Expressions, Equations & Functions

Order of Operations

100

7 + 2(9-3)

19

200

[(2^5 - 5) ÷ 9]11

33

300

Evaluate each expression if a=4 and c=9. c + 3a

21

400

Evaluate each expression if a=4, b=3 and c=9. (a^2 + 2bc) ÷ 7

10

500

One-scoop sundae is $2.75 and two-scoop sundae is $4.25. Find the total cost of a 3 one-scoop sundaes and 2 two-scoop sundaes.

$16.75

Properties

100

Evaluate and name the properties used. 8 x 0.5 x 5

8 x 0.5 x 5 = (8 x 5) x 0.5 Commutative/Associative = 40 x 0.5 Substitution = 20 Substitution

200

Evaluate and name the properties used. (16 - 4^2) + 9

(16 - 4^2) + 9 = 16 - 16 + 9 Substitution = 0 + 9 Additive Inverse = 9 Additive Identity

300

Evaluate and name the properties used. 18 x 3(1 ÷ 3)

18 x 3(1 ÷ 3) = 18 x 3(1/3) Substitution = 18 x 1 Multiplicative Inverse = 18 Multiplicative Identity

400

Use the Distributive Property to solve. -2(5-3)

-2(5) - (-2)(3) -10 - (-6) -10 + 6 -4

500

Rewrite using the Distributive Property and simplify. -4(5 - 2t)

-4(5 - 2t) = -4(5) - (-4)(2t) = -20 - (-8t) = -20 + 8t

Equations

100

Solve the equation. a = 24 - 7(3)

3

200

Find the solution set if the replacement set is y:{6,8,10,12,14} y - 9 = 3

12

300

Find the solution set if the replacement set is y:{6,8,10,12,14} 4y = 32

8

400

Find the solution set if the replacement set is y:{6,8,10,12,14} 42/y = 7

6

500

Shandra's age is four more than three times Sherita's age. Write an equation for Shandra's age. Solve if Sherita is 3 years old.

3K + 4 = E If Sherita is 3, then Shandra is 13

Relations & Functions

100

Is the following mapping a function? explain.

No, it is not a function because.

200

Given the relation: {(1,2) , (3, -2), ( 2, 6) , ( -1, -2)} a. what is the domain and range? b. Is the relation a function? explain.

a.domain = {1,3,2,-1} range = {2, -2, 6, -2} b. Yes because each number in the domain is paired with only one number in the range.

300

If f(x) = -2x^2 + 4, what is f(-3).

f(-3) = -2(-3)^2 + 4 = -2(9) + 4 = -18 + 4 = -14

400

If f(x) = x^2 - 5, what is 2[f(-1)] + 3

f(-1) = (-1)^2 -5 = 1 - 5 = -4 2[-4] + 3 = -8 + 3 = -5

500

If f(x) = -3x - 10, and g(x) = x^2, what is f(m + 2) + g(-1)?

f(m + 2) = -3(m + 2) - 10 g(-1) = (-1)^2 = -3m -6 - 10 = 1 = -3m - 16 f(m+2) + g(-1) = -3m - 16 + 1 = -3m -15

Word Problems

100

Translate the following verbal expression into an algebraic one and then simplify! the sum of six and x decreased by the product of two and x

What is (6 + x) - 2x = 6 -x

200

Translate the following algebraic expression into a verbal one (you may not use the word "minus") 3x^2 - 15

the product of 3 and x sqaured decreased by 15

300

On average, 7 plants grow for every 10 seeds of a certain type planted. Make a table to determine the domain and range to show the relationship between seeds planted and plants growing for 50, 100, 150 and 200 seeds.

Domain Range 50 35 100 70 150 105 200 140

400

The equation y = 10 + 2x represents the cost to join the art club per month. (x represents the number of art projects done in a month). a. write the equation in function notation. b. explain what the domain and the range represent. c. Find f(3). what does this value represent?

a. f(x) = 10 + 2x b. domain = the number of art projects range = cost per month c. f(3) = 10 + 2(3) = 16 it costs $16 for this month.

500

The average math test scores f(t) for 17 year olds is represented by the function f(t) = .8t + 72 where t represents the average science test score. a. what is the domain and range of this function? b. what is the science score that corresponds to a math score of 308?

a. domain is the science scores range is the math scores b. f(308) = .8(308) + 72 = 295