Day 090Unit 6 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 5 (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
Draw a horizontal or vertical number line. Plot and label -4, 0, and 3.
- Previous unit review
Compare -5 ___ -3 using <, >, or =. Sketch a number line to justify.
- Previous unit review
Plot P(-3, 2) on a coordinate plane and name its quadrant.
- Previous unit review
Plot (-7, 2) and (4, 2). Find their distance.
- Current unit
Write 4^4 as repeated multiplication and evaluate.
- Current unit
Write 3^2 as repeated multiplication and evaluate.
- Current unit
Evaluate 8 + 2 × 3. Show the intermediate steps.
- Current unit
Evaluate (7 + 3) × 5^2. Show the intermediate steps.
- Current unit
For 2x + 2y + 3, list terms, coefficients, and the constant.
- Current unit
Write an expression for 5 times the sum of x and 6.
- Current unit
Write an expression for 2 times the sum of x and 4.
- Current unit
Evaluate x^2 + 6y for x = 6 and y = 4.
- Current unit
Evaluate x^2 + 6y for x = 2 and y = 6.
- Current unit
Expand 5(3x + 3). Verify your result at x = 2.
- Current unit
Simplify 4(x + 4) + 6x. Explain which terms combine.
- Current unit
Are 3(x + 3) and 3x + 9 equivalent for every x? Use a property or a counterexample.
- Current unit
Write 5^3 as repeated multiplication and evaluate. Explain why it differs from 5 × 3.
- Current unit
Write 4^4 as repeated multiplication and evaluate. Explain why it differs from 4 × 4.
- Current unit
Evaluate 20 ÷ 4 × 6 + 4^2. Show the intermediate steps.
- Current unit
Evaluate 40 ÷ 5 × 7 + 5^2. Show the intermediate steps.
Answers and reasoning
Reveal the teacher answer key
- -4 < 0 < 3; unit steps
Negative -4 is left of or below 0; 3 is right of or above 0. Use equal intervals.
- <
-5 < -3; greater numbers lie farther right.
- Quadrant II
Move 3 left, then 2 up.
- 11 units
Only one coordinate changes. Opposite sides of 0: 7 + 4 = 11.
- 4 × 4 × 4 × 4 = 256
The exponent counts 4 factors of 4; multiply all factors.
- 3 × 3 = 9
The exponent counts 2 factors of 3; multiply all factors.
- 14
Use parentheses and exponents first, then × and ÷ left to right, then + and -. Result: 14.
- 250
Use parentheses and exponents first, then × and ÷ left to right, then + and -. Result: 250.
- Terms 2x, 2y, 3; coefficients 2, 2; constant 3
Terms are separated by addition; coefficients multiply variables.
- 5(x + 6)
Group the sum before multiplying.
- 2(x + 4)
Group the sum before multiplying.
- 60
Substitute first: 6^2 + 6 × 4 = 60.
- 40
Substitute first: 2^2 + 6 × 6 = 40.
- 15x + 15; both give 45 at x = 2
Multiply the outside factor by every inside term, including the constant.
- 10x + 16
Add coefficients of x terms; add only constants to constants. Distribute first if needed.
- Yes; distribution gives 3x + 9
3(x + 3) = 3x + 9. This matches.
- 5 × 5 × 5 = 125; 5 × 3 = 15
The exponent counts 3 factors of 5; multiply all factors.
- 4 × 4 × 4 × 4 = 256; 4 × 4 = 16
The exponent counts 4 factors of 4; multiply all factors.
- 46
Use parentheses and exponents first, then × and ÷ left to right, then + and -. Result: 46.
- 81
Use parentheses and exponents first, then × and ÷ left to right, then + and -. Result: 81.