MathMastery
Score 0 / 0
Unit 1

Pre-Algebra
Word Problems

10 core problems covering variables, equations, ratios, and more. Choose your answer — instant feedback every time.

0 / 10
Q 01 Variables & Equations ★☆☆
⚡ MEMORY POINT: ISOLATE THE VARIABLEMove numbers to one side, keep the variable alone. Whatever you do to one side, do to the other!
Example
If x + 5 = 12, what is x?
→ Subtract 5 from both sides: x = 12 − 5 = 7

Sarah has some stickers. She gives away 8 stickers and has 15 left. Which equation finds the number of stickers she started with?

📖 Explanation She gave away stickers, meaning subtraction happened. If she started with x stickers and gave 8 away, the equation is:
x − 8 = 15 Add 8 to both sides: x = 23.
✔ Choice A is correct.
Q 02 Ratio & Proportion ★★☆
⚡ MEMORY POINT: CROSS-MULTIPLYa/b = c/d → a×d = b×c. Ratios are equal fractions — cross-multiply to solve!
Example
If 3/4 = x/12 → 3×12 = 4×x → 36 = 4x → x = 9

A recipe uses 3 cups of flour for every 2 cups of sugar. How many cups of flour are needed if you use 8 cups of sugar?

📖 Explanation Set up the proportion: 3/2 = x/8
Cross-multiply: 3 × 8 = 2 × x → 24 = 2x → x = 12 ✔ Choice B is correct.
Q 03 Percent ★★☆
⚡ MEMORY POINT: PERCENT = PART / WHOLE × 100"Of" means multiply. "Is" means equals. Always divide part by whole!
Example
What is 30% of 50? → 0.30 × 50 = 15

A jacket originally costs $80. It is on sale for 25% off. What is the sale price?

📖 Explanation Discount = 25% of $80 = 0.25 × 80 = $20
Sale Price = Original − Discount = 80 − 20 = $60 ✔ Choice C is correct.
Q 04 Integer Operations ★☆☆
⚡ MEMORY POINT: SAME SIGN → ADD, DIFFERENT SIGN → SUBTRACT (keep the bigger sign!)Negative + Negative = more negative. Positive + Negative = subtract & keep bigger sign.

The temperature was −4°F in the morning. By noon it rose 11 degrees, then dropped 7 degrees in the evening. What is the final temperature?

📖 Explanation Start at −4, add 11: −4 + 11 = 7
Then subtract 7: 7 − 7 = 0°F ✔ Choice B is correct.
Q 05 Order of Operations ★★☆
⚡ MEMORY POINT: PEMDASParentheses → Exponents → Multiply/Divide → Add/Subtract. Always left to right for ×÷ and +−!
Example
3 + 4 × 2 = 3 + 8 = 11 (NOT 14, because × comes before +!)

Tom earns $12 per hour. He works 3 hours on Monday and 5 hours on Tuesday, then spends $20 on lunch. Which expression gives the correct amount left?

📖 Explanation Total hours = 3 + 5 = 8 hours. Total earn = 12 × 8 = $96.
12 × (3 + 5) − 20 = 96 − 20 = $76 Parentheses combine the hours first. ✔ Choice B is correct.
Q 06 Fractions ★★☆
⚡ MEMORY POINT: DIVIDE BY FRACTION = MULTIPLY BY RECIPROCALa ÷ (b/c) = a × (c/b). Flip and multiply!

A pizza is cut into equal slices. Maria eats 3/8 of the pizza and her brother eats 1/4. What fraction of the pizza is left?

📖 Explanation Convert 1/4 to 2/8. Total eaten = 3/8 + 2/8 = 5/8
Left = 1 − 5/8 = 8/8 − 5/8 = 3/8 ✔ Choice A is correct.
Q 07 Inequalities ★★☆
⚡ MEMORY POINT: FLIP THE SIGN WHEN MULTIPLYING/DIVIDING BY NEGATIVE!If −2x > 6, divide by −2 → x < −3 (sign flips!). This is the #1 trap!

Jake needs at least $50 to buy a game. He already has $18 and earns $8/hour. What is the minimum number of hours he must work?

