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
B115 feet
C141 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 2 of 10
TEKS 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 3 of 10
TEKS 3A-3DEasy Calc Word Diagram
Which of the following figures has BOTH reflectional and rotational symmetry?
AC (Parallelogram)
BB (Regular hexagon)
CA (Scalene triangle)
DD (Arrow)
Explanation
📌 Step 1: Check each figure
A (Scalene triangle): No lines of symmetry, no rotational symmetry ✗ B (Regular hexagon): 6 lines of symmetry + rotational symmetry at 60° ✓ C (Parallelogram): No lines of symmetry, rotational symmetry at 180° only → partial ✗ D (Arrow): 1 line of symmetry (vertical) but no rotational symmetry ✗
📌 Answer: B (Regular hexagon)
💡 Tip: All regular polygons have BOTH reflectional AND rotational symmetry. The number of symmetry lines = number of sides.
Question 4 of 10
TEKS 11A-11DMedium Calc Word Diagram
Find the volume of the cone shown below. Round to the nearest tenth. (Use π ≈ 3.14)
A565.2 cm³
B1695.6 cm³
C452.2 cm³
D339.1 cm³
Explanation
📌 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)
💡 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 5 of 10
TEKS 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)
A257.0 m²
B278.5 m²
C200.0 m²
D356.0 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 6 of 10
TEKS 1A-1GMedium Calc Word Diagram
Quadrilateral ABCD has the properties shown below. Which type of quadrilateral is ABCD?
ATrapezoid
BRectangle
CParallelogram
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 7 of 10
TEKS 1A-1GEasy Calc Word
A cylindrical water tank has a radius of 3 feet and a height of 8 feet. What is the volume of the tank? (Use π ≈ 3.14)
A150.72 ft³
B75.36 ft³
C226.08 ft³
D301.44 ft³
Explanation
📌 Step 1: Recall the volume formula for a cylinder V = πr²h
📌 Step 2: Plug in the values r = 3 ft, h = 8 ft, π ≈ 3.14 V = 3.14 × 3² × 8 = 3.14 × 9 × 8
💡 Tip: Always check your units — volume is measured in cubic units (ft³, cm³, m³).
Question 8 of 10
TEKS 1A-1GEasy Calc Word
A pizza box is 14 inches on each side and 2 inches tall. What is the volume of the box?
A196 in³
B280 in³
C392 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
TEKS 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)
A88.3 m²
B74.1 m²
C102.5 m²
D64.7 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 10 of 10
TEKS 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)