Part 1 of 2
Pre-Algebra
Variables, equations, ratios, percentages β the building blocks of algebra.
Progress
0 / 10
Quick Memory Points
INVERSE β to solve for x, do the opposite operation Β·
BALANCE β whatever you do to one side, do to the other Β·
PER = divide Β·
OF = multiply Β·
RATIO = part Γ· part Β·
RATE = amount Γ· time
Q 01
Variables & Equations
Easy
Sarah has 3 times as many stickers as Tom. Together they have 48 stickers. How many stickers does Tom have?
π‘ Setup Hint
Let Tom = x. Then Sarah = 3x. Write one equation: x + 3x = 48. Combine like terms first!
Q 02
Unit Rate
Easy
A car travels 240 miles in 4 hours. At the same rate, how far will it travel in 7 hours?
π‘ Key Word: RATE
First find the unit rate (speed per 1 hour): 240 Γ· 4 = ? mph. Then multiply by 7.
Q 03
Percentage
Tricky
A jacket originally costs $80. It is on sale for 25% off. After the discount, a 10% sales tax is added. What is the final price?
β οΈ Common Mistake Alert
Do NOT subtract 25% and add 10% together to get 15% off. You must apply each percentage step by step to the correct base amount!
Q 04
Ratio & Proportion
Easy
A recipe for 12 cookies needs 3 cups of flour. How many cups of flour are needed to make 20 cookies?
π‘ Proportion Setup
Set up: 3/12 = x/20. Cross-multiply: 12x = 60. Then divide both sides by 12.
Q 05
Negative Numbers
Tricky
The temperature at 6 AM was β8Β°C. By noon it rose by 15Β°C, then dropped 6Β°C by evening. What was the evening temperature?
π‘ Number Line Thinking
Think of a number line: start at β8, move right 15, then move left 6. You can also just calculate: β8 + 15 β 6 = ?
Q 06
Two-Step Equations
Medium
A plumber charges a $45 flat fee plus $30 per hour. If the total bill was $165, how many hours did the plumber work?
π‘ Equation Model
Write: 45 + 30h = 165. Step 1 β subtract 45 from both sides. Step 2 β divide both sides by 30. Always undo addition/subtraction FIRST!
Q 07
Percent Change
Tricky
A store raised a $50 shirt price by 20%, then later lowered the new price by 20%. Is the final price equal to, more than, or less than the original $50?
β οΈ Classic Trap!
Most students say $50. Wrong! The 20% increase and 20% decrease apply to different base numbers. Always calculate with actual numbers to avoid this trap.
Q 08
Inequalities
Medium
Jake needs at least 75 points to pass a class. He has scores of 68, 72, and 80 on three tests. What is the minimum score he needs on the 4th test to pass?
π‘ Average Formula
Average = sum Γ· count. Set up: (68 + 72 + 80 + x) Γ· 4 β₯ 75. Multiply both sides by 4, then subtract the known sum.
Q 09
Exponents
Tricky
A bacteria culture doubles every hour. If there are 50 bacteria at noon, how many will there be at 4 PM?
π‘ Exponential Growth Formula
Formula: Amount = Start Γ 2n where n = number of hours. From noon to 4 PM = 4 hours. So: 50 Γ 24 = ?
Q 10
Mixed Operations
Medium
Five friends split a dinner bill equally. Then 2 more friends joined and they re-split the same total bill. Each person now pays $8 less than before. What was the total bill?
π‘ Variable Setup
Let total = T. Original share = T Γ· 5. New share = T Γ· 7. The difference equals $8: T/5 β T/7 = 8. Find common denominator!
Part 2 of 2
Geometry
Angles, area, perimeter, volume β shapes and space made simple.
