Grade: Grade 12 Subject: SAT/ACT Skills Unit: Final Tune-Up SAT: ProblemSolving+DataAnalysis ACT: Math

Mixed Practice Set

Learn

Real tests do not group questions by topic. You encounter algebra, then geometry, then data analysis, then back to algebra - all in unpredictable order. Mixed practice trains your brain to switch between concepts quickly and builds the mental flexibility needed on test day.

Why Mixed Practice Works

  • Interleaving Effect: Research shows that mixing topics during practice leads to better long-term retention and transfer than blocked practice (doing all of one topic, then all of another).
  • Recognition Skills: When topics are mixed, you must first identify what type of problem you are facing - just like on the real test.
  • Cognitive Flexibility: Switching between concepts strengthens your ability to retrieve the right knowledge at the right time.

How to Use Mixed Practice Effectively

  1. Simulate test conditions: Set a timer, no breaks, no notes
  2. First pass strategy: Do easier questions first, mark harder ones to return
  3. Full review: After completing, review every question - even correct ones
  4. Log errors: Add mistakes to your error log with type classification

Mental Transition Phrases

Use these mental cues to switch gears quickly:

  • "This is algebra - I am looking for the variable."
  • "This is geometry - what formula applies?"
  • "This is reading - what does the text actually say?"
  • "This is grammar - what rule is being tested?"
  • "This is data - go straight to the table/graph."

Examples

See how to approach a mixed set with rapid topic switching.

Example Mini-Set (3 questions, different topics)

Q1 (Algebra): If 3x - 7 = 14, what is the value of 6x?

Approach: Solve for x: 3x = 21, so x = 7. Then 6x = 42.

Q2 (Grammar): "The committee have decided to postpone their meeting." - Is this sentence correct?

Approach: Subject-verb agreement. "Committee" is a collective noun (singular in American English). Should be "has decided." Sentence is incorrect.

Q3 (Geometry): A right triangle has legs of length 5 and 12. What is the length of the hypotenuse?

Approach: Pythagorean theorem: 5^2 + 12^2 = 25 + 144 = 169 = 13^2. Hypotenuse = 13.

Notice: Each question required completely different knowledge, but quick recognition of the topic made each solvable in under 60 seconds.

Practice

Complete this 12-question mixed set. Time yourself: aim for 15 minutes or less. These span Math, Reading/Writing, and test-taking skills.

1. (Algebra) If 2(x + 3) = 5x - 9, what is x?

(A) 3 (B) 5 (C) 7 (D) 9

2. (Grammar) Choose the correct version: "Neither the students nor the teacher (was/were) prepared for the fire drill."

(A) was (B) were

3. (Data Analysis) A survey of 200 students found that 45% prefer online classes. How many students prefer in-person classes if 10% have no preference?

(A) 80 (B) 90 (C) 100 (D) 110

4. (Geometry) What is the area of a circle with diameter 10?

(A) 10pi (B) 25pi (C) 50pi (D) 100pi

5. (Vocabulary in Context) "The politician's inflammatory remarks ignited controversy." In this context, "inflammatory" most nearly means:

(A) burning (B) medical (C) provocative (D) accidental

6. (Percent/Ratio) A shirt originally costs $40. It is on sale for 25% off. What is the sale price?

(A) $10 (B) $15 (C) $30 (D) $35

7. (Grammar) Identify the error, if any: "Running through the park, the sunset looked beautiful."

(A) No error (B) Dangling modifier (C) Subject-verb disagreement (D) Comma splice

8. (Functions) If f(x) = x^2 - 3x + 2, what is f(4)?

(A) 2 (B) 4 (C) 6 (D) 8

9. (Reading Inference) "Dr. Chen had published extensively on climate change for twenty years before anyone in government took notice." This sentence suggests that:

(A) Dr. Chen gave up on her research (B) Government response to climate research was delayed (C) Climate change research began twenty years ago (D) Dr. Chen worked for the government

10. (Systems of Equations) If x + y = 10 and x - y = 4, what is x?

(A) 3 (B) 5 (C) 7 (D) 9

11. (Punctuation) Which is correctly punctuated?

(A) The experiment, which lasted three months was a success.

(B) The experiment which lasted three months, was a success.

(C) The experiment, which lasted three months, was a success.

(D) The experiment which lasted three months was a success.

12. (Probability) A bag contains 5 red marbles and 7 blue marbles. If one marble is drawn at random, what is the probability that it is red?

(A) 5/12 (B) 5/7 (C) 7/12 (D) 1/2

Check Your Understanding

Answer key with explanations:

  1. (B) 5 - Distribute: 2x + 6 = 5x - 9. Subtract 2x: 6 = 3x - 9. Add 9: 15 = 3x. Divide: x = 5.
  2. (A) was - With "neither...nor," the verb agrees with the closer subject (teacher = singular).
  3. (B) 90 - 45% online + 10% no preference = 55%. So 45% prefer in-person. 0.45 x 200 = 90.
  4. (B) 25pi - Diameter = 10, so radius = 5. Area = pi x r^2 = pi x 25 = 25pi.
  5. (C) provocative - "Inflammatory" here means intended to arouse anger or controversy, not literally burning.
  6. (C) $30 - 25% of $40 = $10 discount. $40 - $10 = $30.
  7. (B) Dangling modifier - "Running through the park" should modify a person, not "the sunset." The sunset was not running.
  8. (C) 6 - f(4) = 16 - 12 + 2 = 6.
  9. (B) Government response to climate research was delayed - The phrase "before anyone in government took notice" implies the government was slow to respond.
  10. (C) 7 - Add equations: 2x = 14, so x = 7.
  11. (C) - "Which lasted three months" is a non-restrictive clause and needs commas on both sides.
  12. (A) 5/12 - Total marbles = 12. Red = 5. Probability = 5/12.

Score Interpretation

  • 11-12 correct: Excellent - you are ready for final practice tests
  • 9-10 correct: Good - review the topics you missed
  • 7-8 correct: Fair - spend more time on mixed practice before the test
  • Below 7: Focus on the Learn sections of earlier lessons in this unit

Next Steps

  • Complete 1-2 mixed practice sets daily in the final week
  • Focus your remaining study on question types you missed
  • Log all errors and review your error log before test day
  • Move on to Final Practice Tests for full-length simulation