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Pre-Algebra
10 Problems
01
🧠ISOLATE→ move numbers, keep variable alone
One-Step Equations
Solve for x:
x + 14 = 31
⚡ Tricky Part: Students often add 14 instead of subtracting. Remember: do the opposite operation to both sides.
A x = 45
B x = 17
C x = 21
D x = 14
✅ Correct Answer: B (x = 17)
Subtract 14 from both sides: x + 14 − 14 = 31 − 14 → x = 17. Check: 17 + 14 = 31 ✓ | Common trap: adding 14 gives 45 (wrong — do the opposite!).
02
🧠DIVIDE BOTH→ 3x = 24 means x = 24 ÷ 3
One-Step Equations
Solve for n:
7n = 63
⚡ Tricky Part: Some students multiply by 7 instead of dividing. The coefficient next to the variable means multiplication — undo it by dividing.
A n = 56
B n = 441
C n = 9
D n = 7
✅ Correct Answer: C (n = 9)
Divide both sides by 7: 7n ÷ 7 = 63 ÷ 7 → n = 9. Check: 7 × 9 = 63 ✓ | Trap A: 63 − 7 = 56 (subtracted instead of divided).
03
🧠TWO-STEP→ undo + or − first, then × or ÷
Two-Step Equations
Solve for x:
2x − 5 = 11
⚡ Tricky Part: Many students divide by 2 first. Always add/subtract the constant before you divide!
A x = 3
B x = 8
C x = 6
D x = 11
✅ Correct Answer: B (x = 8)
Step 1: Add 5 to both sides → 2x = 16.
Step 2: Divide by 2 → x = 8. Check: 2(8) − 5 = 16 − 5 = 11 ✓
04
🧠RATIO = FRACTION→ 3:4 means 3/4
Ratios & Proportions
A bag has red and blue marbles in the ratio 3 : 5. If there are 24 red marbles, how many blue marbles are there?
⚡ Tricky Part: Don't add 3+5=8 and multiply. Set up a proportion: 3/5 = 24/?
A 32
B 15
C 40
D 8
✅ Correct Answer: C (40)
Set up: 3/5 = 24/b → cross-multiply: 3b = 120 → b = 40.
Alternatively: 24 ÷ 3 = 8 (unit value), then 8 × 5 = 40 ✓
05
🧠PERCENT→ IS / OF × 100
Percents
A jacket originally costs $80. It is on sale for 35% off. What is the sale price?
⚡ Tricky Part: Many students find 35% = $28 and stop. That's the discount, not the price! Subtract from original.
A $28
B $52
C $45
D $108
✅ Correct Answer: B ($52)
Discount: 80 × 0.35 = $28.
Sale price: $80 − $28 = $52.
Shortcut: 80 × (1 − 0.35) = 80 × 0.65 = $52 ✓
Trap A: stopped at the discount amount.
06
🧠DISTRIBUTE→ a(b+c) = ab + ac
Distributive Property
Simplify:
3(2x + 4) − 5
⚡ Tricky Part: Students forget to multiply 3 × 4 (only multiply 3 × 2x). Every term inside the parentheses must be multiplied!
A 6x + 7
B 6x + 4
C 6x + 17
D 5x + 7
✅ Correct Answer: A (6x + 7) 3(2x) + 3(4) − 5 = 6x + 12 − 5 = 6x + 7
Trap B: forgot 3 × 4 → left 12 as 4. Trap C: added instead of subtracted 5.
07
🧠INEQUALITY FLIP→ multiply/divide by negative → flip ≤ or ≥
Inequalities
Solve and choose the correct solution:
−3x + 6 ≤ 18
⚡ Tricky Part: When you divide both sides by −3, the inequality sign FLIPS. This is the #1 mistake!
A x ≤ −4
B x ≤ 4
C x ≥ 8
D x ≥ −4
✅ Correct Answer: D (x ≥ −4)
Step 1: Subtract 6: −3x ≤ 12.
