💡 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 2 of 10
Florida standards 2A-2CMedium Calc Word Diagram
Find the distance between points P and Q shown on the coordinate plane below.
A√10
B√17
C5
D√13
Explanation
📌 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 CBE.
Question 3 of 10
Florida standards 12A-12EMedium Calc Word Diagram
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?
A12
B14
C10
D8
Explanation
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 4 of 10
Florida standards 9A-9BMedium Calc Word Diagram
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)
A101.8 feet
B203.4 feet
C47.9 feet
D169.2 feet
Explanation
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 5 of 10
Florida standards 3A-3DHard Calc Word
Point Q(4, −1) is first reflected across the y-axis, then rotated 180° about the origin. What is the final image?
A(−4, −1)
B(−4, 1)
C(4, −1)
D(4, 1)
Explanation
📌 Step 1: Understand rigid motions (isometries) Transformations that preserve BOTH size and shape: ✅ Translation (slide) ✅ Reflection (flip) ✅ Rotation (turn)
📌 Answer:Translation preserves both size and shape.
💡 Key term: Rigid motions are also called "isometries" (iso = same, metry = measure).
Question 6 of 10
Florida standards 1A-1GMedium Calc Word Diagram
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)
A164 feet
B141 feet
C115 feet
D186 feet
Explanation
📌 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 7 of 10
Florida standards 7A-7BMedium Calc Word Diagram
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?
A30 feet
B27 feet
C36 feet
D24 feet
Explanation
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 8 of 10
Florida standards 11A-11DMedium Calc Word Diagram
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)
A278.5 m²
B356.0 m²
C257.0 m²
D200.0 m²
Explanation
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 9 of 10
Florida standards 4A-4DEasy Calc Word Diagram
Jake claims: "If a quadrilateral has four right angles, then it must be a square." Which figure below is a counterexample?
ASquare
BTrapezoid
CRectangle
DRhombus
Explanation
A rectangle has four right angles but is NOT necessarily a square (it can have unequal side lengths). The rectangle with sides 90×60 is a counterexample to Jake's claim.
Question 10 of 10
Florida standards 7A-7BMedium Calc Word Diagram
In the figure below, DE ∥ BC. If AD = 4, DB = 6, and AE = 5, find EC.
A7.5
B10.0
C6.0
D8.0
Explanation
📌 Step 1: Apply the Triangle Proportionality Theorem Since DE ∥ BC: AD/DB = AE/EC