UTMA Study Guide 2026
Everything you need to pass the UTMA exam in one place: the exam format, every topic to study, real practice questions with explanations, flashcards, and full-length practice tests. Free, no sign-up needed.
📋 UTMA Exam Format at a Glance
📚 UTMA Topics to Study (22)
✍️ Sample UTMA Questions & Answers
1. What is the exact value of sin(45°)?
In a 45-45-90 triangle with hypotenuse √2, each leg is 1, so sin(45°) = 1/√2 = √2/2.
2. Which trigonometric function equals the reciprocal of cosine?
sec(θ) = 1/cos(θ) by definition.
3. Which of the following is a one-to-one function?
A linear function f(x) = 2x + 5 passes the horizontal line test, confirming it is one-to-one.
4. What is the value of x in 3x + 2y = 12 and x = 2?
Substituting x=2: 3(2) + 2y = 12 → 6 + 2y = 12 → y = 3.
5. Solve for x and y: 2x − y = 1 and x + 3y = 10.
From equation 1: y = 2x−1; substituting into equation 2: x + 3(2x−1) = 10 → 7x = 13 → x=13/7... checking answer B: x=1 → y=1 (fails eq 2: 1+3=4≠10). Correct: x=13/7, y=9/7. None of the listed answers match exactly; closest is C.
6. Find the critical points of 𝑓 (𝑥) =𝑥 3−3𝑥2
Critical points are found by taking the first derivative of a function and setting it to zero. If the derivative of a function factors into terms like 3x(x-3)=0, then solving for x would yield x=0 and x=3. These points indicate where the function's slope is horizontal, often corresponding to local maxima or minima.