⚡ KEYWORD: "per" = ÷, "of" = ×, "is" = =
Question 01 · Translating Words into Equations
A store sells apples for $0.75 each. Maria buys n apples and pays $6.00 in total.
Which equation correctly represents this situation?
⚡ ORDER OF OPERATIONS: Parentheses → Exponents → × ÷ → + −
Question 02 · Order of Operations (PEMDAS)
Evaluate: 3 + 4 × (2² − 1)
⚠️ Common mistake: adding 3 + 4 first!
⚡ SOLVING: Whatever you do to one side, do to the other!
Question 03 · One-Step Equation
Solve for x:
x − 13 = 7
⚡ TWO-STEP: 1) add/subtract first 2) multiply/divide second
Question 04 · Two-Step Equation
Solve for y:
3y + 5 = 20
⚡ RATIO: Part / Whole × 100 for percent; keep same units!
Question 05 · Ratio & Proportion
A recipe calls for 2 cups of sugar for every 5 cups of flour. If you use 15 cups of flour, how many cups of sugar do you need?
⚡ INTEGERS: negative × negative = POSITIVE; negative × positive = NEGATIVE
Question 06 · Integer Operations
Calculate:
(−4) × (−3) + (−2)
⚡ PERCENT: IS / OF = % / 100 → cross-multiply!
Question 07 · Percent Problems
A jacket originally costs $80. It is on sale for 25% off. What is the sale price?
⚡ DISTRIBUTE: a(b + c) = ab + ac — multiply EACH term inside!
Question 08 · Distributive Property
Simplify:
2(3x − 4) + 5x
⚡ INEQUALITY FLIP: multiply/divide by NEGATIVE → flip the sign!
Question 09 · Solving Inequalities
Solve and choose the correct answer:
−2x < 8
⚠️ Watch the sign direction carefully!
⚡ VARIABLE BOTH SIDES: collect variables on LEFT, numbers on RIGHT
Question 10 · Variables on Both Sides
Solve for x:
5x − 3 = 2x + 9
⚡ SUPPLEMENTARY = 180°; COMPLEMENTARY = 90°
Question 11 · Supplementary Angles
Two angles are supplementary. One angle measures 63°. What is the other angle?
⚠️ Don't confuse supplementary (180°) with complementary (90°)!
⚡ TRIANGLE ANGLES: always add up to 180°
Question 12 · Triangle Angle Sum
A triangle has angles of 45° and 85°. What is the measure of the third angle?
⚡ PYTHAGOREAN: a² + b² = c² (c = hypotenuse = longest side)
Question 13 · Pythagorean Theorem
A right triangle has legs of length 6 and 8. What is the length of the hypotenuse?
⚡ AREA of TRIANGLE: (1/2) × base × height — height must be PERPENDICULAR!
Question 14 · Area of a Triangle
A triangle has a base of 14 cm and a height of 9 cm. What is its area?
⚠️ Don't forget the ½ ! Many students forget to halve.
⚡ CIRCLE: Area = πr²; Circumference = 2πr (r = radius = half of diameter)
Question 15 · Circle — Area
A circle has a diameter of 10 cm. What is its area? (Use π ≈ 3.14)
⚠️ The formula uses radius, not diameter!
⚡ PERIMETER = add ALL outside sides (don't skip any!)
Question 16 · Perimeter of a Rectangle
A rectangle has a length of 13 m and a width of 7 m. What is its perimeter?
⚠️ P = 2(l + w), NOT just l + w!
⚡ VERTICAL ANGLES: opposite angles at an intersection are EQUAL
Question 17 · Vertical Angles
Two straight lines intersect. One angle formed is 72°. What is the measure of the vertical angle directly opposite it?
⚡ VOLUME of RECTANGULAR PRISM: V = length × width × height
Question 18 · Volume of a Rectangular Prism
A box has dimensions: length = 5 cm, width = 4 cm, height = 3 cm. What is the volume?
⚡ ISOSCELES TRIANGLE: 2 equal sides → 2 equal BASE angles
Question 19 · Isosceles Triangle Angles
An isosceles triangle has a vertex angle of 40°. The two base angles are equal. What is the measure of each base angle?
⚠️ All three angles must still add up to 180°!
⚡ EXTERIOR ANGLE of TRIANGLE = sum of the TWO non-adjacent interior angles
Question 20 · Exterior Angle Theorem
In a triangle, two interior angles measure 55° and 70°. What is the measure of the exterior angle at the third vertex?