Step 2: Divide by −3 → flip the sign: x ≥ −4.
Trap B: divided correctly but forgot to flip the sign.
08
🧠RATE × TIME = DISTANCE→ d = rt
Word Problem · Rate
Maria drives at 60 mph for 2.5 hours. Then she drives at 40 mph for 1 hour. What is her total distance?
⚡ Tricky Part: Students add the speeds (60 + 40 = 100). Calculate each leg separately: d = r × t for each part.
A 100 miles
B 175 miles
C 190 miles
D 150 miles
✅ Correct Answer: C (190 miles)
Leg 1: 60 × 2.5 = 150 miles.
Leg 2: 40 × 1 = 40 miles.
Total: 150 + 40 = 190 miles ✓
09
🧠LIKE TERMS→ same variable + same exponent = can combine
Combining Like Terms
Simplify:
5x² + 3x − 2x² + 7 − x
⚡ Tricky Part: Students combine x² with x (they're NOT like terms!). Only combine same powers.
A 3x² + 2x + 7
B 3x² + 2x + 7
C 7x² + 4x + 7
D 3x + 7
✅ Correct Answer: B (3x² + 2x + 7)
x² terms: 5x² − 2x² = 3x².
x terms: 3x − x = 2x.
Constants: 7.
Result: 3x² + 2x + 7 ✓
Trap D: combined all terms as if they were like terms.
10
🧠CROSS MULTIPLY→ a/b = c/d → ad = bc
Proportions
A recipe needs 2 cups of flour for every 3 cookies. How many cups of flour are needed for 24 cookies?
⚡ Tricky Part: Students multiply 2 × 24 = 48. Remember it's a ratio — 2 cups per 3 cookies, not 1.
A 8 cups
B 36 cups
C 16 cups
D 12 cups
✅ Correct Answer: C (16 cups)
Set up: 2/3 = f/24 → 3f = 48 → f = 16.
Check: 16/24 = 2/3 ✓
Trap A: 24 ÷ 3 = 8 (forgot to multiply by 2).
Geometry
10 Problems
11
🧠PYTHAGOREAN→ a² + b² = c² (c = longest side)
Pythagorean Theorem
Find the missing hypotenuse:
legs: a = 9, b = 12 → c = ?
⚡ Tricky Part: Students add legs first: 9 + 12 = 21. You must square each leg, add, then take the square root.
A 21
B 15
C √225 ≈ 14.1
D 3
✅ Correct Answer: B (15) c² = 9² + 12² = 81 + 144 = 225 c = √225 = 15 ✓ (This is the 3-4-5 triple × 3)
Trap A: added legs without squaring.
12
🧠AREA CIRCLE→ A = πr² (r = radius, NOT diameter)
Circles · Area
A circle has a diameter of 10 cm. What is its area? (Use π ≈ 3.14)
⚡ Tricky Part: The problem gives diameter. You MUST halve it: radius = 5. Using r = 10 gives 4× the correct answer!
A 314 cm²
B 31.4 cm²
C 78.5 cm²
D 62.8 cm²
✅ Correct Answer: C (78.5 cm²)
Radius: r = 10 ÷ 2 = 5 cm.
Area: A = π × 5² = 3.14 × 25 = 78.5 cm² ✓
Trap A: used diameter (10) as radius → 314 cm².
13
🧠TRIANGLE ANGLES→ always add up to 180°
Angles in a Triangle
A triangle has angles of 47° and 83°. What is the third angle?
⚡ Tricky Part: Some subtract only one angle. Sum of ALL THREE angles = 180°, so subtract BOTH given angles.
A 97°
B 133°
C 60°
D 50°
✅ Correct Answer: D (50°) 180° − 47° − 83° = 50° ✓
Trap A: only subtracted 83° from 180°. Trap B: only subtracted 47°.
