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 component form of a vector from point P(1, 2) to point Q(4, 6)? → ⟨3, 4⟩
6. Add together the numbers (2 + 3i) and (-4 + 5i). → -2 + 8i
7. In which quadrant are both sine and cosine positive? → Quadrant I
8. What is the degree of the polynomial 3x⁴ - 2x² + x - 7? → 4
9. What is the domain of f(x) = log_3(x − 4)? → x > 4
10. Solve for x: log_3(x) = 4 → x = 81
11. What is an angle's radian value for a single revolution? → 2π
12. Which of the following is equivalent to log_b(x^4)? → 4·log_b(x)
13. The equation f(x) = 5x^4-8x^3+4x^2-6x+3 has how many roots or zeros? → 4
14. Turn 360 degrees into radians. → 2π
15. A geometric sequence's third term is 96 and its fifth term is 1536. What is the sum of the sequence's first ten terms? → 2,097,150
16. Determine the first six terms in the sequence: aₙ = (n + 1)³ → 8, 27, 64, 125, 216, 343
17. If vector u = ⟨3, −4⟩, what is |u|? → 5
18. Determine the 22nd term of the sequence 5, 8, 11,... → 68
19. The section of a circle that is cut off by a chord. → Segment
20. Which of the following is true about matrix multiplication? → AB ≠ BA in general
21. Which of the following is the general form of an exponential function? → f(x) = a·b^x where b > 0, b ≠ 1
22. How many foci does an ellipse have? → 2
23. The directrix of the parabola x² = 8y is: → y = −2
24. If g(x) = x^4 + 3, then g (2) is equal to? → 19
25. Explain the real and imaginary components of a complex number. → The real part is the constant term, and the imaginary part is the coefficient of i.
26. What is a piecewise function? → A function defined by different expressions for different intervals of the domain
27. To eliminate the parameter t from x = t + 1, y = t² − 3, what is the Cartesian equation? → y = (x−1)² − 3
28. What does the composition of functions mean? → An operation (fog)(x) that is equal to f (g(x)).
29. Given: f(x) = -3x^4 + x^3 - 2x^2 + x - 1, What is the y-intercept of f(x)? → (0, -1)
30. Identify the common ratio between 16, 8, 4, and 2. → r = 1/2