Elementary Algebra
Answer the questions without using a calculator.
1.
Evaluate 2x2 - y2 - z if x = 3, y = -1 and z = -2
a.
15
b.
17
c.
19
d.
21
2.
Solve for x: 1 - 3(x-4) = 2(3x + 1)-7
3.
4.
a.
7
4
b.
2
c.
1
3
d.
7
Solve for y: ax + by = c
a.
y =c-ax-b
b.
y
c.
y
d.
y
c
x b
a
c ax
b
c b
ax
The length of a rectangle is 8 feet longer than its width. If the
perimeter of the rectangle is 236 feet, what is the length of the
rectangle?
a.
114 feet
b.
57 feet
c.
55 feet
d.
63 feet
5.
a.
The graph of 2x+y=4 is
b.
c.
d.
6. Jane donates 2% of her annual salary to charity and Sam donates 1%
of his annual salary to charity. The total of Jane and Sam’s donations
is $620. If Jane makes $1000 more than Sam, how much is Jane’s
annual salary?
a.
$20,000
b.
$21,000
c.
$24,000
d.
$30,000
7.
Find the product of the binomials:
a.
2a2 + ab – 6b2
b.
–12a2b2
c.
2a2 – 6b2
d.
2a2 + 7ab – 6b2
8.
Simplify:
a.
4x 2
2x 4x 2
1
2x 1
b.
2x+1
c.
2x
1 2x
1
2
d.
9.
Raise to the power indicated: (4 3x )2
a.
12x
b.
48x
c.
7x
e.
16 3x
10.
Solve for x:
a.
b.
c.
d.
x2-4a2=0
4a2
+a
+2
+ 2a
Elementary Algebra Answers
1. Answer:
2. Answer:
3. Answer:
4. Answer:
5. Answer:
6. Answer:
7. Answer:
8. Answer:
9. Answer:
10. Answer:
c
b
c
d
a
b
a
c
b
d
(2a – 3b)(a + 2b)
Elementary Algebra Solutions
1. Evaluate 2x² - y² - z if x = 3, y = -1 and z = -2
Substitute the values for the variables; follow order of operations to evaluate:
2(3)² - (-1)² - (-2)
= 2(9) - (1) - (-2)
= 18 - (1) + (+2)
= 17 + 2
= 19
2. Solve for x: 1 - 3(x - 4) = 2(3x + 1) - 7
Distribute:
1 - 3x +12 = 6x + 2 - 7
Collect like terms:
-3x +13 = 6x - 5
Add 3x to both sides of the equal sign:
-3x +13 + 3x = 6x - 5 + 3x
13 = 9x - 5
Add 5 to both sides:
18 = 9x
Divide both sides by 9:
2=x
3. Solve for y: ax + by = c
Subtract ax from both sides:
by = c - ax
Divide both sides by b:
4. Draw a picture of a rectangle.
Setup: Let W = width; L = Length
Translate the phrases into math:
The length of a rectangle is 8 feet longer than its width: L = W + 8
The perimeter is the total distance around the rectangle:
236 = W + L + W + L
236 = 2L + 2W
Substitute L = W + 8 and solve:
236 = 2(W + 8) + 2W
Distribute the 2:
236 = 2W + 16 + 2W
Collect like terms:
236 = 4W + 16
Subtract 16 from both sides:
220 = 4W
Divide both sides by 4:
55 = W
Be sure to answer the question: 'What is the length of the rectangle?'
L = W + 8 = 55 + 8 = 63
The length of the rectangle is 63 feet
5. The graph of 2x + y = 4 is
Find two points that satisfy the given equation; plot them, draw a line through the points.
Easy points to find are the intercepts:
x-intercept: 2x + (0) = 4
2x = 4
x=2
y-intercept: 2(0) + y = 4
y=4
The two points are: (2, 0) and (0, 4). Plot them and draw the line.
6. Setup: Let J = Jane's annual salary; S = Sam's annual salary
Translate the words into math:
Jane donates 2% of her annual salary: 0.02J
Sam donates 1% of his annual salary: 0.01S
The total of Jane and Sam's donations is $620: 0.02J + 0.01S = 620
Jane makes $1000 more than Sam: J = S + 1000 or J - 1000 = S
Substitute J - 1000 for S in the first equation:
0.02J + 0.01(J - 1000) = 620
Solve for J:
0.02J + 0.01J - 10 = 620
0.03J - 10 = 620
Add 10 to both sides:
0.03J = 630
Divide both sides by 0.03:
J = 21000
Jane's annual salary is $21,000
7. Use FOIL to multiply:
(2a - 3b)(a + 2b)
= 2a² + 4ab - 3ab - 6b²
= 2a² + ab - 6b²
8. Factor the denominator and cancel common factors:
9. Raise each factor inside the parentheses to the second power and mulitiply:
10. Solve for x: x² - 4a² = 0
This is a quadratic equation with two solutions.
Isolate x²:
x² = 4a²
Solve for x¹ by taking the positive and negative square root of the right side of the equal
sign:
x = ± 2a