Progress
0 / 10
Formula Cheat Sheet
TRIANGLE Area = Β½ Γ base Γ height Β·
CIRCLE Area = ΟrΒ², Circumference = 2Οr Β·
RECTANGLE Area = l Γ w Β·
VOLUME BOX = l Γ w Γ h Β·
PYTHAGOREAN aΒ² + bΒ² = cΒ² Β·
SUPPLEMENTARY = 180Β° Β·
COMPLEMENTARY = 90Β°
G 01
Area of Triangle
Easy
A triangular garden has a base of 14 meters and a height of 9 meters. What is the area of the garden?
π‘ Remember the Β½!
Area = Β½ Γ b Γ h. Students often forget the Β½! A triangle is exactly half of a rectangle with the same base and height.
G 02
Pythagorean Theorem
Medium
A ladder leans against a wall. The base of the ladder is 6 ft from the wall and the wall is 8 ft tall. How long is the ladder?
π‘ Pythagorean Theorem
aΒ² + bΒ² = cΒ² β the hypotenuse is always c (the longest side, opposite the right angle). Here: 6Β² + 8Β² = cΒ²
G 03
Circle β Circumference
Easy
A circular pond has a diameter of 20 meters. A path runs all the way around the outside of the pond. Approximately how long is the path? (Use Ο β 3.14)
β οΈ Diameter vs Radius
C = 2Οr or C = Οd. The problem gives you the diameter. If you use C = 2Οr, remember r = d Γ· 2 = 10. If you use C = Οd, use 20 directly.
G 04
Supplementary Angles
Easy
Two angles are supplementary. One angle is 3 times the other. What are the two angles?
π‘ SUPPLEMENTARY = 180Β°
Supplementary angles ADD UP to 180Β°. Let smaller = x, larger = 3x. Equation: x + 3x = 180. Solve for x, then find 3x.
G 05
Volume of Rectangular Prism
Medium
A fish tank is 60 cm long, 30 cm wide, and 40 cm tall. It is filled ΒΎ full with water. How many cubic centimeters of water are in the tank?
β οΈ Two-Step Warning
Step 1: Find the full volume (l Γ w Γ h). Step 2: Multiply by ΒΎ for the actual water amount. Many students forget Step 2!
G 06
Perimeter of Composite Shape
Tricky
An L-shaped room is made by removing a 3m Γ 4m rectangle from the corner of a 10m Γ 8m rectangle. What is the perimeter of the L-shape?
β οΈ Perimeter β Remove the corner sides
When you cut a corner, the perimeter stays the same because the 2 removed sides are replaced by 2 new sides of equal total length. Count ALL outer edges carefully!
G 07
Circle β Area
Medium
A pizza has a radius of 7 inches. You eat 3 slices out of 8 equal slices. What area of pizza did you eat? (Use Ο β 3.14)
π‘ Area of a Sector
Find the full circle area first: A = ΟrΒ². Then multiply by the fraction you ate: 3/8.
G 08
Scale / Similar Figures
Tricky
Two similar triangles have corresponding sides in a ratio of 1 : 3. If the area of the smaller triangle is 8 cmΒ², what is the area of the larger triangle?
β οΈ The Area Trap!
If the side ratio is 1:3, students often multiply the area by 3. But area scales by the square of the side ratio! Side ratio 1:3 β Area ratio 1Β²:3Β² = 1:9.
G 09
Angles in a Triangle
Easy
In a triangle, one angle is 90Β° and another is twice the size of the third angle. What are the two unknown angles?
π‘ Triangle Angle Sum
All angles in a triangle ALWAYS add to 180Β°. Known angle: 90Β°. Remaining: 180 β 90 = 90Β° to share between x and 2x.
G 10
Surface Area of a Box
Medium
You want to wrap a gift box that is 20 cm long, 15 cm wide, and 10 cm tall. How much wrapping paper (in cmΒ²) do you need to cover the entire outside surface?
π‘ Surface Area Formula
SA = 2(lw + lh + wh). There are 3 pairs of opposite faces. Calculate each pair's area, add them, then multiply by 2!