📖 Explanation Set up: 18 + 8h ≥ 50
8h ≥ 50 − 18 = 32 → h ≥ 4 He needs to work at least 4 hours. ✔ Choice B is correct.
Q 08 Rate & Speed ★★★
⚡ MEMORY POINT: D = R × T (Distance = Rate × Time)Cover the one you want to find: D = RT, R = D/T, T = D/R. Draw a triangle!
Example
A car goes 60 mph for 2.5 hours → Distance = 60 × 2.5 = 150 miles

Train A travels at 60 mph and Train B at 40 mph, starting from the same station in opposite directions. After how many hours will they be 300 miles apart?

📖 Explanation Moving apart → add speeds: 60 + 40 = 100 mph combined.
Time = Distance ÷ Speed = 300 ÷ 100 = 3 hours ✔ Choice B is correct.
Q 09 Distributive Property ★★☆
⚡ MEMORY POINT: DISTRIBUTE = MULTIPLY OUTSIDE × EACH INSIDEa(b + c) = ab + ac. Don't forget to multiply every term inside the parentheses!

A store sells notebooks for $3 each and pens for $1.50 each. A teacher buys 6 of each item. Which expression using the distributive property gives the total cost?

📖 Explanation 6 notebooks and 6 pens: 6(3 + 1.50) is the distributive form.
6 × 3 + 6 × 1.50 = 18 + 9 = $27 ✔ Choice B is correct.
Q 10 Two-Step Equations ★★★
⚡ MEMORY POINT: UNDO IN REVERSE ORDER (PEMDAS backwards)First undo + or −, THEN undo × or ÷. Work your way back from the answer!
Example
2x + 6 = 14 → Step 1: subtract 6 → 2x = 8 → Step 2: divide by 2 → x = 4

Emma is thinking of a number. She triples it, then subtracts 7, and gets 20. What is her number?

📖 Explanation Let the number = x. Equation: 3x − 7 = 20
Step 1: 3x = 20 + 7 = 27 Step 2: x = 27 ÷ 3 = 9 ✔ Choice C is correct.
Unit 2

Geometry
Word Problems

10 core problems covering area, perimeter, angles, triangles, and circles. Watch for common traps!

0 / 10
Q 01 Perimeter ★☆☆
⚡ MEMORY POINT: PERIMETER = ALL SIDES ADDED"Peri" means around. Just add up every single side. Don't forget any edges!
Example
Rectangle 5×3: Perimeter = 5 + 3 + 5 + 3 = 16 (or use 2l + 2w = 2×5 + 2×3 = 16)

A rectangular garden is 12 m long and 7 m wide. Fencing costs $5 per meter. What is the total cost to fence the garden?

📖 Explanation Perimeter = 2(l + w) = 2(12 + 7) = 2 × 19 = 38 m
Cost = 38 × $5 = $190 Trap: Don't multiply only two sides! ✔ Choice B is correct.
Q 02 Area of Triangle ★★☆
⚡ MEMORY POINT: A = ½ × base × heightTriangle = HALF of a rectangle! The height must be PERPENDICULAR to the base — not the slant side!

A triangular sail has a base of 9 m and a height of 14 m. What is the area of the sail?

📖 Explanation A = ½ × b × h = ½ × 9 × 14 = 63 m² Common trap: forgetting the ½. Without it you get 126. ✔ Choice A is correct.
Q 03 Circles — Circumference ★★☆
⚡ MEMORY POINT: C = 2πr = πdCircumference = "distance around" = π × diameter. Remember π ≈ 3.14. Diameter = 2 × radius!
Example
Circle with radius 5: C = 2π(5) = 10π ≈ 31.4 units

A wheel has a radius of 35 cm. How far does it travel in one complete rotation? (Use π ≈ 3.14)

📖 Explanation One rotation = circumference. C = 2πr = 2 × 3.14 × 35
= 6.28 × 35 = 219.8 cm Trap: C uses choice A (πr only), but the formula needs 2πr. ✔ Choice B is correct.
Q 04 Angle Relationships ★★☆
⚡ MEMORY POINT: SUPPLEMENTARY = 180°, COMPLEMENTARY = 90°"S" (supplementary) = Straight line (180°). "C" (complementary) = Corner / right angle (90°).

