Keystone Algebra Review

Algebra Keystone Exam Practice 102

Review: negative exponents

​What are negative exponents?

Multiple Choice

Which expression is equal to 7^-2?

• 14

• $$\frac{1}{14}$$

• -49

•   $$\frac{1}{49}$$  

Review: simplify expressions

Multiple Choice

Simplify the expression.

$$\left|-6\ -\ 3\right|\ +\ \sqrt[]{81}$$  

• 18

• 9

• 6

• 12

Review: domain & range of equations

​Evaluate different values for the variable:: try integers (positive and negative), zero, fractions, decimals

Multiple Choice

This expression is true for all integers.

$$x^4\ \ge\ x^6$$  

• Yes

• No

Review: simplify roots

​Simplify the radical portion and then multiple by the constant

Multiple Choice

Simplify the expression.

$$3\ \sqrt[]{20}$$  

• $$6\ \sqrt[]{5}$$  

• 60

• 30

• $$12\ \sqrt[]{3}$$  

Review: Greatest Common Factor

​Find the largest number/term that divides evenly into them

GCF of 14 and 21 is 7. 7 is the largest number that divides in 14 (2 times) and 21 (3 times).

GCF of x³ and x⁵ is x³. x³ divides into x⁵ (1 time) and x⁵ (with 2 remaining).

GCF of 10x⁶ and 15x⁹ is 5x⁶. 5 is the GCF of 10 and 15. x⁶ is the GCF of x⁶ and x⁹.

Multiple Choice

What is the greatest common factor of the two given terms?

3x⁴y³ and 6x²y

• 3x²y

• 3xy²

• 6x²y

• 6xy²

Review: Least Common Multiple

​Find the smallest multiple common in each number/term

LCM of 4 and 6 is 12. The multiples of 4 are 4,8,12,16,20... and the multiples of 6 are 6,12,18,24,30... They first match at 12.

LCM of x³ and x⁵ is x⁵. Find the largest exponent of x.

LCM of 10x⁶ and 15x⁹ is 30x⁹. The multiples of 10 and 15 match at 30. The largest exponent of x is x⁹.

Multiple Choice

What is the least common multiple of the two given terms?

10xy⁵ and 15x³y²

• 5x³y⁵

• 5xy

• 30x³y⁵

• 30xy

Review: F.O.I.L.

Multiply two binomials together by multiplying the First terms together, then the Outer terms, then the Inner terms, and then the Last terms. Combine any like-terms for the final answer.

Multiple Choice

What is ONE of the final terms of the following product?

(2x + 3) (x - 4)

• 2x

• 3x²

• -1

• -12

Review: Slope-intercept form

The slope-intercept form of a line is y = mx +b

Multiple Choice

Which equation matches the graph?

• $$y=\frac{1}{2}x+5$$

• $$y=2x+5$$

• $$y=-\frac{1}{2}x-5$$

• $$y=\frac{1}{2}x-5$$

Review: Word problems

For real-world problems, read the problem carefully

1. What do you know?

2. What are you trying to find? Represent this unknown with a variable.

3. Translate the words to math as an equation.

4. Solve the equation.

5. Check your result to verify it answers the question.

Multiple Choice

Company Ace produced 124 items at a cost of $1.22 each. They sold 89 of those items at a price of $8.54 each. How much profit did they make on the 89 which were sold?

• $187.54

• $651.48

• $241.98

• $291.18