Math practice worksheet — 6th Grade (ages 11-12)

1. Which formula gives the area of a parallelogram?

2. A triangle has area 24 cm² and height 8 cm. What is its base?

3. A parallelogram has area 45 m² and height 9 m. What is its base?

4. A triangle has base 8 cm and area 28 cm². Height = 2 × 28 ÷ 8 = ____ cm.

5. A parallelogram with base 6 cm and height 4 cm has the same area as a rectangle 6 cm × 4 cm.

1. What is a line of reflection also known as?

2. Reflecting (−2, 5) in the y-axis gives…

3. A point at (3, 1) is translated by (−4, 2). The new position is…

4. Reflect (3, −2) in the x-axis. y-coordinate changes sign: −(−2) = ____. New point: (3, 2).

5. After a translation, the shape has the same size and orientation as the original.

1. A shop has 3,456,890 products. It sells 1,234,567 and receives 987,654 new products. How many are there now?

2. Which two steps require a written method? Step A: 12,000 + 8,000; Step B: 7,456,123 − 3,214,567; Step C: 20,000,000 − 10,000,000; Step D: 9,876,543 + 8,765,432.

3. A fundraiser collected £4,567,890 in year 1, £3,432,110 in year 2. In year 3 they spent £2,000,000. How much remains?

4. Running total subtracting 1,500,000 each time: 9,000,000; 7,500,000; 6,000,000; ___; 3,000,000.

5. Checking an answer using the inverse operation is a good way to verify whether a calculation is correct.

1. A bag has 24 red and 16 blue balls. What percentage are red?

2. Which set shows 0.125 correctly?

3. In a class, 3/8 passed a test. What percentage did NOT pass?

4. Mark scored 18 out of 24. As a fraction: 18/24 = 3/4. As a decimal: 0.75. As a percentage: ___.

5. A score of 7/10 is the same as 70%.

1. Convert 11/4 to a mixed number.

2. Convert 3 2/5 to an improper fraction.

3. Which improper fraction equals 4 1/3?

4. Convert each to a mixed number: 7/2 = 3½, 9/4 = ___, 11/3 = 3⅔.

5. The improper fraction 15/4 is equal to the mixed number 3 3/4.

1. Which expression gives the greater value when x = −2: 3x + 10 or x²?

2. Evaluate 4 − 3(x + 2) when x = −1.

3. Find the value of (a − b)² when a = 1 and b = −3.

4. Evaluate −2x² + 5x − 1 when x = −1. x² = 1. −2 × 1 = −2. 5 × (−1) = −5. −2 + (−5) − 1 = ___.

5. The expression (−x)² always gives the same result as x².

1. Three friends share a prize in the ratio 1:2:3. The total prize is £120. What is the largest share?

2. A juice drink is made from orange and mango in the ratio 5:3. How many ml of mango is needed for 400 ml of the drink?

3. A model train is built at scale 1:80. The real train is 32 m long. How long is the model in cm?

4. To share 84 in ratio 3:4: Find total parts = 7. Each part = 84 ÷ 7 = 12. First share = 3 × 12 = 36. Second share = ___.

5. When you scale a recipe from 4 servings to 8 servings you double every ingredient.