Practice quiz · by a Quizcard user

Algebra and Geometry: Essential Formulas — quiz

18 multiple-choice questions covering Pythagorean theorem, Triangle inequality theorem, Similar triangles, Equation of a circle, SOH-CAH-TOA. One answer each; you get a score at the end and the explanation for every question. No account needed.

Updated 2026-10-24. Keys 1–4 pick an answer, Enter moves on. Redo it any time, in order or shuffled.

The questions

Answers and explanations are shown after you finish.

1. Pythagorean theorem

   A ladder reaches a wall. Its base sits 6 ft from the wall and the ladder itself is 10 ft long. How high up the wall does the ladder reach?

   • 7 ft
   • 6.63 ft
   • 12 ft
   • 8 ft
2. Triangle inequality theorem

   Which set of three side lengths CANNOT form a triangle?

   • 6, 8, 10
   • 5, 5, 9
   • 3, 4, 5
   • 2, 3, 6
3. Similar triangles

   Two similar triangles have corresponding side lengths in a 2:3 ratio. If the smaller triangle's area is 8 square units, what is the larger triangle's area?

   • 12
   • 24
   • 16
   • 18
4. Equation of a circle

   A circle is given by the equation (x − 3)² + (y + 2)² = 25. What are its center and radius?

   • Center (3, 2), radius 5
   • Center (3, −2), radius 25
   • Center (3, −2), radius 5
   • Center (−3, 2), radius 5
5. SOH-CAH-TOA

   In a right triangle, the side opposite angle θ is 5 and the hypotenuse is 13. What is cos θ?

   • 5/12
   • 5/13
   • 13/12
   • 12/13
6. Special right triangles

   A 30-60-90 right triangle has a hypotenuse of 10. What is the length of the side opposite the 60° angle?

   • 5√3
   • 5√2
   • 10/√3
   • 5
7. Special right triangles

   A 45-45-90 right triangle has a leg of length 7. What is the length of the hypotenuse?

   • 7/√2
   • 7√3
   • 7√2
   • 14
8. Volume of cones and cylinders

   A cone and a cylinder share the same radius and height. What fraction of the cylinder's volume does the cone's volume represent?

   • 3/4
   • 1/3
   • 1/2
   • 2/3
9. Polygon interior angles

   What is the sum of the interior angles of a hexagon (6 sides)?

   • 720°
   • 1080°
   • 900°
   • 540°
10. Slope formula

    What is the slope of the line through the points (2, 3) and (6, 11)?

    • 0.5
    • 2
    • 8
    • 4
11. Discriminant

    For a quadratic equation ax² + bx + c = 0, the discriminant b² − 4ac equals −16. What does this tell you about the solutions?

    • The equation has no solutions of any kind
    • There is exactly one real solution
    • There are two complex (non-real) solutions
    • There are two real solutions
12. Vertex of a parabola

    What is the x-coordinate of the vertex of y = 2x² − 8x + 5?

    • -2
    • -4
    • 2
    • 4
13. Exponent rules

    Simplify (x³)² · x⁻¹.

    • x⁶
    • x⁵
    • x⁴
    • x⁻⁵
14. Difference of squares

    Which factored form is equivalent to x² − 16?

    • (x + 8)(x − 2)
    • (x + 4)²
    • (x − 4)²
    • (x + 4)(x − 4)
15. Distance formula

    What is the distance between the points (1, 2) and (4, 6)?

    • 7
    • √10
    • 25
    • 5
16. Geometric sequences

    A geometric sequence starts at 3 with a common ratio of 2. What is the 5th term?

    • 16
    • 48
    • 96
    • 24
17. Compound interest

    An account compounds interest annually (once per year) at rate r for t years. Which expression correctly gives the final amount A?

    • A = P(1 + rt)
    • A = Prt
    • A = P(1 + r/t)^t
    • A = P(1 + r)^t
18. Point-slope form

    A line passes through the point (4, −1) with a slope of 3. Which equation correctly represents this line in point-slope form?

    • y + 1 = 3(x + 4)
    • y + 1 = 3(x − 4)
    • y − 1 = 3(x + 4)
    • y − 1 = 3(x − 4)