Answer: 7a + 2b
4. Simplify the expression: [1 pt]
7 + 4x - 2 + x
Answer: 5x + 5
5. Evaluate 4x + 3 when x = 5 [1 pt]
Substitute x = 5:
4(5) + 3
= 20 + 3 = 23
Answer:
23
6. Evaluate 15 - 2y when y = 6 [2 pts]
Substitute y = 6:
15 - 2(6)
= 15 - 12 = 3
Answer:
3
7. Solve: x + 7 = 15 [1 pt]
Subtract 7 from both sides:
x = 15 - 7
x = 8
x =
8
8. Solve: 6m = 24 [2 pts]
Divide both sides by 6:
m = 24 ÷ 6
m = 4
m =
4
9. A box has some pencils. 6 pencils are taken out. Now, 14 pencils are left. [4 pts]
a) Write an equation using p:
p - 6 = 14
b) Solve for total pencils (p):
p = 20
Add 6 to both sides: p = 14 + 6 → p = 20 pencils. [2 pts for eqn, 2 pts for solution]
Teacher Answer Key • Math Mastery Final Page 2 of 5
Grade 6 Mathematics Final Test • Answer Key
14 Points
1. A basket has 8 red apples & 12 green apples: [2 pts]
a) Ratio of red to green:
8 : 12 (or 8 to 12)
b) Simplified ratio:
2 : 3 (divide by 4)
2. Simplify the ratio to its lowest terms: [1 pt]
15 : 25
Answer:
3 : 5 (divide both by 5)
3. A car travels 180 km in 3 hours. Find the speed in km per hour. [2 pts]
Speed = Distance ÷ Time
Speed = 180 km ÷ 3 hours
= 60 km/h
Answer:
60 km/h
4. A pack of 5 juice boxes costs $10. Find the cost of 1 juice box. [2 pts]
Unit Cost = Price ÷ Quantity
Unit Cost = $10 ÷ 5
= $2.00
Answer:
$2.00
5. Solve for x: [2 pts]
\[ \frac{3}{4} = \frac{x}{12} \implies \frac{3 \times 3}{4 \times 3} = \frac{9}{12} \]
x =
9
6. Solve for y: [2 pts]
2 : 5 = 10 : y → \( 2 \times 5 = 10 \), so \( 5 \times 5 = 25 \)
y =
25
7. A recipe for 4 pancakes uses 2 cups of milk. How many cups of milk do you need to make 12 pancakes? [3 pts]
1. Ratio of pancakes to milk = 4 : 2 → 2 : 1 (2 pancakes per cup)
2. For 12 pancakes: 12 ÷ 2 = 6 cups of milk.
(Or: 12 pancakes is 3x the recipe, so 2 cups × 3 = 6 cups).
Answer:
6 cups
Teacher Answer Key • Math Mastery Final Page 3 of 5
Grade 6 Mathematics Final Test • Answer Key
14 Points
Complete the table. Write fractions in simplest form.
| Fraction (Simplest Form) | Decimal | Percentage (%) |
|---|---|---|
| \[ \frac{1}{2} \] | 0.5 | 50% |
| \[ \frac{1}{4} \] | 0.25 | 25% |
| \[ \frac{4}{5} \] (accept \(\frac{80}{100}\)) | 0.8 (or 0.80) | 80% |
1. Calculate: 20% of 150 [2 pts]
Method 1: 10% of 150 = 15 → 15 × 2 = 30
Method 2: \(\frac{20}{100} \times 150 = 30\)
Answer:
30
2. Calculate: 75% of 40 [2 pts]
75% = \(\frac{3}{4}\)
\(\frac{3}{4} \times 40 = 3 \times 10 = 30\)
Answer = 30
Answer:
30
3. In a class of 25 students, 12% were absent on Monday. [4 pts]
a) How many students were absent?
\( 0.12 \times 25 = 3 \) students.
Answer:
3 students
b) How many students were present?
25 - 3 = 22 students.
Answer:
22 students
Grade 6 Mathematics Final Test Page 4 of 5
Grade 6 Mathematics Final Test • Answer Key
14 Points
1. Buy for $12 (Cost), sell for $15: [2 pts]
a) Profit or Loss?
Profit
b) Amount ($):
$3 ($15 - $12)
2. Buy for $25 (Cost), sell for $20: [2 pts]
a) Profit or Loss?
Loss
b) Amount ($):
$5 ($25 - $20)
3. A jacket is bought for $40 and sold for $50. [4 pts]
a) Find the Profit Amount ($):
Profit = SP - CP = $50 - $40 = $10.
Profit = $
10
b) Find the Profit Percentage (%):
Profit% = \( \frac{10}{40} \times 100 = \) 25%.
Profit % =
25%
4. A shopkeeper buys a bicycle for $150. He sells it with a 20% profit. [6 pts]
a) What is the profit in dollars?
Profit = 20% of 150 = \( 0.2 \times 150 = \) $30.
Profit = $
30
b) What is the final selling price?
SP = Cost + Profit = $150 + $30 = $180.
Selling Price = $
180
Teacher Answer Key • Math Mastery Final Page 5 of 5
