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December 2025 US Digital SAT Math Module 1 Question 1
Function evaluation is a foundational skill for SAT Math. This question tests whether you can substitute a value into a linear function and calculate the result correctly. This is a perfect example for December 2025 US SAT Math M1 Q1 Explained.
What you will learn: How to evaluate a linear function like h(x) = 100x - 40 by substituting a given x-value. You will also see how to check your work using Desmos, the built-in Digital SAT graphing calculator.
Understanding the Problem
The question presents a linear function and asks you to find its value at a specific input. Linear functions follow the form f(x) = mx + b, where m is the slope and b is the y-intercept. In this case, the function is h(x) = 100x - 40.
Your job is to replace x with the given number and perform the arithmetic. This is a direct application of function notation, a core skill for the Digital SAT Math section.
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Step-by-Step Solution
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Start 1-day free trial →Step 1: Identify the function and the input value. The function is h(x) = 100x - 40. The problem asks for h(5).
Step 2: Substitute 5 for x in the function. This gives you h(5) = 100(5) - 40.
Step 3: Multiply 100 by 5. The result is 500.
Step 4: Subtract 40 from 500. The final result is 460.
Answer: h(5) = 460.
Quick Tip: Always double-check your arithmetic. A simple multiplication or subtraction error is the most common mistake on these questions. Write out each step clearly.
Using Desmos to Verify
The Digital SAT includes the Desmos graphing calculator. You can use it to check your answer quickly. This is a reliable way to confirm your work, especially under time pressure.
Desmos Verification
Follow these steps in the Desmos calculator during the test:
- Type the function: h(x) = 100x - 40
- Press Enter to graph the line.
- Click on the graph at x = 5, or type h(5) in a new line.
- Desmos will display the point (5, 460).
The y-coordinate 460 confirms your calculation.
Common Mistakes to Avoid
- Misreading the input: Make sure you substitute the correct number. The problem might ask for h(5), not h(50) or h(0.5).
- Order of operations: Multiplication comes before subtraction. Always multiply 100 by the input first, then subtract 40.
- Sign errors: If the function includes a negative sign, be careful. For example, h(x) = -100x + 40 would give a different result.
- Skipping steps: Do the math on paper or in the calculator. Mental math under pressure can lead to errors.
Why This Skill Matters
Function evaluation appears in many SAT Math questions, from simple substitution to more complex problems involving composite functions or graphs. Mastering this basic skill saves time and builds confidence for harder questions later in the module.
For this question, the key takeaway is straightforward: substitute carefully, calculate accurately, and verify with Desmos when possible.
Frequently Asked Questions
What if I get a decimal or fraction answer?
Linear functions can produce any real number. The Digital SAT often uses integer answers for early questions, but later questions may include fractions or decimals. The same substitution method applies.
See which question types are costing you points
Start with a free mock, free drills, or preview sample questions before using all 45 question banks.
Can I use Desmos for every function question?
Yes. Desmos is available for the entire Math section. It is especially useful for checking your work on function evaluation, graphing, and solving equations.
What is the best way to practice function evaluation?
Use official College Board practice tests in Bluebook. Focus on accuracy first, then speed. The Test Advantage recommends timed practice to simulate test conditions.
The Test Advantage Explanation
This question is a straightforward test of function notation. The function h(x) = 100x - 40 is linear, and evaluating it at x = 5 requires only basic arithmetic. The correct answer is 460.
Students who rush may misread the input or make a calculation error. Using Desmos as a verification tool is a smart strategy. For more practice, review linear functions in the Bluebook app and focus on accuracy with substitution.
Master function evaluation, and you build a strong foundation for the entire SAT Math section.
For personalized tutoring and more strategies, contact The Test Advantage.
Get Started with The Test AdvantageThe Question
The function h is defined by h(x) = 100x - 40. What is the value of h(x) when x = 5?
