Grade: 9 Subject: SAT/ACT Skills Unit: Skill Mapping Lesson: 3 of 6 SAT: ProblemSolving+DataAnalysis ACT: Math

Guided Practice

Learn

Now that you've identified your weaknesses and created an improvement plan, it's time to put that plan into action with guided practice. This lesson provides structured exercises that target specific SAT/ACT skill domains with step-by-step support.

How to Use Guided Practice

  • Focus on your mapped weaknesses: Spend more time on problem types where you scored lowest
  • Read the explanation before the solution: Understand the approach, not just the answer
  • Take notes: Write down strategies that work for you
  • Time yourself: Build awareness of how long different problem types take

Skill Domains to Practice

These exercises cover the main SAT/ACT math skill areas:

  1. Algebra and Functions
  2. Problem Solving and Data Analysis
  3. Geometry and Measurement
  4. Number and Quantity

Examples

Skill Domain: Algebra

Solve the system: x + y = 10 and 2x - y = 2

Step 1: Add the equations: 3x = 12

Step 2: Solve for x: x = 4

Step 3: Substitute: 4 + y = 10, so y = 6

Answer: x = 4, y = 6

Skill Domain: Geometry

A triangle has angles measuring x, 2x, and 3x degrees. Find x.

Step 1: Sum of angles = 180 degrees

Step 2: x + 2x + 3x = 180

Step 3: 6x = 180, so x = 30

Practice Quiz

Work through these 10 skill-mapped practice questions.

Question 1 (Algebra): Solve for x: 2(x + 5) = 3x - 4

Answer: x = 14

2x + 10 = 3x - 4; 10 + 4 = 3x - 2x; x = 14

Question 2 (Data Analysis): The mean of 5 numbers is 20. If four of the numbers are 15, 18, 22, and 25, find the fifth number.

Answer: 20

Sum = 5 x 20 = 100. Known sum = 15 + 18 + 22 + 25 = 80. Fifth number = 100 - 80 = 20

Question 3 (Geometry): What is the area of a rectangle with length 12 and width 7?

Answer: 84 square units

Area = length x width = 12 x 7 = 84

Question 4 (Algebra): If 3a - 7 = 2a + 5, find a.

Answer: a = 12

3a - 2a = 5 + 7; a = 12

Question 5 (Data Analysis): In a dataset of 4, 7, 9, 11, 14, what is the median?

Answer: 9

The middle value of the ordered set is 9.

Question 6 (Number): What is (-3)^4?

Answer: 81

(-3) x (-3) x (-3) x (-3) = 9 x 9 = 81 (even power, positive result)

Question 7 (Geometry): A circle has radius 5. What is its circumference? (Use pi = 3.14)

Answer: 31.4

C = 2 x pi x r = 2 x 3.14 x 5 = 31.4

Question 8 (Algebra): Evaluate: 2x^2 - 3x + 1 when x = 3

Answer: 10

2(9) - 3(3) + 1 = 18 - 9 + 1 = 10

Question 9 (Data Analysis): If 60% of students passed a test and 15 students failed, how many students passed?

Answer: 22.5, which means approximately 22 or 23 students

If 40% = 15 students, then 100% = 37.5 students. 60% = 22.5 students. (In a real test, the numbers would work out to whole numbers.)

Question 10 (Geometry): The perimeter of a square is 36 cm. What is its area?

Answer: 81 square cm

Side = 36/4 = 9 cm. Area = 9 x 9 = 81 sq cm

Check Your Understanding

  • Which skill domain felt most challenging?
  • Did you notice improvement from your earlier practice?
  • What strategies helped you solve problems faster?

Next Steps

  • Update your skill map based on today's performance
  • Schedule focused practice on your weakest domain
  • Continue to the next lesson on goal setting