Math Mastery Homework Pack
GRADE 7 MATH HOMEWORK DAY 1
Topic: Start, Change, End (Rational Numbers)
Name: __________________________________________________
1
At 5:00 p.m., the temperature in Buffalo was 2°F. During the night, the temperature decreased by 14°F. What was the temperature by midnight?
A −16°F
B −12°F
C 12°F
D 16°F
2
Shannon has $45.00 in her bank account. She makes a withdrawal of $60.00. What is her new balance?
A −$105.00
B −$15.00
C $15.00
D $105.00
3
A submarine at a depth of 450 feet below sea level rises 125 feet. What is the new position of the submarine relative to sea level?
A −575 feet
B −325 feet
C 325 feet
D 575 feet
4
This question is worth 2 points.
A hiker starts at an elevation of 250 feet above sea level. Over the next three hours, the hiker's elevation changes as follows:
- Hour 1: Climbs 120 feet
- Hour 2: Descends 310 feet
- Hour 3: Climbs 45 feet
What is the hiker's final elevation relative to sea level?
Show your work.
Answer: _________________________ feet relative to sea level
GO ON
GRADE 7 MATH HOMEWORK DAY 2
Topic: Evaluating and Solving Equations
Name: __________________________________________________
1
Which value of \(x\) makes the equation below true?
\(4x + 12 = 36\)
A 6
B 11
C 12
D 24
2
Which expression is equivalent to \(3(2x - 5) + 4x\)?
A \(10x - 5\)
B \(10x - 15\)
C \(6x - 15\)
D \(9x - 15\)
3
Mr. Jensen bought a package of 4 shirts for a total of $58.00. This price included a $6.00 shipping fee. Which equation can be used to find \(s\), the price of each shirt?
A \(4s + 6 = 58\)
B \(4s - 6 = 58\)
C \(6s + 4 = 58\)
D \(4(s + 6) = 58\)
4
This question is worth 2 points.
A repair technician charges a flat fee of $45.00 plus $32.50 per hour. If the total bill for a repair was $175.00, how many hours did the technician work?
Show your work.
Equation: __________________________________________________
Answer: _________________________ hours
GO ON
GRADE 7 MATH HOMEWORK DAY 3
Topic: Evaluating and Solving Inequalities
Name: __________________________________________________
1
What is the solution to the inequality below?
\(−5x + 10 < 25\)
A \(x < −3\)
B \(x > −3\)
C \(x < 3\)
D \(x > 3\)
2
Which graph represents the solution to the inequality \(x + 4 \ge 2\)?
A
B
C
D
(Note: Identify circle type and arrow direction.)
3
A student has $40.00 to spend at the fair. Admission is $12.00 and each ride ticket costs $2.50. Which inequality represents the maximum number of ride tickets, \(t\), the student can buy?
A \(12 + 2.50t \le 40\)
B \(12 + 2.50t \ge 40\)
C \(2.50 + 12t \le 40\)
D \(2.50(t + 12) \le 40\)
4
This question is worth 2 points.
A gym membership costs $25.00 per month plus $5.00 for each group class. Samantha wants to spend no more than $60.00 this month. What is the maximum number of group classes she can attend?
Show your work.
Answer: _________________________ classes
GO ON
GRADE 7 MATH HOMEWORK DAY 4
Topic: Constant of Proportionality (Tables)
Name: __________________________________________________
1
The table below shows a proportional relationship. What is the constant of proportionality (\(k = \frac{y}{x}\))?
A 3
B 4
C 8
D 12
2
Which table shows a relationship that is NOT proportional?
<table class="border-collapse border border-slate-400 text-center text-xs"><tbody><tr class="bg-slate-100 font-bold"><td>A</td><td>x</td><td>y</td></tr><tr><td></td><td>2</td><td>6</td></tr><tr><td></td><td>4</td><td>12</td></tr></tbody></table>
<table class="border-collapse border border-slate-400 text-center text-xs"><tbody><tr class="bg-slate-100 font-bold"><td>B</td><td>x</td><td>y</td></tr><tr><td></td><td>3</td><td>8</td></tr><tr><td></td><td>6</td><td>14</td></tr></tbody></table>
<table class="border-collapse border border-slate-400 text-center text-xs"><tbody><tr class="bg-slate-100 font-bold"><td>C</td><td>x</td><td>y</td></tr><tr><td></td><td>1</td><td>5</td></tr><tr><td></td><td>3</td><td>15</td></tr></tbody></table>
<table class="border-collapse border border-slate-400 text-center text-xs"><tbody><tr class="bg-slate-100 font-bold"><td>D</td><td>x</td><td>y</td></tr><tr><td></td><td>5</td><td>10</td></tr><tr><td></td><td>8</td><td>16</td></tr></tbody></table>
3
The cost of organic blueberries is $4.50 for 6 ounces. Which equation can be used to determine \(y\), the total cost for \(x\) ounces?
