Florida B.E.S.T. Geometry EOC Practice Test

10 free B.E.S.T. Geometry practice questions below, each with the correct answer and a worked explanation you can read straight away. Every question is written in-house to the standards the course is tested on — none is reproduced from any official Florida assessment.

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Practice questions with answers

Question 1
Find the distance between points P and Q shown on the coordinate plane below. xy123-112P(1, 2)Q(−1, −1)
  1. A. √10
  2. B. √13
  3. C. √17
  4. D. 5
Show the answer and explanation

Correct answer: B. √13

📌 **Step 1: Apply the distance formula** d = √((x₂ − x₁)² + (y₂ − y₁)²) 📌 **Step 2: Plug in P(1, 2) and Q(−1, −1)** d = √((1 − (−1))² + (2 − (−1))²) = √(2² + 3²) = √(4 + 9) 📌 **Answer:** d = **√13** ≈ 3.61 💡 **Tip:** Leave your answer in √ form when exact values are expected on the EOC.
Question 2
A tangent line touches circle O at point T. OT = 5 and the external point P is 13 units from the center O. What is the length of tangent segment PT? OTP5?13
  1. A. 8
  2. B. 10
  3. C. 12
  4. D. 14
Show the answer and explanation

Correct answer: C. 12

The tangent is perpendicular to the radius at the point of tangency. Using the Pythagorean theorem: PT = √(OP² − OT²) = √(13² − 5²) = √(169 − 25) = √144 = 12.
Question 3
In the figure below, DE ∥ BC. If AD = 4, DB = 6, and AE = 5, find EC. ABCDE465?∥
  1. A. 6.0
  2. B. 7.5
  3. C. 8.0
  4. D. 10.0
Show the answer and explanation

Correct answer: B. 7.5

📌 **Step 1: Apply the Triangle Proportionality Theorem** Since DE ∥ BC: AD/DB = AE/EC 📌 **Step 2: Set up the proportion** 4/6 = 5/EC 📌 **Step 3: Cross-multiply and solve** 4 × EC = 6 × 5 = 30 EC = 30/4 = **7.5** 💡 **Verification:** AD/DB = 4/6 = 2/3. AE/EC = 5/7.5 = 2/3. ✓ The ratios match!
Question 4
A kite is flying at the end of a 200-foot string. The string makes a 55° angle with the ground. How high above the ground is the kite? Round to the nearest foot. (sin 55° ≈ 0.819) h = ?55°200 ft
  1. A. 115 feet
  2. B. 141 feet
  3. C. 164 feet
  4. D. 186 feet
Show the answer and explanation

Correct answer: C. 164 feet

📌 **Step 1: Identify the trig ratio** We know the hypotenuse (200 ft) and want the opposite side (height). Use **sine**: sin = opposite / hypotenuse 📌 **Step 2: Set up and solve** sin(55°) = h / 200 0.819 = h / 200 h = 200 × 0.819 = 163.8 📌 **Answer:** ≈ **164 feet** 💡 **Tip:** Angle of elevation from ground = angle between the string and the horizontal, NOT the vertical.
Question 5
A swimming pool has the shape shown below — a rectangle with a semicircle on each end. Find the total area of the pool. (Use π ≈ 3.14) 20 m10 mr = 5
  1. A. 200.0 m²
  2. B. 257.0 m²
  3. C. 278.5 m²
  4. D. 356.0 m²
Show the answer and explanation

Correct answer: C. 278.5 m²

Rectangle area = 20 × 10 = 200 m². Two semicircles = one full circle with r = 5: π × 5² = 3.14 × 25 = 78.5 m². Total = 200 + 78.5 = 278.5 m².
Question 6
Find the volume of the cone shown below. Round to the nearest tenth. (Use π ≈ 3.14) h = 15 cmr = 6 cm
  1. A. 339.1 cm³
  2. B. 452.2 cm³
  3. C. 565.2 cm³
  4. D. 1695.6 cm³
Show the answer and explanation

Correct answer: C. 565.2 cm³

📌 **Step 1: Recall the cone volume formula** V = (1/3)πr²h 📌 **Step 2: Plug in values** r = 6 cm, h = 15 cm V = (1/3)(3.14)(36)(15) 📌 **Step 3: Calculate step by step** 3.14 × 36 = 113.04 113.04 × 15 = 1695.6 1695.6 / 3 = **565.2 cm³** 💡 **Common mistake:** Don't forget to divide by 3! A cone is 1/3 the volume of a cylinder with the same base and height.
Question 7
Quadrilateral ABCD has the properties shown below. Which type of quadrilateral is ABCD? ABCD1622AB ∥ DCAB ≠ DC
  1. A. Parallelogram
  2. B. Rhombus
  3. C. Trapezoid
  4. D. Rectangle
Show the answer and explanation

Correct answer: C. Trapezoid

A quadrilateral with exactly one pair of parallel sides is a trapezoid. AB ∥ DC but AB ≠ DC (16 ≠ 22), confirming it is a trapezoid, not a parallelogram.
Question 8
From the top of a lighthouse 90 feet tall, the angle of depression to a boat is 28°. How far is the boat from the base of the lighthouse? (tan 28° ≈ 0.532) 28°90 ftd = ?
  1. A. 47.9 feet
  2. B. 101.8 feet
  3. C. 169.2 feet
  4. D. 203.4 feet
Show the answer and explanation

Correct answer: C. 169.2 feet

The angle of depression equals the angle of elevation from the boat. tan(28°) = opposite/adjacent = 90/d d = 90/tan(28°) = 90/0.532 ≈ 169.2 feet.
Question 9
A tree casts a shadow 18 feet long. At the same time, a 5-foot-tall fence post casts a shadow 3 feet long. How tall is the tree? h = ?18 ft5 ft3 ftSimilar triangles (AA)
  1. A. 24 feet
  2. B. 27 feet
  3. C. 30 feet
  4. D. 36 feet
Show the answer and explanation

Correct answer: C. 30 feet

The tree and fence post form similar triangles with their shadows (same sun angle). tree height / tree shadow = fence height / fence shadow h / 18 = 5 / 3 h = 18 × 5/3 = 30 feet.
Question 10
In right triangle ABC, an altitude CD is drawn from the right angle C to hypotenuse AB. If AD = 5 and DB = 12, what is the length of CD? ABCD512h = ?Geometric Mean
  1. A. √17 ≈ 4.12
  2. B. 2√15 ≈ 7.75
  3. C. √85 ≈ 9.22
  4. D. 8.5
Show the answer and explanation

Correct answer: B. 2√15 ≈ 7.75

The altitude to the hypotenuse is the geometric mean of the two segments: CD = √(AD × DB) = √(5 × 12) = √60 = 2√15 ≈ 7.75.

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