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Grade 7 Review Quiz — Easy Version 1
Grade 7 · MathSheets Name: ____________________ Date: __________
Answer every question. The lesson name before each question tells you which skill it checks — open that lesson if you need a reminder.
How to solve
This quiz mixes questions from different lessons, like a real test. Read each question carefully: the lesson name in front tells you what kind of problem it is. Check your answers, then practise the lessons where you made mistakes.
Example
Order of Operations with Negative Numbers: 9 × (-5) + 2 = ___
Answer: -43
✓ Correct!
Not quite. The answer is
💡 How to solve: Constant of Proportionality
In a proportional relationship y = kx, the constant of proportionality is k = yx — the unit rate. Pick any pair (x, y) with x not 0, divide y by x, and simplify. For an equation like 4y = 12x, solve for y first: y = 3x, so k = 3.
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The table shows a proportional relationship between x and y. What is the constant of proportionality k?
| x | y |
|---|---|
| 1 | 3 |
| 2 | 6 |
| 3 | 9 |
| 4 | 12 |
✓ You've got it! Press Next to keep going. Not yet — the answer is . Read the steps above once more.
| x | y |
|---|---|
| 1 | 2 |
| 2 | ___ |
| ___ | 6 |
| 4 | 8 |
✓ Correct!
Not quite. The answer is
💡 How to solve: Proportional Relationships: Tables, Graphs & Equations
A proportional relationship has the equation y = kx, where k is the unit rate (the y-value when x = 1). Find k by dividing any y by its x. To fill a missing y, multiply its x by k; to fill a missing x, divide its y by k. Each pair (x, y) is a point on the graph, and the points line up on a straight line through (0, 0). Example: 4 pages every minute gives y = 4x, so 3 minutes → 12 pages and 20 pages → 5 minutes.
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A cyclist rides 3 miles each hour. Let x be the hours and y the miles. Write the equation for this relationship.
| x | y |
|---|---|
| 1 | 3 |
| 2 | ___ |
| ___ | 9 |
| 4 | 12 |
✓ You've got it! Press Next to keep going. Not yet — the answer is . Read the steps above once more.
✓ Correct!
Not quite. The answer is
💡 How to solve: Multiplying Integers
Multiply the sizes, then decide the sign. Same signs give a positive answer: (-4) × (-3) = 12. Different signs give a negative answer: (-4) × 3 = -12. With more factors, count the negatives: an even number of negatives makes the answer positive, an odd number makes it negative.
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2 × (-3) = ___
✓ You've got it! Press Next to keep going. Not yet — the answer is . Read the steps above once more.
✓ Correct!
Not quite. The answer is
💡 How to solve: Hour & Minute Hand Angles
A full turn is 360°, so the hour marks are 30° apart. The minute hand turns 6° every minute, and the hour hand turns 30° every hour, which is 0.5° every minute. At h:m, measured from 12, the minute hand is at 6m° and the hour hand is at (30h + 0.5m)°. Subtract the two; if the result is more than 180°, take 360° minus it to get the smaller angle. The reflex angle is 360° minus the smaller angle. Example: at 7:25 the hour hand is at 222.5° and the minute hand at 150°, so the angle is 72.5°.
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Find the smaller angle between the hands at 6:00.
✓ You've got it! Press Next to keep going. Not yet — the answer is . Read the steps above once more.
✓ Correct!
Not quite. The answer is
💡 How to solve: Order of Operations with Negative Numbers
Follow the order of operations: parentheses and brackets first (innermost first), then exponents, then multiplication and division from left to right, then addition and subtraction from left to right. Multiplication does not come before division: 24 ÷ 4 × 2 = 6 × 2 = 12. Watch the signs: a negative times a negative is positive, so (-3) × (-4) = 12. An exponent belongs only to what it touches: (-4)² = (-4) × (-4) = 16, but -4² means -(4 × 4) = -16. Treat absolute value bars like parentheses: |3 - 8| = |-5| = 5.
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8 + 3 × 9 = ___
✓ You've got it! Press Next to keep going. Not yet — the answer is . Read the steps above once more.
✓ Correct!
Not quite. The answer is
💡 How to solve: Dividing Integers
Divide the sizes, then decide the sign with the same rule as multiplication. Same signs give a positive answer: (-36) ÷ (-4) = 9. Different signs give a negative answer: (-15) ÷ 3 = -5 and 24 ÷ (-6) = -4. Zero divided by any nonzero number is 0.
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(-25) ÷ 5 = ___
✓ You've got it! Press Next to keep going. Not yet — the answer is . Read the steps above once more.
✓ Correct!
Not quite. The answer is
💡 How to solve: Simple Interest
Simple interest is I = P × r × t: the principal (the amount borrowed or saved), times the yearly rate as a decimal, times the time in years. $500 at 4% for 3 years: I = 500 × 0.04 × 3 = $60. Time in months must be changed to years first: 18 months = 1.5 years.
