Topic 1: Addition or subtraction of fractions with the same denominator
- Simplify: 3/8 + 5/8: 1.
- Compute: 7/12 - 4/12: 1/4.
Topic 2: Using a calculator to approximate a square root
- Use a calculator to approximate √20 to two decimal places: 4.47.
- Approximate √50 to two decimal places using a calculator: 7.07.
Topic 3: Exponents and fractions
- Evaluate: (1/2)³: 1/8.
- Compute: (3/4)²: 9/16.
Topic 4: Perimeter of a square or a rectangle
- Find the perimeter of a rectangle with length 6 cm and width 4 cm: 20 cm.
- Calculate the perimeter of a square with a side length of 5 meters: 20 meters.
Topic 5: Area of a square or a rectangle
- Find the area of a rectangle with length 8 cm and width 3 cm: 24 cm².
- Calculate the area of a square with a side length of 7 meters: 49 m².
Topic 6: Square root of a perfect square
- Find the square root of 16: 4.
- Compute the square root of 81: 9.
Topic 7: Writing a one-step expression for a real-world situation
- Write an expression for the cost of buying n books at $10 each: 10n.
- Write an expression for the total distance traveled at 60 mph for t hours: 60t.
Topic 8: Translating a phrase into a one-step expression
- Translate "five more than a number x" into an expression: x + 5.
- Write an expression for "twice a number y": 2y.
Topic 9: Translating a phrase into a two-step expression
- Translate "three times a number x plus 4" into an expression: 3x + 4.
- Write an expression for "double a number y minus 7": 2y - 7.
Topic 10: Evaluating a linear expression: Integer multiplication with addition or subtraction
- Evaluate 3x + 5 when x = 2: 11.
- Compute 4y - 6 when y = -3: -18.
Topic 11: Evaluating a quadratic expression: Integers
- Evaluate x² + 2x + 1 when x = 3: 16.
- Compute 2y² - 4 when y = -2: 4.
Topic 12: Combining like terms: Whole number coefficients
- Simplify: 3x + 5x + 2: 8x + 2.
- Combine like terms: 7y + 4 + 2y: 9y + 4.
Topic 13: Combining like terms: Integer coefficients
- Simplify: 4x - 2x + 5: 2x + 5.
- Combine like terms: -3y + 7 - 5y: -8y + 7.
Topic 14: Multiplying a constant and a linear monomial
- Multiply: 5(3x): 15x.
- Compute: -2(4y): -8y.
Topic 15: Distributive property: Whole number coefficients
- Simplify: 3(x + 4): 3x + 12.
- Expand: 6(2y + 1): 12y + 6.
Topic 16: Distributive property: Integer coefficients
- Simplify: -2(x + 3): -2x - 6.
- Expand: -4(2y - 5): -8y + 20.
Topic 17: Using distribution and combining like terms to simplify: Univariate
- Simplify: 2(x + 3) + 4x: 6x + 6.
- Combine and simplify: 3(y - 2) + 5y: 8y - 6.
Topic 18: Combining like terms in a quadratic expression
- Simplify: 2x² + 3x² + 4x - 2x: 5x² + 2x.
- Combine like terms: 5y² - 2y + 3y² + 7y: 8y² + 5y.
Topic 19: Distinguishing between the area and perimeter of a rectangle
- A rectangle has length 10 cm and width 4 cm. Calculate its perimeter and area, and explain the difference: Perimeter: 28 cm, Area: 40 cm²; perimeter measures the boundary, area measures the enclosed space.
- For a rectangle with length 7 m and width 3 m, find the perimeter and area, and distinguish between the two: Perimeter: 20 m, Area: 21 m²; perimeter is the total length around, area is the space inside.
Topic 20: Greatest common factor of 2 numbers
- Find the greatest common factor of 12 and 18: 6.
- Determine the greatest common factor of 24 and 36: 12.