A = (−5)×(−3) = +15 | B = (−2)×(−8) = +16 | C = −15 | D = −15. B is the greatest. Both A and B are positive (negative × negative), but 16 > 15. Don't be tricked by larger-looking negative numbers!
Keep \(\frac{3}{4}\), Change ÷ to ×, Flip \(\frac{2}{5}\) to \(\frac{5}{2}\):
\(\frac{3}{4} \times \frac{5}{2} = \frac{15}{8}\) ✓
Choice A is what you get if you just multiply without flipping. Choice C is the flipped result (wrong direction).
Q 04Pre-AlgebraPercent⚡ Tricky
🧠Memory Key:PERCENT = "per hundred" · Percent of a number: multiply by decimal (÷100)
A jacket costs $80. It is on sale for 35% off. What is the sale price?
Common mistake: students calculate 35% correctly but then forget to subtract it from the original price.
35% of $80 = 0.35 × 80 = $28 (this is the discount amount — that's choice B, a trap!)
Sale price = $80 − $28 = $52. Choice D ($108) is what you'd get if you added instead of subtracted.
Q 05Pre-AlgebraSolving Equations★ Core
🧠Memory Key:UNDO in reverse order — what was done last, undo first (inverse operations)
Solve for \(x\): \( 2x + 7 = 19 \)
Balance both sides equally — whatever you do to one side, do to the other.
\(2x + 7 = 19\) → subtract 7 from both sides → \(2x = 12\) → divide both sides by 2 → \(x = 6\)
Check: \(2(6)+7 = 12+7 = 19\) ✓
Choice B (13) is the mistake of doing \(19-7=12\) then adding instead of dividing.
Q 06Pre-AlgebraRatio & Proportion⚡ Tricky
🧠Memory Key:CROSS-MULTIPLY to solve proportions: \(\frac{a}{b}=\frac{c}{d}\) → \(ad = bc\)
A car travels 150 miles in 3 hours. At the same speed, how many miles will it travel in 5 hours?
Set up a proportion and cross-multiply. Make sure your units match!
Solution is \(x < -3\).
Check each: A: −3 is NOT less than −3. B: 0 > −3, not a solution. C: −5 < −3 ✓ D: 2 > −3, not a solution. Answer: C. Don't forget to flip the sign when dividing by a negative number!
Q 08Pre-AlgebraExponents★ Core
🧠Memory Key:ZERO POWER = 1 (anything!), NEGATIVE EXPONENT = flip to denominator
Which expression is equal to \(1\)?
Exponent rules are frequently misapplied. Trust the rules, not your instincts!
A: \((-7)^0 = 1\) ✓ (any nonzero base to the power 0 = 1)
B: \(7^{-1} = \frac{1}{7}\) (not 1)
C: \(0^7 = 0\) (zero stays zero)
D: \((-1)^7 = -1\) (negative base, odd exponent = negative) Answer: A
Q 09Pre-AlgebraWord Problems⚡ Tricky
🧠Memory Key:DEFINE A VARIABLE first — let \(x\) = what you're looking for, then write the equation
Emma has twice as many stickers as Liam. Together they have 48 stickers. How many stickers does Emma have?
Translate words into algebra. "Twice as many" means multiply by 2, not add 2!
Setup
Let Liam = \(x\). Then Emma = \(2x\). Together: \(x + 2x = 48\) → \(3x = 48\) → \(x = 16\). Emma = \(2x\) = ?
📘 Explanation
Liam = 16, Emma = 2 × 16 = 32. Check: 16 + 32 = 48 ✓
Choice C (16) is Liam's count — students often stop there and forget the question asked for Emma's stickers!
Q 10Pre-AlgebraNumber Patterns★ Core
🧠Memory Key:FIND THE RULE: check differences (arithmetic) or ratios (geometric) between terms
Is this +4 each time, or ×3 each time? Always check if it's addition or multiplication!