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Find the simple interest on $600 at 3% per year for 1 year.
✓ You've got it! Press Next to keep going. Not yet — the answer is . Read the steps above once more.
✓ Correct!
Not quite. The answer is
💡 How to solve: Surface Area & Volume of Prisms (Mixed Review)
Rectangular prism: Volume = length × width × height, and Surface Area = 2(lw + lh + wh). Triangular prism: Volume = (12 × base × height of the triangle) × length of the prism.
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Find the volume of a rectangular prism with length 4, width 4, and height 5.
✓ You've got it! Press Next to keep going. Not yet — the answer is . Read the steps above once more.
✓ Correct!
Not quite. The answer is
💡 How to solve: Hanger Diagrams & Balanced Equations
A balanced hanger means both sides are equal. Take the same amount off both sides and it stays balanced. For 3x + 4 = 19, take 4 off both sides: 3x = 15. Split both sides into 3 equal groups: x = 5. For 2(x + 3) = 16, split into 2 groups first: x + 3 = 8, so x = 5.
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Find x.
✓ You've got it! Press Next to keep going. Not yet — the answer is . Read the steps above once more.
✓ Correct!
Not quite. The answer is
💡 How to solve: Discount and Sale Price
Find the discount, then subtract it from the price: 25% of $80 is $20, so the sale price is $80 - $20 = $60. Shortcut: 25% off means you pay 75%, so 0.75 × $80 = $60. For two discounts, take the second percent off the new sale price, not the original price.
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A guitar costs $110. It is on sale for 10% off. What is the sale price?
✓ You've got it! Press Next to keep going. Not yet — the answer is . Read the steps above once more.
✓ Correct!
Not quite. The answer is
💡 How to solve: One-Variable Equations
Do the opposite operation to get x alone. For x + b = c, subtract b from both sides; for x - b = c, add b to both sides; for ax = c, divide both sides by a.
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x + 4 = 8
✓ You've got it! Press Next to keep going. Not yet — the answer is . Read the steps above once more.
✓ Correct!
Not quite. The answer is
💡 How to solve: Triangle Angle Sum & Side Lengths
The three angles of any triangle add up to 180°, so a missing angle is 180° minus the other two. Three lengths make a triangle only if the two shorter lengths add up to MORE than the longest one: 4, 5, 8 works (4 + 5 > 8), but 3, 4, 7 does not (3 + 4 = 7).
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Find the value of x.
✓ You've got it! Press Next to keep going. Not yet — the answer is . Read the steps above once more.
✓ Correct!
Not quite. The answer is
💡 How to solve: Volume of Composite Prisms & Pyramids
Split a composite solid into rectangular prisms, find each volume with V = l × w × h, and add them. A pyramid holds one third of a prism with the same base and height: V = 13 × B × h, where B is the area of the base. For a square base of side 6 and height 5, V = 13 × 36 × 5 = 60.
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The solid is made of two rectangular prisms. Find its volume in cubic units.
✓ You've got it! Press Next to keep going. Not yet — the answer is . Read the steps above once more.
✓ Correct!
Not quite. The answer is
💡 How to solve: Random Samples & Making Predictions
A random sample gives every member of the population the same chance of being chosen, so it represents the population well; a biased sample favors some group. To predict, use the sample as a ratio: if 12 out of 50 sampled students walk to school, then about 1250 of 600 students walk, which is 1250 × 600 = 144.
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To learn how many hours students sleep, a counselor assigns every student a number and uses a random number generator to pick 50 of them. Is the sample biased or random?
✓ You've got it! Press Next to keep going. Not yet — the answer is . Read the steps above once more.
✓ Correct!
Not quite. The answer is
💡 How to solve: Proportional Relationships
Cross-multiply: in ab = cx, a × x = b × c, so x = (b × c) ÷ a. You can also find what the first numerator was multiplied by to get the second and multiply the denominator by the same number.
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14 = 2x, x = ___
✓ You've got it! Press Next to keep going. Not yet — the answer is . Read the steps above once more.
✓ Correct!
Not quite. The answer is
💡 How to solve: Solving & Graphing Two-Step Inequalities
Solve an inequality like an equation: undo the addition or subtraction, then the multiplication or division. If you multiply or divide both sides by a negative number, flip the inequality sign. To graph, use an open circle for < or > and a closed circle for ≤ or ≥, then shade toward the numbers that work.
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Solve and graph: 4x - 7 < -27
✓ You've got it! Press Next to keep going. Not yet — the answer is . Read the steps above once more.
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Grade 7 Review Quiz — Easy Version 1
Answer every question. The lesson name before each question tells you which skill it checks — open that lesson if you need a reminder.