Mr. Sault's Classroom - Mr. Sault's Thoughts



Unit 6 Practice Test

Multiple Choice Identify the choice that best completes the statement or answers the question.

____ 1. Which linear system has the solution x = –2 and y = 6?

|a. |x + 3y = 16 |c. |x + 2y = –2 |

| |4x + 4y = 16 | |2x + 4y = –4 |

|b. |x + 3y = 17 |d. |2x + y = –2 |

| |2x + y = 15 | |x + y = 16 |

____ 2. Create a linear system to model this situation:

A collection of nickels and dimes contains four times as many dimes as nickels. The total value of the collection is $20.25.

|a. |d = 4n |b. |d = 4n |c. |n = 4d |d. |d + n = 15 |

| |5n + 10d = 2025 | |5d + 10n = 2025 | |5n + 10d = 2025 | |5n + 10d = 2025 |

____ 3. Create a linear system to model this situation:

A length of outdoor lights is formed from strings that are 5 ft. long and 11 ft. long. Fourteen strings of lights are 106 ft. long.

|a. |5x + 11y = 14 |c. |x + y = 14 |

| |x + y = 106 | |5x + 11y = 106(14) |

|b. |x + y = 14 |d. |x + y = 14 |

| |5x + 11y = 106 | |x + 2y = 106 |

____ 4. Which graph represents the solution of the linear system:

–3x – y = –5

4x – y = [pic]

[pic][pic]

[pic][pic]

|a. |Graph A |c. |Graph C |

|b. |Graph B |d. |Graph D |

____ 5. Use the graph to approximate the solution of the linear system:

[pic]

[pic]

[pic]

|a. |(–3, 0.2) |c. |(0.2, –3) |

|b. |(0, –2.8) |d. |(–2.8, 0) |

____ 6. Car A left Calgary at 8 A.M. to travel 500 mi. to Regina, at an average speed of 63 mph.

Car B left Regina at the same time to travel to Calgary at an average speed of

37 mph. A linear system that models this situation is:

d = 500 – 63t

d = 37t,

where d is the distance in miles from Regina, and t is the time in hours since 8 A.M. Which graph would you use to determine how far the cars are from Regina when they meet? What is this distance?

|[pic] |[pic] |

|[pic] |[pic] |

|a. |Graph C: |b. |Graph D: |c. |Graph A: |d. |Graph B: |

| |195.8 mi. | |200 mi. | |185 mi. | |92.5 mi. |

____ 7. Use the graph to approximate the solution of this linear system:

6x – 7y = –4

– [pic]y = 3x + 7

[pic]

|a. |(–0.1, 3.8) |b. |(–2.1, –1.2) |c. |(–1.2, 3.8) |d. |(–2.1, –0.1) |

____ 8. Use substitution to solve this linear system.

x = 2y – 56

5x + 13y = 410

|a. |(4, –30) |b. |(–4, 30) |c. |(4, 30) |d. |(–4, –30) |

____ 9. Identify two like terms and state how they are related.

–10x + 20y = 460

30x + 60y = 1620

|a. |–10x and 30x; by a factor of –3 |c. |30x and 60y; by a factor of 2 |

|b. |–10x and 20y; by a factor of –2 |d. |–10x and 460; by a factor of [pic] |

____ 10. Use substitution to solve this linear system:

x – y = 18

[pic]x + [pic]y = [pic]

|a. |x = 4; y = 18 |b. |x = –14; y = –14 |c. |x = 4; y = –14 |d. |x = 4; y = 4 |

____ 11. For each equation, identify a number you could multiply each term by to ensure that the coefficients of the variables and the constant term are integers.

(1) [pic]x + [pic]y = [pic]

(2) [pic]x – [pic]y = [pic]

|a. |Multiply equation (1) by 35; multiply equation (2) by 12. |

|b. |Multiply equation (1) by 12; multiply equation (2) by 35. |

|c. |Multiply equation (1) by 2; multiply equation (2) by 3. |

|d. |Multiply equation (1) by 3; multiply equation (2) by 2. |

____ 12. Write an equivalent system with integer coefficients.

[pic]x + [pic]y = [pic]

[pic]x + 5y = [pic]

|a. |[pic]x + [pic]y = 1 |c. |[pic]x + [pic]y = [pic] |

| |[pic]x + [pic]y = 1 | |[pic]x + [pic]y = [pic] |

|b. |[pic]x + [pic]y = [pic] |d. |[pic]x + [pic]y = [pic] |

| |[pic]x + [pic]y = [pic] | |[pic]x + [pic]y = [pic] |

____ 13. Use an elimination strategy to solve this linear system.

[pic]

[pic]

|a. |[pic] and [pic] |c. |[pic] and [pic] |

|b. |[pic] and [pic] |d. |[pic] and [pic] |

____ 14. Write an equivalent linear system where both equations have the same x-coefficients.

[pic]

[pic]

|a. |[pic] and [pic] |c. |[pic] and [pic] |

|b. |[pic] and [pic] |d. |[pic] and [pic] |

____ 15. Use an elimination strategy to solve this linear system.

[pic]

[pic]

|a. |[pic] and [pic] |c. |[pic] and [pic] |

|b. |[pic] and [pic] |d. |[pic] and [pic] |

Short Answer

16. Create a linear system to model this situation:

A sack of wheat costs $10.75 and a sack of oats costs $12.75. If the total cost was $778.75 and

65 sacks were ordered, how many sacks of each grain were purchased?