- A) 540
- B) 460
- C) 145
- D) 65
The Correct Answer: B) 460
To find h(5), substitute 5 for x in the function:
h(5) = 500 - 40
h(5) = 460
The calculation is straightforward: multiply 100 by 5 to get 500, then subtract 40 to get 460. This is a classic example of this type of problem: direct substitution with linear functions.
Visualize with Desmos Calculator
The Digital SAT provides a built-in Desmos calculator. Here is how to verify this answer graphically:
Open Desmos Calculator- Type
h(x) = 100x - 40in the first expression line - Type
(5, h(5))in the second line to plot the point - You will see the point appears at (5, 460) on the graph
- Alternatively, just type
100(5) - 40and Desmos will show 460
Desmos Formula:
Point: (5, 460)
Why the Other Answers Are Wrong
- A) 540: This would be 100(5) + 40. The student added instead of subtracted. Watch your signs.
- C) 145: This appears to come from a miscalculation. It does not follow from the function.
- D) 65: This might come from misreading the function or making an arithmetic error.
The TTA Strategy for Function Evaluation
- Identify what you're substituting. The question asks for h(5), so x = 5.
- Replace every x with the given value. h(x) = 100x - 40 becomes h(5) = 100(5) - 40.
- Follow order of operations. Multiply first, then subtract.
- Verify with Desmos if unsure. Graph the function and check the y-value when x = 5.
Understanding Linear Functions
The function h(x) = 100x - 40 is a linear function in the form y = mx + b. The slope is 100 and the y-intercept is -40. For every increase of 1 in x, the output increases by 100. This is the core pattern you need to recognize for the linear function question.
At The Test Advantage, we make sure students are comfortable with all function types. Building strong fundamentals on simpler questions prepares you for harder ones on the Digital SAT.
Frequently Asked Questions
When should I use Desmos for function questions?
Use Desmos to verify your answer or when you are unsure of your arithmetic. Calculating by hand is faster, but Desmos provides confirmation.
What is function notation?
h(x) is read as "h of x." It means h is a function that takes an input x and produces an output. h(5) means the output when the input is 5.
Where can I practice more function questions?
Create a free account at TheTestAdvantage.com. We have hundreds of function questions with detailed solutions.
Build Your Function Skills
Function evaluation is a building block for SAT Math success. At The Test Advantage, we provide targeted practice on every skill the SAT tests.
Create Your Free AccountMaster Comprehensive Topic Guide Index
- Digital SAT Preparation Advanced Execution Foundations
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References and Further Reading
- Official SAT Suite - What Is on the SATSupports: Function evaluation is a foundational skill for SAT Math.- Official Test Publisher: Official College Board source directly supports the claim that function evaluation is a foundational skill for SAT Math, providing authoritative test content specifications.
- National Center for Education StatisticsSupports: The Digital SAT includes the Desmos graphing calculator.- Official Test Publisher: Government education research source adds credibility to the factual claim about the Digital SAT including the Desmos graphing calculator, as it provides broader educational context and statistical backing.
- Institute of Education SciencesSupports: Use official College Board practice tests in Bluebook.- Official Test Publisher: U.S. Department of Education research institute supports the recommendation to use official College Board practice tests in Bluebook, reinforcing evidence-based test preparation.
Frequently Asked Questions
How do you solve December 2025 US SAT Math M1 Q1?
Substitute 5 into h(x)=100x-40: h(5)=100(5)-40=500-40=460.
What is the answer to h(5) for h(x)=100x-40?
The answer is 460.
How can I use Desmos to check my answer on the Digital SAT?
Type h(x)=100x-40 into Desmos, press Enter, then type h(5) or click the graph at x=5 to see the point (5, 460).
What common mistakes should I avoid on SAT function evaluation questions?
Avoid misreading the input, forgetting order of operations (multiply before subtract), sign errors, and skipping steps.
Why is function evaluation important for the SAT Math section?
It is a foundational skill that appears in many questions, from simple substitution to composite functions and graphs.