Arithmetic vs. Geometric
Arithmetic: add a constant \(2, 5, 8, 11, ...\) (+3 each time)
Geometric: multiply by a constant \(2, 6, 18, 54, ...\) (×3 each time)
📘 Explanation
Each term is multiplied by 3: \(2 \times 3 = 6\), \(6 \times 3 = 18\), \(18 \times 3 = 54\), \(54 \times 3 = \mathbf{162}\) ✓
Choice A (108) is the mistake of doubling (×2) instead of tripling. Choice B (58) is just adding the difference of the last two terms.
Geometry
Angles, triangles, area, perimeter, the Pythagorean Theorem, and circles — visualize first, calculate second.
Q 11GeometryAngles★ Core
🧠Memory Key:STRAIGHT LINE = 180° · FULL TURN = 360° · Supplementary = sum 180°, Complementary = sum 90°
Two angles are supplementary. One angle measures \(47°\). What is the other angle?
Supplementary ≠ Complementary! Mixing these up is extremely common.
Key Pairs
Supplementary: \(A + B = 180°\) | Complementary: \(A + B = 90°\)
Trick: Supplementary → Straight line (180°) · Complementary → Corner (90°)
📘 Explanation
Supplementary means the two angles add to 180°.
Other angle = 180° − 47° = 133°.
Choice A (43°) = 90° − 47° → that's complementary, not supplementary!
Q 12GeometryTriangles⚡ Tricky
🧠Memory Key:TRIANGLE ANGLE SUM = 180° always, without exception
A triangle has angles measuring \(x\), \(2x\), and \(x + 20°\). Find the value of \(x\).
Set up an equation using the triangle angle sum. Don't forget to combine like terms first!
\(x + 2x + x + 20 = 180\) → \(4x + 20 = 180\) → \(4x = 160\) → \(x = 40°\) ✓
Check: 40 + 80 + 60 = 180° ✓
Choice C (60°) is a common answer when students forget to add the +20° from the third angle.
Q 13GeometryPythagorean Theorem⚡ Tricky
🧠Memory Key:a² + b² = c² where c is always the HYPOTENUSE (longest side, opposite right angle)
A right triangle has legs of length 9 and 12. What is the length of the hypotenuse?
The hypotenuse is ALWAYS the side opposite the right angle — the longest side. Never use legs on both sides of c².
\(9^2 + 12^2 = 81 + 144 = 225\) → \(c = \sqrt{225} = \mathbf{15}\)
This is a 3-4-5 triple scaled by 3: (9, 12, 15) = 3×(3, 4, 5).
Choice B (21) = 9 + 12, a common mistake of just adding the legs.
Q 14GeometryArea★ Core
🧠Memory Key:Triangle Area = ½ × base × height · The HEIGHT must be PERPENDICULAR to the base
A triangle has a base of 14 cm and a height of 9 cm. What is its area?
The most common mistake: forgetting the ½. Triangles are half of rectangles!
Visual Reminder
Rectangle area = base × height → Triangle = ½ of that rectangle
\(A = \dfrac{1}{2} \times b \times h\) The height ⊥ base (perpendicular, not the slant side!)
📘 Explanation
\(A = \frac{1}{2} \times 14 \times 9 = \frac{1}{2} \times 126 = \mathbf{63 \text{ cm}^2}\)
Choice A (126 cm²) is the rectangle area — students who forget the ½ get this.
Choice C (46) = 14 + 9 + 23 → perimeter thinking, not area.
Q 15GeometryCircles⚡ Tricky
🧠Memory Key:Circumference = π × d | Area = π × r² | radius = diameter ÷ 2
A circle has a diameter of 10 cm. What is its area? (Use \(\pi \approx 3.14\))
Watch out! The formula uses RADIUS, but the problem gives you DIAMETER. Always halve it first.
Radius = 10 ÷ 2 = 5 cm. \(A = \pi r^2 = 3.14 \times 25 = \mathbf{78.5 \text{ cm}^2}\)
Choice A (314) = students who used diameter (10) instead of radius: \(3.14 \times 10^2 = 314\) — very common mistake!
Choice B (31.4) = circumference, not area.
Q 16GeometryPerimeter★ Core
🧠Memory Key:PERIMETER = total distance AROUND the shape · add ALL sides · rectangle: P = 2(l + w)
A rectangle has a perimeter of 54 cm. Its length is 16 cm. What is its width?