Verify that 25 sacks of wheat and 40 sacks of oats represent the solution of the linear system.

17. Solve this linear system by graphing.

–3x – 2y = 16

–x + y = –8

[pic]

18. Use substitution to solve this linear system:

[pic]

[pic]

19. Use an elimination strategy to solve this linear system.

[pic]

[pic]

20. Model this situation with a linear system:

The perimeter of a rectangle is 234 ft. When its length is doubled, the perimeter increases by 58 ft.

Problem

21. a) Write a linear system to model this situation.

Mrs. Cheechoo paid $155 for one-day tickets to Silverwood Theme Park for herself, her husband, and 3 children. Next month, she paid $285 for herself, 3 adults, and 5 children.

b) Use a graph to solve this problem:

What are the prices of a one-day ticket for an adult and for a child?

22. a) Write a linear system to model the situation:

For the school play, the cost of one adult ticket is $6 and the cost of one student ticket is $4. Twice as many student tickets as adult tickets were sold. The total receipts were $2016.

b) Use substitution to solve the related problem:

How many of each type of ticket were sold?

23. Use an elimination strategy to solve this linear system. Verify the solution.

[pic]

[pic]

Gr.10 Precalculus Practice Test

Answer Section

MULTIPLE CHOICE

1. ANS: A REF: 7.1 Developing Systems of Linear Equations

2. ANS: A REF: 7.1 Developing Systems of Linear Equations

3. ANS: B REF: 7.1 Developing Systems of Linear Equations

4. ANS: A REF: 7.2 Solving a System of Linear Equations Graphically

5. ANS: C REF: 7.2 Solving a System of Linear Equations Graphically

6. ANS: C REF: 7.2 Solving a System of Linear Equations Graphically

7. ANS: B REF: 7.2 Solving a System of Linear Equations Graphically

8. ANS: C REF: 7.4 Using a Substitution Strategy to Solve a System of Linear Equations

9. ANS: A REF: 7.4 Using a Substitution Strategy to Solve a System of Linear Equations

10. ANS: C REF: 7.4 Using a Substitution Strategy to Solve a System of Linear Equations

11. ANS: B REF: 7.4 Using a Substitution Strategy to Solve a System of Linear Equations

12. ANS: D REF: 7.4 Using a Substitution Strategy to Solve a System of Linear Equations

13. ANS: C REF: 7.5 Using an Elimination Strategy to Solve a System of Linear Equations

14. ANS: C REF: 7.5 Using an Elimination Strategy to Solve a System of Linear Equations

15. ANS: A REF: 7.5 Using an Elimination Strategy to Solve a System of Linear Equations

SHORT ANSWER

16. ANS:

Let w represent the number of sacks of wheat and o represent the number of sacks of oats.

A linear system is:

w + o = 65

10.75w + 12.75o = 778.75

Since [pic] and [pic] satisfy each equation, these numbers are the solution of the linear system.

17. ANS:

(0, –8)

[pic]

18. ANS:

x = –55; y = –18

19. ANS:

[pic]

[pic]

20. ANS:

[pic]

[pic]

PROBLEM

21. ANS:

a) Let a represent the cost in dollars for a one-day adult ticket, and c represent the cost in dollars for a one-day child ticket.

Then, a system of equations is:

2a + 3c = 155

4a + 5c = 285

b)

[pic]

Since the intersection point is at (40, 25), the cost of a one-day adult ticket is $40, and the cost of a one-day child ticket is $25.

22. a) Let a represent the number of adult tickets sold, and s represent the number of student tickets sold.

There were twice as many student tickets as adult tickets.

The first equation is:

2a = s

The total receipts were $2016.

The second equation is:

6a + 4s = 2016

The linear system is:

2a = s (1)

6a + 4s = 2016 (2)

b) Solve for s in equation (1).

2a = s (1)

s = 2a

Substitute s = 2a in equation (2).

6a + 4s = 2016 (2)

6a + 4(2a) = 2016

6a + 8a = 2016

14a = 2016

a = [pic]

a = 144

Substitute a = 144 in equation (1).

2a = s (1)

2(144) = s

288 = s

144 adult tickets and 288 student tickets were sold.

23. [pic] [pic]

[pic] [pic]

Multiply equation [pic] by 3, then add to eliminate c.

3 × equation [pic]: [pic]

[pic] [pic]

Add:

[pic] [pic]

[pic] [pic]

Substitute [pic] in equation [pic].

[pic]

Verify the solution.

In each equation, substitute: [pic] and [pic]

|[pic] |[pic] |

|[pic] |[pic] |

For each equation, the left side is equal to the right side, so the solution is: [pic] and [pic]

................
................

In order to avoid copyright disputes, this page is only a partial summary.

Google Online Preview   Download