ACT Math · Elementary Algebra
Substitution and evaluation
Plugging values into an expression and simplifying.
What's tested in this subtopic
A value or set of values is given for the variables; substitute and compute. The arithmetic can be tricky when negatives or fractions are involved.
Tactics that actually move your score
Substitute with parentheses around each value to avoid sign mistakes. Compute one operation at a time. The single biggest leverage point on most subtopics isn't learning more math — it's recognizing the test's preferred surface forms quickly enough that you don't burn 30 seconds re-reading the question. The first time you see a particular phrasing it might take you a full minute. The tenth time you see it, you should be reaching for your method before you've finished the sentence. Repetition is what builds that recognition. Fifteen problems in a row of the same shape is more useful than fifty mixed.
Practice questions (14)
- Easy If f(x) = 4x² − 2, what is the value of f(5)?
- Easy If f(x) = 3x² + 4, what is the value of f(-3)?
- Medium If f(x) = 2x² + 3, what is the value of f(6)?
- Medium If f(x) = 4x² − 3, what is the value of f(-2)?
- Medium If f(x) = 3x² − 1, what is the value of f(6)?
- Hard If f(x) = 3x² − 3, what is the value of f(6)?
- Easy If f(x) = 2x² + 3, what is the value of f(-1)?
- Easy If f(x) = 3x² − 2, what is the value of f(5)?
- Medium If f(x) = 3x² − 4, what is the value of f(6)?
- Medium If f(x) = 5x² − 2, what is the value of f(3)?
- Medium If f(x) = 3x² + 1, what is the value of f(1)?
- Hard If f(x) = 5x² − 2, what is the value of f(6)?
- Easy If f(x) = 5x² − 4, what is the value of f(5)?
- Easy If f(x) = 3x² − 3, what is the value of f(6)?
How to drill
Work through the questions above untimed. After each one, read the worked solution from start to finish — even when you got it right. Note which solution method you used, and which method we used; if they differ, ask yourself which would have been faster on test day. Speed in ACT math comes from shortening your method-selection step, not from doing arithmetic faster. Most fast students are doing the same arithmetic everyone else is — they're just spending less time deciding what to do.
Once you can clear the easy and medium items in this subtopic at 90% accuracy, attempt a timed mini-set of ten hard items at 75 seconds each. If you finish in time and score 7+ correct, you've effectively mastered the subtopic for test purposes and can move on.