Grade: 9 Subject: SAT/ACT Skills Unit: Diagnostic Assessment Lesson: 6 of 6 SAT: ProblemSolving+DataAnalysis ACT: Math

Mixed Set

Learn

This final lesson in the Diagnostic Assessment unit brings together everything you've learned. A mixed practice set simulates the actual test experience where you encounter different problem types in random order.

Why Mixed Practice Works

  • Builds flexibility: You learn to switch between problem types quickly
  • Improves recall: You must identify the correct strategy for each problem
  • Simulates test conditions: Real tests mix topics together
  • Reveals weak spots: Gaps become apparent when topics are interleaved

Strategies for Mixed Practice

  1. Read each question carefully before choosing a strategy
  2. Don't assume the next question is similar to the last
  3. Budget your time - don't spend too long on any single problem
  4. Mark questions you're unsure about for review

Examples

Mixed Example Set

Notice how these three problems require completely different approaches:

Problem A (Algebra): Solve 2x - 5 = 9. Answer: x = 7

Problem B (Percentage): What is 25% of 120? Answer: 30

Problem C (Data): If the mean of 3, 5, and x is 5, find x. Answer: x = 7

Practice Quiz

Complete this mixed set of 10 problems covering all skill areas.

Question 1: Solve: 4x + 7 = 31

Answer: x = 6

4x = 24, x = 6

Question 2: A store has a 40% off sale. What is the sale price of a $75 item?

Answer: $45

Discount = 0.40 x 75 = $30. Sale price = 75 - 30 = $45

Question 3: What is the median of: 12, 5, 8, 15, 10?

Answer: 10

Ordered: 5, 8, 10, 12, 15. The middle value is 10.

Question 4: If the ratio of red to blue marbles is 2:5, and there are 35 marbles total, how many are red?

Answer: 10

7 parts = 35, so 1 part = 5. Red = 2 x 5 = 10

Question 5: Solve: -2(x + 4) = 10

Answer: x = -9

-2x - 8 = 10; -2x = 18; x = -9

Question 6: A number increased by 15% becomes 92. What was the original number?

Answer: 80

1.15x = 92; x = 92/1.15 = 80

Question 7: What is the range of: 7, 3, 9, 12, 5?

Answer: 9

Range = highest - lowest = 12 - 3 = 9

Question 8: If f(x) = 3x - 2, what is f(4)?

Answer: 10

f(4) = 3(4) - 2 = 12 - 2 = 10

Question 9: A car travels 180 miles in 3 hours. At this rate, how far will it travel in 5 hours?

Answer: 300 miles

Rate = 180/3 = 60 mph. Distance in 5 hours = 60 x 5 = 300 miles

Question 10: Solve: 3x - 4 = 2x + 7

Answer: x = 11

3x - 2x = 7 + 4; x = 11

Check Your Understanding

  • How quickly could you identify the problem type for each question?
  • Did you use appropriate strategies for each problem type?
  • Which problem types still need more practice?

Next Steps

  • Record your score and add any mistakes to your error log
  • Review any problem types where you struggled
  • Move on to the Skill Mapping unit to create your improvement plan