Don't confuse perimeter (all around) with area (inside). Set up the formula and solve for the missing side.
\(54 = 2(16 + w)\) → \(27 = 16 + w\) → \(w = 11\) cm ✓
Check: \(2(16+11) = 2 \times 27 = 54\) ✓
Choice B (22) = students who found 27 but forgot that 27 = l + w (not just w), so subtracted incorrectly.
Q 17GeometryParallel Lines⚡ Tricky
🧠Memory Key:ALTERNATE INTERIOR ANGLES are EQUAL · CO-INTERIOR (same-side) angles are SUPPLEMENTARY (180°)
Two parallel lines are cut by a transversal. One alternate interior angle measures \(65°\). What is the co-interior angle on the same side of the transversal?
Students mix up which angle pairs are equal and which add up to 180°. Learn the names carefully!
Co-interior angles are supplementary: they add to 180°.
Co-interior angle = 180° − 65° = 115° ✓
Choice A (65°) confuses co-interior with alternate interior (which would be equal).
Choice B (25°) = 90° − 65°, treating them as complementary — completely wrong rule here.
Q 18GeometryVolume⚡ Tricky
🧠Memory Key:PRISM volume = base area × height · PYRAMID/CONE = ⅓ × base area × height
A rectangular box (prism) has length 8 cm, width 5 cm, and height 4 cm. What is its volume?
Volume is 3-dimensional — multiply length × width × height. Don't confuse with surface area!
Volume vs. Surface Area
Volume \(= l \times w \times h\) (cubic units, e.g. cm³)
Surface Area = 2(lw + lh + wh) (square units — the outside wrapping)
These are different — know which one the question is asking!
📘 Explanation
\(V = 8 \times 5 \times 4 = \mathbf{160 \text{ cm}^3}\)
Choice A (184 cm²) = surface area: \(2(8×5 + 8×4 + 5×4) = 2(40+32+20) = 184\) — different formula, different concept!
Choice D (17) = just adding all three dimensions.
Q 19GeometryCoordinate Geometry⚡ Tricky
🧠Memory Key:SLOPE = rise ÷ run = \(\dfrac{y_2 - y_1}{x_2 - x_1}\) · always subtract in the SAME order
What is the slope of the line passing through \((2, 3)\) and \((6, 11)\)?
The most common mistake: mixing up x and y, or reversing the subtraction order for one coordinate.
Formula
\(m = \dfrac{y_2 - y_1}{x_2 - x_1} = \dfrac{11 - 3}{6 - 2}\) ← subtract y's on top, x's on bottom, SAME order
📘 Explanation
\(m = \frac{11-3}{6-2} = \frac{8}{4} = \mathbf{2}\)
Choice B (½) = flipping the formula: \(\frac{4}{8} = \frac{1}{2}\) — putting x-difference on top, y on bottom.
Choice C (4) = just taking the x-difference as the slope.
Q 20GeometrySimilar Figures⚡ Tricky
🧠Memory Key:SIMILAR FIGURES: sides are proportional · SCALE FACTOR applies to sides (area scale = factor²)
Two similar triangles have corresponding sides in a ratio of 3:5. If the area of the smaller triangle is 27 cm², what is the area of the larger triangle?
This is the hardest question on the sheet. Area does NOT scale the same way as sides — it squares the ratio!
Scale Factor Rule
Side ratio = \(3:5\) → Scale factor = \(\dfrac{3}{5}\)
Area ratio = (scale factor)² = \(\left(\dfrac{3}{5}\right)^2 = \dfrac{9}{25}\)
So: \(\dfrac{27}{A_{\text{large}}} = \dfrac{9}{25}\)
📘 Explanation
Area ratio = \(\left(\frac{3}{5}\right)^2 = \frac{9}{25}\)
\(\frac{27}{A} = \frac{9}{25}\) → \(9A = 27 \times 25 = 675\) → \(A = 75 \text{ cm}^2\) ✓
Choice A (45) = multiplying 27 × (5/3) — using the side ratio, not the area ratio. Very common trap!
Choice B (135) = multiplying 27 × 5 = 135, forgetting to use the ratio properly.