Mixed Set
Learn
On the actual SAT and ACT, you will encounter problems from different domains mixed together. This lesson provides a realistic mixed practice set that combines all the skills you have learned in this unit.
Why Mixed Practice Matters
- Builds Flexibility: Switching between problem types keeps your mind sharp and adaptable.
- Simulates Real Test Conditions: The actual test does not group problems by type.
- Improves Problem Recognition: You must quickly identify what type of problem you are facing.
- Reveals Weaknesses: Mixed sets expose which problem types you struggle with most.
Approach for Mixed Practice
- Read Carefully: Do not assume what type of problem it is. Read the entire question.
- Identify the Type: Take 5 seconds to categorize the problem.
- Choose Your Strategy: Select the best approach for that problem type.
- Solve Efficiently: Show your work but do not waste time on unnecessary steps.
- Check Your Answer: Does it make sense? Did you answer what was asked?
Mixed Set Guidelines
This set contains 12 problems of varying difficulty. Try to complete them in 15-18 minutes. Use the strategies from previous lessons:
- Skip problems that are taking too long and return to them
- Show your work to avoid careless errors
- After finishing, review any mistakes using the error log method
Examples
Before starting the mixed set, review these examples of different problem types you might encounter.
Example: Data Table Analysis
The table below shows the number of students in each grade at a school.
| Grade | Students |
|---|---|
| 9 | 240 |
| 10 | 220 |
| 11 | 200 |
| 12 | 180 |
Question: What percent of the total students are in Grade 10?
Solution: Total = 240 + 220 + 200 + 180 = 840. Grade 10 percent = (220/840) x 100 = 26.2% (approximately)
Example: Multi-Step Problem
Question: A store offers a 15% discount on all items. If the tax rate is 8%, what is the final price of an item originally marked at $50?
Solution:
- Discount: $50 x 0.15 = $7.50
- Price after discount: $50 - $7.50 = $42.50
- Tax: $42.50 x 0.08 = $3.40
- Final price: $42.50 + $3.40 = $45.90
Practice: Mixed Set
Instructions: Set a timer for 18 minutes. Complete all 12 problems. Show your work on scratch paper.
1. The ratio of red to blue marbles in a bag is 5:7. If there are 60 marbles total, how many are blue?
2. A cyclist travels 36 miles in 3 hours. At this rate, how long will it take to travel 60 miles?
3. The mean of a data set is 45. If the data set has 5 values and four of them are 40, 42, 48, and 52, what is the fifth value?
4. A jacket originally costs $80. It is on sale for 30% off. What is the sale price?
5. The table shows test scores for 5 students. What is the median score?
| Student | Score |
|---|---|
| A | 78 |
| B | 92 |
| C | 85 |
| D | 88 |
| E | 76 |
6. Convert 4,500 grams to kilograms.
7. A fair coin is flipped 3 times. What is the probability of getting exactly 2 heads?
8. If 2/3 of a number is 48, what is 1/4 of that number?
9. A price increased from $25 to $30. What is the percent increase?
10. The scatterplot shows a line of best fit with equation y = 2x + 10. According to this model, what is the predicted y-value when x = 15?
11. A rectangle has a length of 12 cm and a width of 8 cm. A second rectangle has the same area but a length of 16 cm. What is the width of the second rectangle?
12. In a class of 30 students, 18 play soccer, 12 play basketball, and 5 play both. How many students play neither sport?
Check Your Understanding
Answer Key
- 35 blue marbles (7/12 x 60 = 35)
- 5 hours (rate = 12 mph, time = 60/12 = 5)
- 43 (sum must be 225, so 225 - 182 = 43)
- $56 (80 x 0.70 = 56)
- 85 (ordered: 76, 78, 85, 88, 92; median is middle value)
- 4.5 kilograms (4500/1000 = 4.5)
- 3/8 (outcomes with exactly 2 heads: HHT, HTH, THH = 3 out of 8)
- 18 (number = 72, so 72/4 = 18)
- 20% ((30-25)/25 x 100 = 20%)
- 40 (y = 2(15) + 10 = 40)
- 6 cm (area = 96 sq cm, so 96/16 = 6)
- 5 students (using inclusion-exclusion: 18 + 12 - 5 = 25 play at least one; 30 - 25 = 5)
Scoring Guide
- 11-12 correct: Excellent! You are ready for more challenging practice.
- 9-10 correct: Good work! Review the problems you missed.
- 7-8 correct: Solid foundation. Focus on your weak areas.
- Below 7: More practice needed. Revisit earlier lessons in this unit.
Post-Practice Reflection
- Which problem types did you find easiest?
- Which problem types were most challenging?
- Did you finish within 18 minutes?
- What mistakes did you make, and what type were they?
- Add any errors to your error log for future review.
Next Steps
- Review any incorrect answers using the error log method from the previous lesson
- If you scored below 9, revisit the specific lessons for problem types you missed
- Practice mixed sets regularly to maintain all skills
- Move on to the next unit in your SAT/ACT Skills track
- Consider creating your own mixed practice sets from problems you have collected
Unit Complete!
Congratulations on completing the Domain Practice unit! You have learned to:
- Apply English conventions in practice
- Solve data analysis problems
- Identify different question types quickly
- Work under timed conditions
- Analyze and learn from your mistakes
- Handle mixed problem sets
Continue building these skills with regular practice, and remember to review your error log weekly!