Calculator vs No-Calculator Strategies

SAT Math Structure

• Section 3: No Calculator (20 questions, 25 minutes)
• Section 4: Calculator Allowed (38 questions, 55 minutes)

When to Use Your Calculator

✓ ALWAYS Use for:

1. Complex Arithmetic

• $147 \times 23$
• $\frac{2847}{93}$
• $15.7 + 23.8 + 41.9$

2. Long Division

• Any division that doesn't simplify nicely
• Decimal calculations

3. Square Roots of Non-Perfect Squares

• $\sqrt{47}$
• $\sqrt{123.5}$

4. Checking Your Work

• Plug answers back into equations
• Verify solutions

5. Statistics Problems

• Mean, median calculations with many numbers
• Standard deviation

✗ DON'T Use for:

1. Simple Mental Math

• $25 \times 4 = 100$
• $\frac{1}{2} + \frac{1}{4} = \frac{3}{4}$

2. Problems Testing Concepts

• Factoring quadratics
• Simplifying expressions
• Understanding function notation

3. When Mental Math is Faster

• $50\% \text{ of } 80 = 40$
• $2^3 = 8$

Calculator Section Strategies

Strategy 1: Graphing Function Behavior

Use your graphing calculator to:

• Find intersections of two functions
• Determine maximum/minimum values
• Visualize transformations

Example: Where does $y = x^2 - 4x + 3$ cross the x-axis?

Calculator method:

1. Graph $y = x^2 - 4x + 3$
2. Use "zero" or "root" function
3. Find $x = 1$ and $x = 3$

Strategy 2: Testing Answer Choices

For "which equation..." questions:

Example: Which equation has solutions $x = 2$ and $x = 5$?

Calculator method:

1. Plug in $x = 2$ to each answer choice
2. See which equals zero
3. Verify with $x = 5$

Strategy 3: Table Feature

Use tables to:

• Evaluate functions quickly at multiple x-values
• Find patterns
• Check which x gives a certain y

Example: For what value of $x$ does $f(x) = 2x^2 - 5x + 1 = 10$?

Calculator method:

1. Enter $y = 2x^2 - 5x + 1$
2. Make table
3. Look for where $y = 10$

No-Calculator Section Strategies

Strategy 1: Fraction Sense

Keep answers in fraction form:

• $\frac{2}{3} + \frac{1}{4} = \frac{8}{12} + \frac{3}{12} = \frac{11}{12}$

Don't convert to decimals (more error-prone)

Strategy 2: Factor and Simplify

Example: $\frac{x^2 - 9}{x - 3} = ?$

Solution: $\frac{(x+3)(x-3)}{x-3} = x + 3$

Strategy 3: Recognize Patterns

Perfect squares: $x^2 \pm 2xy + y^2 = (x \pm y)^2$

Difference of squares: $x^2 - y^2 = (x+y)(x-y)$

Example: $49 - x^2 = (7+x)(7-x)$

Strategy 4: Estimation

When stuck, estimate:

Example: Which is closest to $\frac{51}{9.8}$?

• Think: $\frac{50}{10} = 5$
• Answer should be slightly more than 5

Strategy 5: Properties of Exponents

Memorize:

• $x^a \cdot x^b = x^{a+b}$
• $(x^a)^b = x^{ab}$
• $x^0 = 1$
• $x^{-a} = \frac{1}{x^a}$

Time Management

Calculator Section (55 minutes, 38 questions)

Recommended pace:

• First 15 questions: ~1 minute each (15 min)
• Next 15 questions: ~1.5 minutes each (22.5 min)
• Last 8 questions: ~2 minutes each (16 min)
• Review: 1.5 minutes

If stuck: Skip and come back (you have your calculator as backup)

No-Calculator Section (25 minutes, 20 questions)

Recommended pace:

• First 10 questions: ~1 minute each (10 min)
• Next 10 questions: ~1.3 minutes each (13 min)
• Review: 2 minutes

If stuck: Must rely on algebra/mental math skills

Common Calculator Mistakes

❌ Over-relying on calculator for simple problems (wastes time)
❌ Rounding too early (keep extra decimals until final answer)
❌ Mistyping parentheses (e.g., typing $1/2+3$ instead of $1/(2+3)$)
❌ Not checking mode (degrees vs radians, though SAT uses degrees)
❌ Forgetting to clear previous calculations

Calculator Tips for SAT

Parentheses are Your Friend

Always use parentheses for fractions:

• WRONG: $1/2x$ (calculator reads as $\frac{1}{2x}$)
• RIGHT: $(1/2)x$ or $1/(2x)$ depending on what you mean

Store Values in Memory

For multi-step problems:

1. Calculate first part
2. Store in calculator memory (STO button)
3. Recall for next calculation (RCL button)

Prevents rounding errors and saves time

Know Your Calculator

Practice with YOUR calculator before test day:

• Where is the ² button?
• How to enter fractions?
• How to use graphing features?
• Where is ANS (previous answer)?

The Golden Rule

ASK YOURSELF: "Is the calculator making this easier or am I just avoiding thinking?"

✓ Calculator for: computation
✗ Calculator for: conceptual understanding

Remember: The no-calculator section exists to test your understanding. If you can't solve those problems, practice more mental math and algebraic manipulation!

Quick Decision Chart

Deciding whether to use your calculator:

1. Is it in the calculator section?
   • NO → Must use mental math/algebra
   • YES → Continue to #2
2. Is it simple mental math?
   • YES → Do it in your head (faster)
   • NO → Continue to #3
3. Is it testing a concept?
   • YES → Work it out (calculator won't help)
   • NO → Use calculator to compute