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Math 7/8 Study Guide
Unit: Algebraic Expressions
Name___________________
Knowledge and Understanding
1. What is scientific notation and how is it useful?
It takes really large or really small numbers and puts them into forms that are easier to
work with.
2. What is an algebraic expression?
An algebraic expression is a sentence that contains at least one variable.
Proficiency of Skills
3. Translate the phrase into an algebraic expression:
The product of two and y less than twelve
12 – 2y
4. Change to standard notation:
2.7 x 10-6
.0000027
5. Evaluate the expression if a = 16, b = -3, and c = -8.
2
+ 3b - 6c + 2 2
a
-56 ¼
6. Simplify:
6y (4 – 5y)
24y – 30y²
7. Simplify and rewrite with positive exponents.
9a-2 g³ y-1
(9g³) / (a²y)
8. Simplify and rewrite with positive exponents.
60 x-6 y-7
12 x-2
(60x²) / (12x6 y7)
9. Change to standard form:
7.9 x 10-6
.0000079
Application
10. Florence bought five sweaters at Macys for $29.99 each and two pairs of
pants for $39.99 each. Write an expression for the total cost.
$29.99s + $39.99p = T
11. Fred started a bank account with $55.00. On the 2nd of each month for 6 months she deposited
$22.00. Write an expression for her total funds.
55 + 6(22) = T
12. A pencil is 21.3 cm long. If you were to lay 10,000 pencils end-to-end, how many millimeters
long would they be? Write the answer in scientific notation.
2.13 x 106
13. Simplify: 12(2 - 3k)
24 – 36k
14. Evaluate the expression if p = -7 and s = 5
21 + 3p + 7s
21 + 3(-7) + 7(5) = 35
15. Name the property that is shown.
7 + (6 + x) = (7 + 6) + x
Associative of addition
16. Translate the phrase into an algebraic expression
Ten more than the product of twenty-one and a number
10 + 21x
17. How would you write .0000397 in scientific notation?
3.97 x 105
18. What is 5(n  4) when n=2 ?
5(2-4) = 5-2 = 1/25
19. A mechanic measured the gap in a spark plug and found it to be 4.5x 10 2 inches. What is the
standard form of 4.5x 10 2 ?
.045
20. What is the product of 70,000 and 30 written in scientific notation?
(70,000)(30) = 21,00000 = 2.1 x 106