 2 = x/3.
Multiply all terms by 3/7, so the y have a 1 coefficient.
Subtract the constant terms from both sides/

10. Find the slope, y–intercept, and x–intercept of the line whose equation is 2x – 3y = 12.
The y-intercept is where x=0 and the x intercept is where y=0.
The slope is -y intercept / x intercept

11. Identify the slope-intercept form of the line with slope –3 that passes through the point (–1, 12).   Start with y - 12 = -3(x+1) and convert it to y = mx + b; it looks like m = -3
and b = 12 - 3 = 9; that what you see?
12. Use the table below to find a prediction equation to show how altitude (in thousands of feet) relates to rainfall (in inches).

ALTITUDE:  0 2 4 6 12
RAINFALL:  3 4 5 6 9
Note that each time x increases by 2, y only increases by 1/2.
Use y = x/2 + C and solve for C.  If (0,3) is put in, the value of C should be seen.