Self-Study Workbook · 2024 Edition

Math Mastery
Pre-Algebra & Geometry

Core concepts, tricky problems, and instant feedback — built for solo practice.

20Problems
2Chapters
∞Retries
Score
0 / 0
📐 Chapter 1

Pre-Algebra
Word Problems

Variables, equations, ratios, and number sense — the foundations of algebra thinking.

🧠
Quick Memory Points
UNKNOWN = variable IS / EQUALS = = OF = × PER = ÷ MORE THAN = + LESS THAN = − TWICE = × 2 CONSECUTIVE = n, n+1, n+2
Q 01 Variables

Emma has some stickers. After she gives 7 stickers to her friend and receives 3 more from her mom, she has 18 stickers. How many stickers did Emma start with?

💡 Hint: Let x = starting stickers. Write the equation step by step.
x − 7 + 3 = 18
Q 02 Ratios

In a class, the ratio of boys to girls is 3 : 5. If there are 24 boys, how many students are in the class altogether?

💡 Key: boys/girls = 3/5 → find girls first, then total.
Q 03 ⚠ Tricky

The sum of three consecutive integers is 78. What is the largest of the three integers?

💡 Trap: Don't just divide 78 ÷ 3 = 26 and stop! That gives the middle number, not the largest.
n + (n+1) + (n+2) = 78
Q 04 Percentages

A jacket originally costs $80. It is on sale for 25% off. If sales tax is 10%, what is the final price you pay?

💡 Order matters! Apply discount first, then tax. Tax is added on the discounted price — not the original.
Q 05 ⚠ Tricky

A train travels at 60 mph. A car travels the same distance but takes 1.5 times longer. What is the car's speed?

💡 Remember: Speed = Distance ÷ Time. If time increases by ×1.5, speed decreases by ÷1.5.
Q 06 Proportions

A recipe needs 2 cups of flour for every 3 dozen cookies. How many cups of flour are needed to make 12 dozen cookies?

💡 Set up a proportion: 2/3 = x/12, then cross-multiply.
Q 07 ⚠ Tricky

Lucas is twice as old as Maya. In 6 years, Lucas will be 1.5 times as old as Maya. How old is Maya now?

💡 Trap: Many students forget to add 6 to BOTH ages in the future equation.
Now: Lucas = 2m  |  Future: 2m+6 = 1.5(m+6)
Q 08 Integers

The temperature at 6 AM was −8°C. By noon, it rose by 15°C, then dropped 4°C in the evening. What was the final temperature?

💡 Work left to right: start with a negative and be careful adding/subtracting.
Q 09 ⚠ Tricky

A store sells pens for $2 each and notebooks for $5 each. Jake buys a total of 10 items and spends exactly $29. How many pens did he buy?

💡 This is a system of equations. Let p = pens, n = notebooks. Write 2 equations.
p + n = 10    and    2p + 5n = 29
Q 10 ⚠ Tricky

A number is multiplied by 4, then 9 is subtracted, and the result is doubled. The final answer is 46. What is the original number?

💡 Build the equation step-by-step from left to right. Common mistake: forgetting to distribute the "doubled" multiplication.
2 × (4x − 9) = 46
📏 Chapter 2

Geometry
Word Problems

Area, perimeter, angles, the Pythagorean theorem, and spatial reasoning.

🧠
Quick Memory Points
AREA = space inside PERIMETER = outside edge Triangle Area = ½ b×h Circle Area = πr² a²+b²=c² (right triangle) angles in triangle = 180° complementary = 90° supplementary = 180°
Q 11 Area

A rectangular garden is 12 meters long and 7 meters wide. You want to put a fence around the entire garden. How many meters of fence do you need?

💡 Fence = Perimeter, NOT area. P = 2(l + w).
Q 12 ⚠ Tricky

In a triangle, the angles are in the ratio 2 : 3 : 4. What is the measure of the largest angle?

💡 Trap: Don't forget angles in any triangle ALWAYS add up to 180°.
2x + 3x + 4x = 180°
Q 13 Pythagorean

A ladder leans against a wall. The bottom of the ladder is 6 feet from the wall, and the ladder reaches 8 feet up the wall. How long is the ladder?

8 ft 6 ft ?
Q 14 ⚠ Tricky

A circular pizza has a diameter of 14 inches. What is the area of the pizza? (Use π ≈ 3.14)

💡 Trap: The formula uses RADIUS, not diameter. Don't forget: r = d ÷ 2.
A = πr²  →  r = 14 ÷ 2 = 7
Q 15 Angles

Two angles are supplementary. One angle is three times the other. What are the two angle measures?

💡 Supplementary = adds to 180°. Equation: x + 3x = 180°
Q 16 ⚠ Tricky

A rectangle has a perimeter of 56 cm. Its length is 8 cm more than its width. What is the area of the rectangle?

💡 Two-step trap! First find the dimensions, THEN calculate area. Many students stop after finding width.
2(w + w + 8) = 56  →  find w, then A = l × w
Q 17 Volume

A rectangular box is 10 cm long, 4 cm wide, and 5 cm tall. How much water can the box hold, in cubic centimeters?

💡 Volume = length × width × height (multiply all three!)
Q 18 ⚠ Tricky

A right triangle has legs of length 5 and 12. A square is drawn on the outside of the hypotenuse. What is the area of that square?

💡 First find the hypotenuse using a² + b² = c², THEN square it for the area. Area of square = c²
5² + 12² = c²  →  Area of square = c²
Q 19 Composite Shapes

An L-shaped floor is made of two rectangles: one is 6 m × 4 m and the other is 3 m × 2 m. What is the total area of the floor?

💡 Composite shape = add the areas of both parts separately, then combine.
Q 20 ⚠ Tricky

A circle is inscribed inside a square with side length 10 cm. What is the area of the region inside the square but outside the circle? (π ≈ 3.14)

💡 The diameter of the circle = side of the square = 10, so r = 5. Answer = Area(square) − Area(circle).
Region = 10² − π × 5² = 100 − 78.5
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