14
🧠VOLUME BOX→ V = l × w × h
Volume · Rectangular Prism
A rectangular box is 8 cm long, 5 cm wide, and 3 cm tall. What is its volume?
⚡ Tricky Part: Students find the surface area instead (adding all faces). Volume = multiply ALL THREE dimensions.
A 120 cm³
B 158 cm²
C 79 cm³
D 16 cm³
✅ Correct Answer: A (120 cm³) V = 8 × 5 × 3 = 120 cm³ ✓
Note: volume uses cm³, NOT cm². Trap B is the surface area, not volume.
15
🧠COMPLEMENTARY→ add to 90° | SUPPLEMENTARY → add to 180°
Angle Relationships
Two angles are supplementary. One angle is 112°. What is the other angle?
⚡ Tricky Part: Students confuse supplementary (180°) with complementary (90°). "S"upplementary = "S"traight line = 180°.
A 22°
B 68°
C 248°
D 112°
✅ Correct Answer: B (68°)
Supplementary = sum is 180°. 180° − 112° = 68° ✓
Trap A: used 90° (complementary formula instead).
16
🧠PERIMETER→ add ALL sides (don't multiply like area!)
Perimeter
A rectangle has a length of 14 m and width of 6 m. What is the perimeter?
⚡ Tricky Part: Students only add one length and one width (14 + 6 = 20). A rectangle has TWO of each side!
A 84 m
B 20 m
C 40 m
D 48 m
✅ Correct Answer: C (40 m) P = 2(l + w) = 2(14 + 6) = 2 × 20 = 40 m ✓
Trap B: forgot to double → only added one of each side.
17
🧠AREA TRIANGLE→ A = ½ × base × height
Area · Triangle
A triangle has a base of 10 cm and a height of 7 cm. What is the area?
⚡ Tricky Part: Students forget the ½. A triangle is exactly HALF of a rectangle with the same base and height.
A 70 cm²
B 35 cm²
C 17 cm²
D 34 cm²
✅ Correct Answer: B (35 cm²) A = ½ × 10 × 7 = ½ × 70 = 35 cm² ✓
Trap A: forgot the ½ → got 70 cm².
18
🧠CIRCUMFERENCE→ C = πd = 2πr
Circles · Circumference
A circle has a radius of 7 cm. What is the circumference? (Use π ≈ 3.14)
⚡ Tricky Part: C = πd or C = 2πr. If given radius, double it first (d = 2r = 14). Don't skip the ×2 step!
A 21.98 cm
B 153.86 cm
C 43.96 cm
D 49 cm
✅ Correct Answer: C (43.96 cm) C = 2πr = 2 × 3.14 × 7 = 43.96 cm ✓
Trap A: used C = π × r (forgot ×2). Trap B: calculated area instead of circumference.
Two parallel lines are cut by a transversal. One angle is 65°. What is the measure of its co-interior (same-side interior) angle?
⚡ Tricky Part: Alternate interior angles are EQUAL, but co-interior (same-side) angles add to 180°. Don't mix them up!
A 65°
B 115°
C 25°
D 295°
✅ Correct Answer: B (115°)
Co-interior angles are supplementary → sum = 180°. 180° − 65° = 115° ✓
Trap A: 65° is the alternate interior angle (equal), not co-interior.
20
🧠SIMILAR TRIANGLES→ corresponding sides are PROPORTIONAL
Similar Triangles
Triangle ABC is similar to triangle DEF. Side AB = 6, BC = 9, and DE = 10. What is the length of EF?
⚡ Tricky Part: Students add the difference (10 − 6 = 4, then add to 9). Instead, find the scale factor and multiply.
A 13
B 6
C 5.4
D 15
✅ Correct Answer: D (15)
Scale factor: DE/AB = 10/6 = 5/3. EF = BC × (5/3) = 9 × 5/3 = 15 ✓
Trap A: added scale difference (9 + 4 = 13). Trap C: divided instead of multiplied.