PEMDAS (Order of Operations)
Simplify: 8 + (6 ÷ 2) × 3
8+(6÷2)×3=8+3×3=8+9=178 + (6 ÷ 2) × 3 = 8 + 3 × 3 = 8 + 9 = 17
= 17
A number increased by 5 equals 12. What is the number?
x+5=12⇒x=7 + 5 = 12 ⇒x = 7
x = 7
Find the hypotenuse of a right triangle with legs of 6 and 8.
c^2 = 6^2 + 8^2
c^2 = 36 + 64 = 100
square root of 100 =10
c = 10
What is the probability of rolling an even number on a six-sided die?
3/6 = 50%
=50%
If two angles are complementary and one is 35°, what is the other angle?
90−35=55°90 - 35 = 55°
=55°
Evaluate: (4^2 - 6) ÷ 2 + 3
(4^2 - 6) ÷ 2 + 3=(16−6)÷2+3=10÷2+3=5+3=8(4^2 - 6) ÷ 2 + 3 = (16 - 6) ÷ 2 + 3 = 10 ÷ 2 + 3 = 5 + 3=8
= 8
If 3x - 7 = 14, find x.
3x−7=14⇒ 3x=21⇒ 21 -7 = 14⇒ x = 7
x = 7
A ladder leans against a wall. The base is 5 feet from the wall, and the ladder is 13 feet long. How high does it reach?
13^2 = 5^2 + b^2
169 = 25 + h^2 ⇒169 - 25 = 144 ⇒ b=12
= 12 feet
Find the mean, median, and mode of {3, 7, 7, 10, 15, 15, 15, 20}.
Mean: 11.875, Median: 12.5, Mode: 15
Mean: Add all numbers and divide by the total count.; Median: The middle numbers are 10 and 15, so 10 +15/2 = 12.5; Mode: The number that appears most frequently is 15.
A triangle has angles measuring 40° and 75°. Find the third angle.
180=40+75+x ⇒ 180 - (40 + 75) = 65°
x= 65°
Create an expression using all four operations that equals 25.
Answers may vary.
Example: (10÷2)+15=25(10 ÷ 2) + 15 = 25
Two consecutive numbers add up to 35. What are they?
17 + 18 = 35
17 and 18
Prove whether a triangle with sides 7, 24, and 25 is a right triangle.
a^2 + b^2 = c^2 ⇒ 49+576=625, so it is a right triangle.
Determine if the statement "If a shape is a square, then it is a rectangle" is true or false.
True, because all squares are rectangles.
Explain why vertical angles are always equal.
Vertical angles are equal because they are opposite angles formed by two intersecting lines.
Why does multiplication precede addition in PEMDAS? Provide an example.
Example: 2+3×4=2+12=142 + 3 × 4 = 2 + 12 = 14, not (2+3)×4=20(2+3) × 4 = 20.
Multiplication precedes addition because of the standard order of operations - PEMDAS (Parenthesis, Exponent, Multiplication, Division, Addition, Subtraction)
Create and solve a problem that involves two variables.
Answers will vary.
Example: "If 2x + y = 10 and y - x = 4, find x and y." (Answer: x=2,y=6x = 2, y = 6)
Develop a word problem that requires using the Pythagorean Theorem.
Answers will vary.
Example: "A ladder leans against a house. If it is 15 ft long and the base is 9 ft from the wall, how high does it reach?" (Answer: 12 ft)
Write the converse of the statement: "If it is raining, then the ground is wet."
"If the ground is wet, then it is raining."
Develop a problem involving a transversal and parallel lines.
Answers will vary.
Example: "A transversal cuts two parallel lines creating one angle of 60°. Find all angles."
Design a real-world problem that requires using PEMDAS to solve.
Answers will vary.
Example: "A store sells shirts for $15 each. If a customer buys 3 shirts and uses a $10 discount, what is the total cost?" (3×15)−10=35(3 × 15) - 10 = 35
How does understanding problem-solving strategies help in real-life scenarios? Provide an example.
Answers will vary.
Real-life example: "If a recipe needs 2 eggs for every 3 cups of flour, how many eggs are needed for 9 cups?" (Answer: 6 eggs)
Why is the Pythagorean Theorem fundamental to distance calculations in coordinate geometry?
The theorem helps find distances between points in coordinate geometry. Example: Find the distance between (3,4) and (7,1). (Answer: 5)
How does logical reasoning apply to coding and AI development?
Logic is used in programming, law, and decision-making.
How can knowledge of angles help in real-world design?
Real-world example: "Architects use angle properties to ensure buildings are structurally sound."