PRE CALCULUS Cheat Sheet 2026

The 30 highest-yield PRE CALCULUS facts, distilled from real exam questions. Print it, save it as a PDF, or study it here — free, no sign-up.

1. The diagram below depicts a triangle with 6-inch sides. How much area does this triangle take up? → 9√3
2. The hypotenuse of a triangle with sides 30-60-90 is 6. Determine the size of the smallest side. → 3
3. All you'll see in the diagram below are straight lines. Find its circumference. → 42
4. Which of the following represents exponential growth rather than decay? → f(x) = 3·(1.2)^x
5. What is the remainder when f(x) = x⁴ - 3x² + 2 is divided by (x + 1)? → 0
6. If sin(θ) = -3/5 and θ is in the third quadrant, what is cos(θ)? → -4/5
7. The diagonals of a rhombus have lengths 10 and 24. What is the side length of the rhombus? → 13
8. In a 30-60-90 triangle, if the hypotenuse is 10, the side opposite 60° is: → 5√3
9. What is the component form of a vector from point P(1, 2) to point Q(4, 6)? → ⟨3, 4⟩
10. Add together the numbers (2 + 3i) and (-4 + 5i). → -2 + 8i
11. What is the value of i⁴ where i = √(−1)? → 1
12. Which identity correctly expresses cos(2θ) in terms of sin(θ) only? → 1 − 2sin²θ
13. If f(x) = 5x - 2 and f(a) = 13, what is a? → 3
14. In which quadrant are both sine and cosine positive? → Quadrant I
15. What is the degree of the polynomial 3x⁴ - 2x² + x - 7? → 4
16. What does the identity 1 + cot²θ = csc²θ follow from? → Dividing sin²θ + cos²θ = 1 by sin²θ
17. How many terms are in the arithmetic sequence 7, 11, 15, …, 99? → 24
18. What is the sum of all zeros of f(x) = 3x⁴ − 12x³ + 5x − 1? → 4
19. What is the domain of f(x) = log_3(x − 4)? → x > 4
20. What is the domain of f(x) = ln(x - 1)? → (1, ∞)
21. If f(4) = 7 and g(7) = -1, what is g(f(4))? → -1
22. Solve for x: log_3(x) = 4 → x = 81
23. What is an angle's radian value for a single revolution? → 2π
24. Two consecutive terms of a geometric sequence are 48 and 12. What is the common ratio? → 1/4
25. The product-to-sum formula converts sin(A)cos(B) into: → [sin(A+B) + sin(A-B)]/2
26. Using synthetic division, what is the quotient when x³ + 2x² - 5x - 6 is divided by (x - 2)? → x² + 4x + 3
27. Which of the following is equivalent to log_b(x^4)? → 4·log_b(x)
28. The equation f(x) = 5x^4-8x^3+4x^2-6x+3 has how many roots or zeros? → 4
29. What is the area of an equilateral triangle with side length 6? → 9√3
30. A cubic polynomial with positive leading coefficient has which end behavior? → Down left, up right