Trident Math101 full course (all case and SLP) 5 modules

CAse 1

MAT 101 Case 1

Complete the following problems using the Case 1 Answer Template.

The symbol*stands for multiplication.

1. Identify the coefficients, variable terms, and constants in the following expression.

2x³+5y²-3z+1

2. Identify the coefficients, variable terms, and constants in the following expression.

4z⁵-8x²-6

3. Combine like terms in the following expression. (Hint: You can color code the like terms.)

8x²+3x+9-x²+7x-2+y

4. Distribute and combine like terms in the following expression.

3(6y²-9+7x-2x²-3x-6)

5. Write and simplify an expression that applies the distributive property. Include at least 3 different terms.

6. Simplify the expression using the order of operations. (Note: * stands for multiplication)

(6*2-4) – 3(8-5) * 7

2

7. Simplify the expression using the order of operations.

(3-5) * -| -2²- 5² * 4|

8. Translate the following statement.

The product of 3 more than a number and 3 less than the same number.

9. Translate and solve the following statement.

The quotient of 2x and 4 is the same as the product of 6 and 3.

10. Write and translate your own statement using at least two different operations (i.e. - add, subtract, multiply, divide).

11. Simplify the expression. (Hint: Careful with the signs)

-6(-4²-7)

12. Simplify the expression.

(-10)² * -|2³-7+12|

For problems 13-14, evaluate the expressions using the following values.

x= -3 y= 8 z= -12

13. 2y+3z

4x

14. 4x²-2z²

For problems 15-16, evaluate the expressions using the following values.

a= -1 b= 11 c= -7

15. 14a + (7- 6b)

c

16. (a²+b²)(b²-c²)

For problems 17-20, solve the equation. Check your answer by plugging it back into the equation.

17. 10x = 9x-15

18. 4x-9 = 7x+3

19. -3(8x-2x) = 72

20. 9(4y-3)-12y = 4(27+5y)

MAT 101 SLP 1

Complete the following problems using the SLP 1 Answer Template.

Write the final answer in the terms being asked such as dollars/cents, degrees, tickets, etc.

1. Companies often sell products at or below cost in order to draw in and retain customers. Redman Manufacturers is tracking 5 items from last month’s sales. On item #1 they make $15; item #2 loses $4; item #3 makes $9; item #4 loses $6; and item #5 makes $12. Last month’s sales are as follows:

Item #1: 90 units sold

Item #2: 103 units sold

Item #3: 78 units sold

Item #4: 45 units sold

Item #5: 164 units sold

Write, simplify, and, calculate the profit or loss for the month.

2. When principal (P) is invested at a rate of (R) over a period of time (T) in years, simple interest (I) is earned. The simple interest is calculated by multiplying the principal, rate, and time. Write an equation to represent this scenario.

3. Using the formula above, calculate the interest earned for an investment of $15,000 at a rate of 5% over 10 years.

4. The perimeter of a rectangle is P=2L+2W where L is the length and W is the width. Find the perimeter when L=15 and W=25. Show your work.

5. The formula for a triangle is A=bh. If the area of a triangle is 36 and the height is 9, what is the base?

6. The formula F=C+32 relates Celsius and Fahrenheit temperature. If the current temperature is -20°C, what is the temperature in Fahrenheit?

7. A triangle has sides measuring x+7, 2x+3, and 5x-6. Write and simplify an expression that represents the perimeter of the triangle.

8. Floral Solutions is calculating their profits for the previous month. Profit is determined by revenue minus the cost. The cost of producing floral arrangements is represented by the equation C= 18+35x and the revenue is represented by the equation R=80x+12.

a. Find the simplified expression that represents the profit.

b. Find the profit made when 110 arrangements are sold.

9. Jamie sold her house for x dollars. The real estate agent received a 5% commission and Jamie received $197,125. Write and solve an equation to determine the selling price of the house.

10. Dan works on commission and earns 4% on all of his sales. In month 1, he sold $25,000; month 2 was $17,000; and month 3 was $34,000. 18% of his total earnings are taken out for taxes. Calculate the total net (after taxes) pay Dan earned over the 3 months. Write and simplify an expression that represents this scenario.

CAse 2

Solve for the given variable. Check your answers.

