Point A(3, 2) is reflected across the x-axis. What are the coordinates of the image?
A(2, 3)
B(−3, 2)
C(3, −2)
D(−3, −2)
Explanation
📌 Step 1: Understand cross sections A cross section is the shape you get when you "slice" a 3D object with a flat plane.
📌 Step 2: Visualize the cut Slicing a cylinder parallel to its base is like cutting a log straight across.
📌 Step 3: Determine the shape The base of a cylinder is a circle. A parallel cut produces the exact same shape → Circle
💡 Cross section rules: • Cut parallel to base → same shape as base • Cut perpendicular to base of cylinder → rectangle • Cut at an angle through cylinder → ellipse
Question 2 of 9
TEKS 13A-13EEasy Calc Word
In how many ways can 5 students be arranged in a line?
A720
B120
C60
D25
Explanation
📌 Step 1: Understand permutations Arranging n objects in a line uses n! (n factorial).
💡 Key difference: • Permutation = order matters (arranging in a line) • Combination = order doesn't matter (choosing a team) • Formula: P(n,r) = n!/(n-r)! and C(n,r) = n!/(r!(n-r)!)
Question 3 of 9
TEKS 3A-3DMedium Calc Word Diagram
Trapezoid WXYZ has vertices W(−4, 2), X(−1, 2), Y(0, −1), and Z(−5, −1). It is translated 6 units right, then reflected over the x-axis. What are the coordinates of W′?
AW′(2, −2)
BW′(10, −2)
CW′(−4, −2)
DW′(2, 2)
Explanation
Step 1: Translate 6 right → add 6 to x: W(−4,2) → (−4+6, 2) = (2, 2). Step 2: Reflect over x-axis → negate y: (2, 2) → (2, −2). So W′ = (2, −2).
Question 4 of 9
TEKS 10A-10BEasy Word
What shape is the cross section when a plane cuts through a cylinder parallel to its base?
ATriangle
BEllipse
CRectangle
DCircle
Explanation
📌 Step 1: Find the rotational symmetry angle For a regular n-sided polygon: Smallest rotation = 360° / n
📌 Step 2: Apply to a pentagon (n = 5) 360° / 5 = 72°
📌 Answer:72°
💡 Tip: A figure has rotational symmetry if it maps onto itself after a rotation less than 360°. A regular pentagon maps to itself at 72°, 144°, 216°, and 288°.
Question 5 of 9
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?
A448 in³
B280 in³
C392 in³
D196 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 6 of 9
TEKS 12A-12EEasy Calc Word
A central angle of a circle is 90°. What is the measure of the intercepted arc?
A180°
B270°
C45°
D90°
Explanation
📌 Step 1: Recall the central angle-arc relationship A central angle equals its intercepted arc.
📌 Step 2: Apply Central angle = 90° → Arc = 90°
💡 Key relationships in circles: • Central angle = intercepted arc • Inscribed angle = ½ × intercepted arc • Two inscribed angles intercepting the same arc are equal
Question 7 of 9
TEKS 13A-13EMedium Calc Word
A card is drawn from a standard 52-card deck. What is the probability of drawing a heart or a king?
A16/52
B13/52
C4/52
D17/52
Explanation
📌 Step 1: Use the Addition Rule P(A or B) = P(A) + P(B) − P(A and B)
📌 Step 2: Count each • Hearts: 13 cards • Kings: 4 cards • King of Hearts (counted in both): 1 card