Transcript 7th Grade Test Prep - Algebra

th
7
Grade Test Prep
Algebra
Evaluate 8a – 2b when a = 7 and b = 4
48
Evaluate x² + y³ when x = 3 and y = 2
17
How do you evaluate 6c + d² when c = 9 and d = 5
79
Joanna receives $8 per hour when she works at the
coffee shop. Last week she earned $256. Write an
equation that can be used to find the number of
hours Joanna worked last week.
Let h = Hours Joanna worked
8h = 256
Write an equation to represent the following. The sum
of 7 and a number, divided by 15, is equal to 33.
Let n = the number
(7 + n) ÷ 15 = 33
Solve for n:
n - 19 = 7
8
Step 1: Start with the term that does NOT include the variable. Use the
inverse operation (subtraction) to ‘move’ the 19.
n/8 – 19 (+ 19) = 7 + 19
n/8 = 26
Step 2: To isolate the variable, use the inverse operation (multiplication), to
‘move’ the 8.
n/8 (* 8) = 26 (* 8)
n = 208
Step 3: Check your work by substituting and solving.
n = 208
208 / 8 – 19 = 7
√
A car uses 9 gallons of gasoline for a 162-mile drive. How many gallons of gasoline
will the same car use in a 216-mile drive?
Step 1: Write the ratio given in the problem.
The ratio is “162 miles uses 9 gallons.”
As a fraction, the ratio miles/ gallons is 162/9
Step 2: Represent the unknown by a variable.
g = gallons of gasoline for a 216-mile drive
Step 3: Write the ratio and fraction for the unknown variable.
The ratio is “216 miles uses ‘g’ gallons.”
As a fraction, the ratio miles/ gallons is 216 / g
Step 4: Write the ratios as proportions. Cross-multiply to solve.
162 216

9
g
162g = 1944
g = 12
The car will use 12 gallons of gasoline for a 216-mile drive
.
Eighteen less than twice a number
A number squared, plus nineteen
2t - 18
n² + 19
The product of eleven and a number, divided by sixty
11 × k ÷ 60
One hundred more than the quotient of a number
and two hundredths
n ÷ 0.02 + 100
Polynomial – an algebraic expression that is the
sum of any number of monomials.
Which of the following expressions are polynomials:
7n - 35
Five less than a number, times seven
7(n – 35) = 63
-m + n2
n>5
Simplify the following expression:
3ac + 4 – 2ac + 9 – 5bc
Step 1: Identify the like terms.
+3ac - 2ac
+4+9
- 5bc
Step 2: Combine the like terms
+ ac
+ 13
- 5bc
Step 3: Rewrite the expression using the combined terms
ac + 13 – 5bc
Simplify the following expressions:
a)
3x + 4y – 4x
b)
-1/2t + 6t – 6
c)
pq – 2pq2
d)
3ab – 3a – 3ab + 2a
e)
-4t + 26m – mt + tm
2x + 12 = 3 – x
+x
+x
3x + 12 = 3
- 12 -12
3x
÷3
= -9
÷3
x
= -3
Combine like terms
Add x to each side.
Simplify
Combine the second set of like terms
Subtract 12 from each side.
Simplify
Divide each side by 3
Substitute & complete the check
7 (x – 2) = 5x + 10
7 x – 14 = 5x + 10
- 5x
-5x
2 x – 14 =
+ 14 =
2 x = 24
÷2
÷2
x = 12
10
14
Use the distributive property to remove the
parenthesis
Multiply (x – 2) by 7.
Combine like terms
Add a negative 5x to both sides.
Simplify
Combine the second set of like terms
Add 14 to each side.
Simplify
Divide each side by 2
Simplify
Substitute & complete the check
1.
2.
3.
4.
7y + 8 = -2y – 64
4 (2b – 6) + 11 = 8b - 13
9y + 3 = 5y – 13
5n + 3 = 2(n + 2) – 3n
Solve and graph each of the following inequalities
4g > 28
5+k≤3
2 < 90/j
98 ≥ d - 6
k > 72 ÷ 8
y/2 < 9
g>7
k ≤ -2
2 < 45
104 ≥ 104
k>9
y < 18
John is a data entry professional. His typing
rate is 70 words per minute. At this rate, how
long will it take to complete a memo of 665
words?
9.5 minutes.
The formula for the mass of an object is
density times volume (M = DV). What is the
mass of a 49-cc object with a density of 63
g/cc?
3,087 g
The formula for the mass of an object is M =
DV, where m is the mass, d is the density and v
is the volume. What is the volume of a 17-kg
solid with a density of 0.05 kg/cc
340 cc
If a decaminute is equivalent to 10 minutes of
time, how many decaminutes are equivalent to
2 hours?
12 decaminutes
Complete the tables and graph the equations (on a coordinate plane)
2y – x = 6
x
y
1
y=½x
2
x
0
0
6
2
y
4
5
x + 2y = 4
x
y
-1
-2
2
4
Consider the sequence 3, 5, 7, 9, …
Write an expression for the nth term.
** use a table to help you.
Consider the sequence 2, 5, 8, 11, …
Write an expression for the nth term.
** use a table to help you.
Name of Polygon
Number of Sides
Sum of Measure of
Interior Angles
Triangle
3
180˚
4
Pentagon
6
Septagon
8
Nonagon
10
N-gon
n
Write each equation, then complete the table.
y = ___________
x
y
7
4
10
7
x
y
10
2
2
4
4
16
y = ___________
8
16
y = ___________
x
y
5
2
10
4
6
20