A \(y = 0.75x\)
B \(y = 1.33x\)
C \(y = 4.50x\)
D \(y = 6x\)
4
This question is worth 2 points.
A recipe for fruit punch uses 4 cups of orange juice for every 3 cups of pineapple juice. Complete the table below and identify the constant of proportionality of orange juice to pineapple juice.
| Orange (x) | Pineapple (y) |
|---|
| 4 | 3 |
| 8 | |
| 9 |
Show your work.
Constant of Proportionality: _________________________
GO ON
GRADE 7 MATH HOMEWORK DAY 5
Topic: Constant of Proportionality (Graphs)
Name: __________________________________________________
1
The graph of a proportional relationship passes through the point (4, 10). What is the constant of proportionality?
A 0.4
B 2.5
C 4
D 10
2
On the graph of a proportional relationship, what does the point (1, \(r\)) represent?
A The origin
B The unit rate
C The total cost for 10 items
D The point where the line ends
3
Which statement about the graph of a proportional relationship is NOT true?
A The graph must be a straight line.
B The graph must pass through the origin (0, 0).
C The constant of proportionality is always positive.
D The constant of proportionality can be found using any point (\(x, y\)) except the origin.
4
This question is worth 3 points.
The graph below represents the distance, in miles, a car travels over time, in hours.
(2, 110)
Distance (miles)
Time (hours)
Identify the constant of proportionality and explain what the point (2, 110) represents in the context of the problem.
End of Pack
Math Mastery Answer Key
Answer Key
Math Mastery Homework Pack • Grade 7
Single Topic Per Day Edition
DAY 1: START, CHANGE, END
Topic: Rational Number Word Problems
1. B (2 − 14 = −12)
2. B (45 − 60 = −15)
3. B (−450 + 125 = −325)
4. Constructed Response (2 Points)
- Calculation: 250 + 120 − 310 + 45
- Sum: 370 − 310 + 45 = 60 + 45 = 105
Answer: 105 feet above sea level
DAY 2: EQUATIONS
Topic: Setting Up and Solving Two-Step Equations
1. A (4x = 24 → x = 6)
2. B (6x − 15 + 4x = 10x − 15)
3. A (4s + 6 = 58)
4. Constructed Response (2 Points)
Equation: 32.50h + 45 = 175
- 175 − 45 = 130
- 130 ÷ 32.50 = 4
Answer: 4 hours
DAY 3: INEQUALITIES
Topic: Linear Inequalities
1. B (−5x < 15 → x > −3; flip when dividing by negative)
2. A (x \(\ge\) −2; closed circle, shaded right)
3. A (12 + 2.50t \(\le\) 40)
4. Constructed Response (2 Points)
Inequality: 5c + 25 \(\le\) 60
- 5c \(\le\) 35
- c \(\le\) 7
Answer: 7 classes
DAY 4: COP (TABLES)
Topic: Proportionality in Tables
1. B (12/3 = 4)
2. B (8/3 \(\approx\) 2.67, while 14/6 \(\approx\) 2.33)
3. A (4.50/6 = 0.75; y = 0.75x)
4. Constructed Response (2 Points)
- 8 Orange → 6 Pineapple (Ratio 3/4)
- 12 Orange ← 9 Pineapple
- Constant of Proportionality (y/x): 0.75
Answer: 0.75
DAY 5: COP (GRAPHS)
Topic: Constant of Proportionality in Graphs
1. B (10 ÷ 4 = 2.5)
2. B (Unit Rate)
3. C (Constant of proportionality must be positive for valid proportional relationships in Grade 7 context, but 'straight line' and 'through origin' are more fundamental defining traits. Note: Standard 7.RP.2 context is typically positive.)
4. Constructed Response (3 Points)
- Constant of Proportionality: 110 ÷ 2 = 55
- Meaning of (2, 110): The car traveled 110 miles in 2 hours.
- Unit Rate: The car travels 55 miles per hour.
