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UTMA Cheat Sheet 2026

The 30 highest-yield UTMA facts, distilled from real exam questions. Print it, save it as a PDF, or study it here β€” free, no sign-up.

30 questions
60 min time limit
70% to pass
  1. What is the determinant of the matrix [[2, 3],[1, 4]]? β†’ 5
  2. Which of the following is an irrational number? β†’ √7
  3. A card is drawn from a standard 52-card deck. What is the probability of drawing a king? β†’ 1/13
  4. Which number is divisible by both 4 and 6 but not by 24? β†’ 36
  5. What operation is NOT allowed in Gaussian elimination? β†’ Multiplying a row by zero
  6. What is the remainder when 2²⁰ is divided by 3? β†’ 1
  7. In a class of 30, 18 like math and 14 like science. If 8 like both, how many like at least one? β†’ 24
  8. In how many ways can 3 items be chosen from 7 (order does not matter)? β†’ 35
  9. A car travels 240 miles in 4 hours. What is its average speed in miles per hour? β†’ 60 mph
  10. What is the complement of event A if P(A) = 0.65? β†’ 0.35
  11. What is the greatest common divisor (GCD) of 84 and 126? β†’ 42
  12. A 10-meter ladder leans against a wall. If the base is 6 meters from the wall, how high does it reach? β†’ 8 m
  13. What is the least common multiple (LCM) of 12, 18, and 24? β†’ 72
  14. What is the period of the function f(x) = sin(2x)? β†’ Ο€
  15. Evaluate the limit: limπ‘₯β†’2 (3π‘₯+1) β†’ 7
  16. The vertical line test is used to determine whether a graph represents: β†’ A function
  17. What is the circumference of a circle with a radius of 7 cm? β†’ 14Ο€ cm
  18. In a right-angled triangle, if one angle is 30Β° and the hypotenuse is 10 cm, what is the length of the side opposite the 30Β° angle? β†’ 5 cm
  19. Solve the inequality 3π‘₯βˆ’4<2π‘₯+5 β†’ x<9
  20. Which of the following represents a linear equation? β†’ y = 2x + 5
  21. What are the x-intercepts of f(x) = xΒ² βˆ’ 5x + 6? β†’ x = 2 and x = 3
  22. A car's value depreciates by 15% per year. If it costs $20,000 new, what is it worth after 2 years? β†’ $14,450
  23. A bag has 5 red and 3 green balls. Two are drawn without replacement. What is P(both red)? β†’ 5/14
  24. What is 3/8 expressed as a decimal? β†’ 0.375
  25. If f(x) = 2x + 1 and g(x) = xΒ², what is (f ∘ g)(3)? β†’ 19
  26. Which function is an even function? β†’ f(x) = x⁴ βˆ’ 2xΒ²
  27. What is the value of tan(45Β°)? β†’ 1
  28. What is the integral of 𝑓 (x)=2x? β†’ π‘₯2 + 𝐢
  29. Which angle has a cosine value of 0? β†’ 90Β°
  30. What is the product of matrices A = [[1,0],[0,1]] and B = [[3,4],[5,6]]? β†’ [[3,4],[5,6]]
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