Day 105Unit 7 Test
I can apply the skills taught so far, show my reasoning, and check my answers.
Show what you know
Questions 1–4 review Unit 6 (20%). The remaining 16 questions assess the current unit. Show your work, simplify exact answers, label units, and explain when asked.
Unit Test
Begin with the review questions, then continue through the current-unit questions.
- Previous unit review
Evaluate 4 + 2 × 6. Show the intermediate steps.
- Previous unit review
Write an expression for 5 less than n.
- Previous unit review
Evaluate 7x + 4 for x = 6.
- Previous unit review
Are 7(x + 7) and 7x + 49 equivalent for every x? Use a property or a counterexample.
- Current unit
Does x = 6 solve 8x + 3 = 43? Show substitution.
- Current unit
Solve x + 4 = 7. Check in the original equation.
- Current unit
Solve x - 2 = 1. Check in the original equation.
- Current unit
Solve 2 × x = 5. Check in the original equation.
- Current unit
Solve x ÷ 5 = 3/5. Check in the original equation.
- Current unit
7 identical lengths of rope total 42 m. Let x be the length of one piece. Write and solve an equation, then check.
- Current unit
Let x be any real number. Write and graph: x is less than 35. Label the endpoint and shade the solution ray.
- Current unit
Which values in {7, 8, 9} satisfy x ≤ 8? Test each by substitution.
- Current unit
Let x be any real number. Write and graph: x is less than 9. Label the endpoint and shade the solution ray.
- Current unit
A shop charges $3 for each of n notebooks plus a single $6 delivery fee. Name the independent and dependent variables and write a cost rule. What does the cost at n = 0 mean in this model?
- Current unit
For y = 5x + 5, make a table for x = 0, 1, 2, 4. Plot the ordered pairs and label both axes. Explain what happens to y each time x increases by 1.
- Current unit
For y = 4x + 5, make a table for x = 0, 1, 2, 3. Plot the ordered pairs and label both axes. Explain what happens to y each time x increases by 1.
- Current unit
Does x = 4 solve 7x + 7 = 35? Show substitution.
- Current unit
Solve x + 3/2 = 5. Check in the original equation.
- Current unit
Solve x - 5/2 = 1/2. Check in the original equation.
- Current unit
Solve 1 × x = 7/2. Check in the original equation.
Answers and reasoning
Reveal the teacher answer key
- 16
Use parentheses and exponents first, then × and ÷ left to right, then + and -. Result: 16.
- n - 5
Start with n, then subtract the named amount.
- 46
Substitute first: 7 × 6 + 4 = 46.
- Yes; distribution gives 7x + 49
7(x + 7) = 7x + 49. This matches.
- No; left side = 51
8 × 6 + 3 = 51; compare with 43.
- x = 3
Subtract 4 on both sides. Then x = 3; substitution gives 7 on each side.
- x = 3
Add 2 on both sides. Then x = 3; substitution gives 1 on each side.
- x = 5/2
Divide by 2 on both sides. Then x = 5/2; substitution gives 5 on each side.
- x = 3
Multiply by 5 on both sides. Then x = 3; substitution gives 3/5 on each side.
- 7x = 42; x = 6 m
Divide the total by 7: 42 ÷ 7 = 6.
- x < 35; open circle at 35, shade left
“less than” means <; exclude the endpoint.
- 7, 8
Values below 8 work; the endpoint works too.
- x < 9; open circle at 9, shade left
“less than” means <; exclude the endpoint.
- Independent n = notebooks; dependent C = cost; C = 3n + 6; C(0) = $6, the fee
The chosen notebook count is the input; multiply it by price and add any fixed fee to get the cost.
- (0, 5); (1, 10); (2, 15); (4, 25); y increases by 5
Substitute each input into y = 5x + 5; x is horizontal and y vertical.
- (0, 5); (1, 9); (2, 13); (3, 17); y increases by 4
Substitute each input into y = 4x + 5; x is horizontal and y vertical.
- Yes; left side = 35
7 × 4 + 7 = 35; compare with 35.
- x = 7/2
Subtract 3/2 on both sides. Then x = 7/2; substitution gives 5 on each side.
- x = 3
Add 5/2 on both sides. Then x = 3; substitution gives 1/2 on each side.
- x = 7/2
Divide by 1 on both sides. Then x = 7/2; substitution gives 7/2 on each side.