Two angles are supplementary. One angle is 3x + 10° and the other is x + 30°. What is the value of x?

📖 Explanation Supplementary means sum = 180°
(3x + 10) + (x + 30) = 180 4x + 40 = 180 → 4x = 140 → x = 35 ✔ Choice B is correct.
Q 05 Pythagorean Theorem ★★★
⚡ MEMORY POINT: a² + b² = c² (c = HYPOTENUSE, always opposite the right angle!)The hypotenuse is ALWAYS the longest side. Know your triples: 3-4-5, 5-12-13, 8-15-17!
Example (Pythagorean Triple)
a = 3, b = 4: c² = 9 + 16 = 25 → c = 5 ✓

A ladder leans against a wall. The ladder is 13 ft long, and its base is 5 ft from the wall. How high up the wall does the ladder reach?

📖 Explanation The ladder is the hypotenuse (c = 13), base is a leg (a = 5).
a² + b² = c² → 5² + b² = 13² 25 + b² = 169 → b² = 144 → b = 12 ft This is a 5-12-13 Pythagorean triple! ✔ Choice C is correct.
Q 06 Area of Circle ★★★
⚡ MEMORY POINT: A = πr² (Area uses RADIUS squared!)TRAP: "diameter" given → must divide by 2 to get radius FIRST, then square it. Most mistakes happen here!

A circular pizza has a diameter of 16 inches. What is the area of the pizza? (Use π ≈ 3.14)

📖 Explanation Diameter = 16 → Radius = 8. A = πr²
A = 3.14 × 8² = 3.14 × 64 = 200.96 in² Trap: Using diameter (16) directly gives 803.84 — wrong! ✔ Choice A is correct.
Q 07 Volume of Rectangular Prism ★★☆
⚡ MEMORY POINT: V = l × w × hVolume = filling 3D space. Always multiply ALL THREE dimensions. Units will be CUBED (cm³, m³)!

A fish tank is 60 cm long, 30 cm wide, and 40 cm tall. It is filled ¾ full with water. What is the volume of water in the tank?

📖 Explanation Total volume = 60 × 30 × 40 = 72,000 cm³
¾ of 72,000 = 72,000 × 0.75 = 54,000 cm³ ✔ Choice A is correct.
Q 08 Triangle Angles ★★☆
⚡ MEMORY POINT: ALL TRIANGLE ANGLES SUM TO 180°Any triangle, any shape — always 180°. Find the missing angle: 180° − (sum of the other two)!

In a triangle, one angle is 90° (right angle), and another is 2x − 10°. The third angle is x + 20°. What is the value of x?

📖 Explanation Sum of all angles = 180°
90 + (2x − 10) + (x + 20) = 180 90 + 3x + 10 = 180 → 3x = 80 → x = 26.67 ✔ Choice B is correct.
Q 09 Composite Shapes ★★★
⚡ MEMORY POINT: SPLIT INTO SIMPLE SHAPES, THEN ADD OR SUBTRACTBig shape = rectangle + triangle? Calculate each separately, then combine. Watch for "shaded region" (subtract)!

An L-shaped floor plan is made of two rectangles. One is 10 × 4 m and the other is 6 × 3 m. What is the total floor area?

📖 Explanation Separate areas: 10 × 4 = 40 m² and 6 × 3 = 18 m²
Total = 40 + 18 = 58 m² ✔ Choice B is correct.
Q 10 Similar Triangles ★★★
⚡ MEMORY POINT: SIMILAR = SAME SHAPE, PROPORTIONAL SIDESCorresponding sides are in the same RATIO. Set up a proportion: small/big = small/big. Cross-multiply!
Example
If small triangle sides are 3, 4, 5 and big triangle's shortest side is 6 → scale factor = 2 → sides are 6, 8, 10.

A 6 ft tall person casts a shadow of 4 ft. At the same time, a nearby tree casts a shadow of 18 ft. How tall is the tree?

📖 Explanation Similar triangles: height/shadow = height/shadow
6/4 = x/18 → cross-multiply: 4x = 108 → x = 27 ft ✔ Choice C is correct.