1. A = 1/2bh; solve for h

2. F = 9/5C + 32; solve for C

3. P = 2L + 2W; solve for W

4. 2(z – 6) + 10z = 8(z – 2)

5. 7 – 6(5 – y) = 10(y – 4)

6. 1/4x – 18 = 1/2x – 6

7. 5/6 = -2/5b + 1/3b

8. -0.08(x – 100) + 0.07x = 90

9. 0.75(a – 35.8) = a – 22.4

Solve the following absolute value equations. Hint:There may be two answers.

10. |14 – y| = 12

11. 3|6 – d| = 18

12. |2(p – 4) – 5| = 23

13. 2 + 4|5x – 7| = 46

14. 1/4|6x – 3| = 18.75

Solve and graph the following inequalities on a number line.

Example graph:

Note: When completing this assignment in the Case 2 Answer Template, go to "insert" then "shapes" to select the circles and line(s). Use "shape fill" to make the circle either open or solid.

15. x + 7 > 11

16. 1/8 ? 1 – 1/4x

17. -1 ? 2 – 3x < 8

18. 2 > 4y – 4 ? – 4
3 3

19. -8x > 16 or 5/6x > 5

20. -7 + z ? 3z + 7 and 2(z – 3) < -4z + 2

SLp 2

1. A firm pays $1.75 for each copy of a magazine and sells each one for $2.50. There is a fixed monthly cost of $40 for printing the publication. If the firm wants to make $550 dollars next month, how many magazines do they have to sell? Write and solve an equation that represents this scenario.

2. Martin sold his computer and software for $900, receiving three times as much for the computer than the software. What was the selling price of the computer and the software? Write and solve an equation.

3. The perimeter of a pool is 64 feet and has a width of x and a length of x-4. Write an equation and find both the width and length of the pool.

4. The tax on a purchase was $9.33. If the sales tax rate is 6%, how much was the purchase? Write and solve an equation.

5. Mike needs at least a 75% average to pass his math course. The class contains 5 exams that are equally weighted. If he scored a 64%, 86%, 71%, and 90% on the first 4 tests, what score does he need on the final test to earn at least a 75% in the class. Write and solve an inequality.

6. The Parker’s are installing a wooden fence in their backyard. They have 330 feet of wood. The length can be no more than 90 feet. Write and solve an inequality to find the maximum width of the fence.

7. Paula is an office manager for ABC Advertising. She has been tasked with finding a

copy machine that falls within a budget of $750 per month. She finds a company that will lease the machine for $275 a month. Each copy costs 4 and a ream of 500 sheets of paper costs $5.00. If she estimates that they will make 10,500 copies per month, is leasing this machine a good choice? Write and solve an inequality and explain your reasoning.

8. Peter is throwing a surprise party for his friend Tammy. He has a budget of $350. If

the restaurant charges $20 per person for drinks and food and a cleanup fee of $35, what is the maximum number of people that he can invite to stay within budget? Write and solve an inequality. Hint: Don’t forget to include both Peter and Tammy as guests.

9. Sally calculated that she will lose 4.6 calories per minute walking at a rate of 3 miles

per hour. How many minutes does she need to walk to burn at least 250 calories?

Write and solve an inequality, rounding to the nearest tenth. (Hint: Check your final

answer.)

10. When solving an inequality, when is the sign reversed?

Module 5 Case

MAT101 CASE 5

Simplify

1. (4²)³

2. ⁴

3.²

4. (a⁴b⁶)⁰

5. (-2x)^-6

Evaluate each polynomial for the given value of the variable.

6. –x²-5x+6; x= -3

7. 2x²-4x-1; x= 5

Add the polynomials.

8. (4y+5y²) + (2y³-8y²)

9. (3x²-2x-3) + (-7x²+5-8x)

Subtract the polynomials.

10. (4a²+9b⁵) - (-2a²-6b⁵)

11. (-7-2z³+4y) - (3z³+12-6y)

Use the FOIL method to simplify the binomials.

12. (x-10) (x-9)

Calculations:

13. (2x-2) (x+5)

Calculations:

14. (3y-4)²

Calculations:

15. 3x(x-1) (5x+9)

Calculations:

16. (y-2) (3y³-5y+7)

Calculations:

Compute and write your answer in scientific notation.

17. (5.2 x 10¹³) (7.1 x 10^-22)

18. (4.3 x 10^-8) (1.5 x 10⁹)

Calculations:

19. 8.2 x 10⁵

2.75 x 10^-3

Calculations:

20. 6.3 x 10^-7

3.25 x 10^-12

Calculations