Find the distance between points P and Q shown on the coordinate plane below.
A√17
B√13
C5
D√10
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 2 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?
A27 feet
B24 feet
C36 feet
D30 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 3 of 10
Florida standards 1A-1GHard Calc Word
A composite figure is made of a rectangle (10 m × 6 m) with a semicircle attached to one of the shorter sides. What is the total area? (Use π ≈ 3.14)
A102.5 m²
B64.7 m²
C88.3 m²
D74.1 m²
Explanation
📌 Step 1: Break into simple shapes Rectangle: 10 m × 6 m Semicircle: radius = 6/2 = 3 m (attached to the 6 m side)
📌 Step 2: Calculate each area Rectangle = 10 × 6 = 60 m² Semicircle = ½πr² = ½ × 3.14 × 3² = ½ × 28.26 = 14.13 m²
📌 Step 3: Add them Total = 60 + 14.13 = 74.13 ≈ 74.1 m²
💡 Strategy for composite figures: Always break them into shapes you know (rectangles, triangles, circles), calculate each, then add (or subtract for holes).
Question 4 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
C186 feet
D115 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 5 of 10
Florida standards 1A-1GMedium Calc Word Diagram
Quadrilateral ABCD has the properties shown below. Which type of quadrilateral is ABCD?
ARectangle
BParallelogram
CTrapezoid
DRhombus
Explanation
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 6 of 10
Florida standards 6A-6EEasy Calc Word Diagram
In the triangle below, ∠A = 55° and ∠B = 65°. What is the measure of ∠C?
A75°
B60°
C70°
D50°
Explanation
📌 Step 1: Recall the Triangle Angle Sum Theorem All angles in a triangle add up to 180°.
📌 Step 2: Set up the equation ∠A + ∠B + ∠C = 180° 55° + 65° + ∠C = 180°
📌 Step 3: Solve ∠C = 180° − 55° − 65° = 60°
💡 Quick check: 55 + 65 + 60 = 180° ✓
Question 7 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)
A169.2 feet
B203.4 feet
C101.8 feet
D47.9 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 8 of 10
Florida standards 1A-1GEasy Calc Word
A pizza box is 14 inches on each side and 2 inches tall. What is the volume of the box?
A280 in³
B392 in³
C196 in³
D448 in³
Explanation
📌 Step 1: Identify the shape A pizza box is a rectangular prism (cuboid).
📌 Step 2: Apply the volume formula V = length × width × height V = 14 × 14 × 2
📌 Step 3: Calculate = 392 in³
💡 Quick check: Volume is always in cubic units. If your answer is in square units, something went wrong!
Question 9 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)