Math Final 25-26

Expressions Summative Study Guide

KEY

1. Evaluate the expression for the given amount. Simplify your answer completely.

• a. Evaluate expression:

  • Expression: x^2 + 8 when x = 4

  • Calculation:

  • 4^2 + 8 = 16 + 8 = 24

• b. Evaluate expression:

  • Expression: 3x - 2 when x = 3

  • Calculation:

  • 3(3) - 2 = 9 - 2 = 7

• c. Evaluate expression:

  • Expression: 2x^2 + 2 when x = 2

  • Calculation:

  • 2(2^2) + 2 = 2(4) + 2 = 8 + 2 = 10

• d. Evaluate expression:

  • Expression: 3x + y^2 when x = 2 and y = 9

  • Calculation:

  • 3(2) + 9^2 = 6 + 81 = 87

• e. Evaluate expression:

  • Expression: 7x - 3 when x = 3

  • Calculation:

  • 7(3) - 3 = 21 - 3 = 18

• f. Evaluate expression:

  • Expression: 5 + xy - 2 when x = 9 and y = 3

  • Calculation:

  • 5 + (9)(3) - 2 = 5 + 27 - 2 = 30

2. Evaluate the following expressions using PEMDAS:

• a. Evaluate:

  • Expression: 44 + 6(3)

  • Calculation:

  • 44 + 18 = 62

• b. Evaluate:

  • Expression: 9 + 3^2 + 5 + 27 - 2

  • Calculation:

  • 9 + 9 + 5 + 27 - 2 = 48

• c. Evaluate:

  • Expression: 63 / 9

  • Calculation:

  • 63 / 9 = 7

• d. Evaluate:

  • Expression: (3^3)(21)

  • Calculation:

  • 27 imes 21 = 567

• e. Evaluate:

  • Expression: 9^2 - 1.9

  • Calculation:

  • 81 - 1.9 = 79.1

• f. Evaluate:

  • Expression: (27+9)(1)

  • Calculation:

  • 36 imes 1 = 36

• g. Evaluate:

  • Expression: 81 + 2 - 1.9

  • Calculation:

  • 81 + 2 - 1.9 = 81 + 0.1 = 81.1

3. The relationship between ages:

• a. Mrs. Johnson is 12 years older than Ms. Kim.

  • When Mrs. Johnson is 42,

  • Calculation:

  • Ms. Kim’s age = 42 - 12 = 30

• b. When Ms. Kim is 21,

  • Calculation:

  • Mrs. Johnson’s age = 21 + 12 = 33

• c. Age relationship representation:

  • Ms. Kim’s age when Mrs. Johnson is x years old:

  • Expression: x - 12

4. Age relationships involving Kayla and Mary:

• a. Kayla is 3 years younger than her sister Mary.

  • When Mary is 10:

  • Calculation:

  • Kayla’s age = 10 - 3 = 7

• b. When Kayla is 14:

  • Calculation:

  • Mary’s age = 14 + 3 = 17

• c. Age representation:

  • Kayla’s age if Mary is x years old:

  • Expression: x - 3

5. Use the distributive property:

• a. Write equivalent expression for:

  • Expression: 4(x + 3)

  • Equivalent: 4x + 12

• b. Write equivalent expression for:

  • Expression: 7(2x + 4)

  • Equivalent: 14x + 28

• c. Write equivalent expression for:

  • Expression: 8(x + 1)

  • Equivalent: 8x + 8

• d. Write equivalent expression for:

  • Expression: x(9 - 4)

  • Equivalent: 5x

• e. Write equivalent expression:

  • Expression: (x + 16)

  • Equivalent: Not clearly defined, skipping.

• f. Write equivalent expression for:

  • Expression: 9(x - rac{1}{1})

  • Equivalent: 9x - 9

6. Ticket costs at Six Flags:

• a. Adult ticket costing 1.75 times as much as child ticket:

  • If child's ticket costs 45,

  • Calculation:

  • Adult ticket cost = 45 imes 1.75 = 78.75

• b. Expression for adult ticket if child’s costs c:

  • Expression: 1.75c

7. Meal costs:

• a. Adult meal costs 3.5 times child's meal.

  • Expression for adult meal if child’s cost c:

  • Expression: 3.5c

• b. Adult meal price if child's meal costs 5.50:

  • Calculation:

  • 3.5 imes 5.50 = 19.25

8. Combine like terms to make equivalent expressions:

• a. Expression: 3x + 2y + 5 - x + 9

  • Combined:

  • Result: 2x + 2y + 14

• b. Expression: 4xy + 2x - 2xy + 3y

  • Combined:

  • Result: 2xy + 2x + 3y

• c. Expression: 4x^2 - 3x + 4 - x^2 + 2x - 4

  • Combined:

  • Result: 3x^2 + 5x

• d. Expression: 3x + 4 - 3x - 4

  • Combined:

  • Result: 0

• e. Expression: 2x^2 + 3x - 6 + 4x + 9x^2

  • Combined:

  • Result: 11x^2 + 7x - 6

9. Write algebraic expressions:

• a. 35 less than a number:

  • Expression: x - 35

• b. The product of a number and 3:

  • Expression: 3x

• c. Twice a number plus 12:

  • Expression: 2x + 12

• d. The sum of a number and 16:

  • Expression: x + 16

• e. The quotient of 6 and x:

  • Expression: rac{6}{x}

• f. 15 more than the product of 6 and y:

  • Expression: 15 + 6y

• g. The difference of a number and 13:

  • Expression: x - 13

• h. Half of a number:

  • Expression: rac{1}{2}x

10. Write expressions for situations:

• a. Janice is twice Sally's age:

  • Expression: 2x

• b. Isla is 3 years older than Aadya:

  • Expression: x + 3

• c. Austin scored half as many points as Mason:

  • Expression: rac{1}{2}y

• d. Lauren wrote 4 times as much as Jackson:

  • Expression: 4x

• e. Dia scored 10 points higher than Ishan:

  • Expression: x + 10

• f. Shelley dove 20 feet into the water:

  • Expression: x - 20

• g. Amber paid 50 times more than the original price:

  • Expression: 50x

11. Tell the operation that words represent:

• a. Difference: Subtraction

• b. Quotient: Division

• c. Sum: Addition

• d. Product: Multiplication

• e. Twice: Multiplication by 2

• f. Split Equally: Division

• g. More than: Addition

• h. Less than: Subtraction

12. The word "than" means to do what to the numbers when writing an expression?

• Answer: Switch the order of the numbers.

  • Example: 4 ext{ less than } x is written as x - 4

  • Example: x ext{ less than } 4 is written as 4 - x