20 carefully selected questions — the ones students miss most. Pick your answer, then learn why.
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Algebra 1
Equations & Expressions
Q·01Easy
ISOLATE → OPPOSITE OPERATION
Solve for \(x\): \(3x - 7 = 14\)
Quick Example
To solve \(2x + 5 = 11\): subtract 5 from both sides → \(2x = 6\), then divide by 2 → \(x = 3\). Trap: Students forget to apply the operation to both sides.
✓ CORRECT
Add 7 to both sides: \(3x = 21\). Divide by 3: \(x = 7\). Always undo addition/subtraction first, then multiplication/division.
Q·02Medium
DISTRIBUTE FIRST → COMBINE LIKE TERMS
Simplify: \(2(3x + 4) - 5x + 1\)
Quick Example
\(3(x+2) - 4x = 3x + 6 - 4x = -x + 6\) Trap: Forgetting to multiply every term inside the parentheses when distributing.
✓ CORRECT
Distribute: \(6x + 8 - 5x + 1\). Combine like terms: \((6x-5x) + (8+1) = x + 9\).
Q·03Hard
VARIABLES BOTH SIDES → MOVE ALL x TO ONE SIDE
Solve: \(5x - 3 = 2x + 12\)
Quick Example
\(4x + 1 = x + 10\) → subtract \(x\): \(3x + 1 = 10\) → subtract 1: \(3x = 9\) → \(x = 3\) Trap: Students subtract the wrong term or move both variables to the wrong side.
✓ CORRECT
Subtract \(2x\) from both sides: \(3x - 3 = 12\). Add 3: \(3x = 15\). Divide by 3: \(x = 5\).
Q·04Medium
SLOPE = RISE ÷ RUN = (y₂−y₁)/(x₂−x₁)
What is the slope of the line passing through \((1, 3)\) and \((4, 12)\)?
Quick Example
Points \((2, 5)\) and \((6, 13)\): slope \(= \dfrac{13-5}{6-2} = \dfrac{8}{4} = 2\) Trap: Mixing up which point is "first." Order matters — be consistent!
✓ CORRECT
\(m = \dfrac{12-3}{4-1} = \dfrac{9}{3} = 3\). The line rises 3 units for every 1 unit it runs horizontally.
Q·05Hard
INEQUALITY FLIP → MULTIPLY/DIVIDE BY NEGATIVE
Solve and graph: \(-4x + 2 \leq 18\)
Quick Example
\(-2x \leq 10\) → divide by \(-2\), flip sign → \(x \geq -5\) Trap: The #1 error in algebra — forgetting to flip the inequality when dividing by a negative!
✓ CORRECT
Subtract 2: \(-4x \leq 16\). Divide by \(-4\) — flip the sign! → \(x \geq -4\). This is the most commonly missed step.
Q·06Medium
SUBSTITUTION → REPLACE ONE VARIABLE
System of equations: \(y = 2x + 1\) and \(y = -x + 7\)
Find \(x\).
Quick Example
\(y = x + 3\) and \(y = 4x\) → Set equal: \(x + 3 = 4x\) → \(3 = 3x\) → \(x = 1\) Trap: Forgetting to find the second variable (y) after finding x.
✓ CORRECT
Set the two expressions equal: \(2x+1 = -x+7\). Add \(x\): \(3x+1=7\). Subtract 1: \(3x=6\). Divide: \(x=2\). (And \(y=5\).)
Q·07Easy
EXPONENT RULES: x^a · x^b = x^(a+b)
Simplify: \(x^3 \cdot x^5\)
Quick Example
\(a^2 \cdot a^4 = a^6\) (add exponents, same base) Trap: Students multiply the exponents instead of adding them. That rule is for \((x^3)^5\).
✓ CORRECT
\(x^3 \cdot x^5 = x^{3+5} = x^8\). When multiplying powers with the same base, ADD the exponents. \(x^{15}\) would be the answer for \((x^3)^5\).
Q·08Hard
PERCENT WORD PROBLEM → IS/OF = %/100
A shirt originally costs $40. It is on sale for 25% off. What is the sale price?
Quick Example
30% off $50: discount = \(0.30 \times 50 = \$15\) → sale price = \(50 - 15 = \$35\)
Or shortcut: \(0.70 \times 50 = \$35\) Trap: Giving the discount amount ($10) instead of the final price.
Train A travels at 60 mph. Train B travels at 90 mph in the same direction, starting 1 hour later from the same point. How many hours after Train B departs does it catch Train A?
Quick Example
Set distances equal: A's head start = 60 mi. B gains 30 mph. Time = \(\frac{60}{30} = 2\) hours. Trap: Forgetting Train A had a 1-hour head start of 60 miles.
✓ CORRECT
Let \(t\) = hours after B departs. Train A's distance: \(60(t+1)\). Train B's distance: \(90t\). Set equal: \(90t = 60t+60\) → \(30t = 60\) → \(t = 2\) hours.
Geometry
Shapes, Angles & Space
Q·11Easy
PYTHAGOREAN: a² + b² = c² (c = HYPOTENUSE)
A right triangle has legs \(a = 6\) and \(b = 8\). What is the length of the hypotenuse \(c\)?
Quick Example
Legs 3 and 4: \(3^2 + 4^2 = 9 + 16 = 25\) → \(c = \sqrt{25} = 5\) Trap: Adding the legs directly (6 + 8 = 14) instead of using squares.
✓ CORRECT
\(6^2 + 8^2 = 36 + 64 = 100\). So \(c = \sqrt{100} = 10\). The 6-8-10 triangle is a Pythagorean triple (double of 3-4-5).
Q·12Easy
AREA CIRCLE = πr² | CIRCUMFERENCE = 2πr
A circle has radius \(r = 5\). What is its area? (Use \(\pi \approx 3.14\))
Quick Example
Radius 3: Area = \(\pi \cdot 3^2 = 9\pi \approx 28.26\) Trap: Using diameter instead of radius, or forgetting to square the radius.
✓ CORRECT
\(A = \pi r^2 = 3.14 \times 5^2 = 3.14 \times 25 = 78.5\) sq units. Common mistake: using \(\pi \times 5 = 15.7\) (forgot to square).
Q·13Medium
TRIANGLE ANGLES → ALWAYS SUM TO 180°
A triangle has angles \(47°\) and \(65°\). What is the measure of the third angle?
Quick Example
Angles 50° and 70°: third = \(180 - 50 - 70 = 60°\) Trap: Students use 360° (that's for a quadrilateral, not a triangle!).
✓ CORRECT
\(47 + 65 = 112\). Third angle = \(180 - 112 = 68°\). All triangles: \(\angle A + \angle B + \angle C = 180°\).
Q·14Medium
COMPLEMENTARY = 90° | SUPPLEMENTARY = 180°
Angle \(A\) and Angle \(B\) are supplementary. If \(\angle A = 3x + 10\) and \(\angle B = x + 30\), find \(x\).
Quick Example
Supplementary: set their sum = 180°. Then solve the equation. Trap: Confusing supplementary (180°) with complementary (90°). Memory trick: Supplementary = Straight line!
Two parallel lines are cut by a transversal. One angle measures \(115°\). What is the measure of its co-interior (same-side interior) angle?
Quick Example
Co-interior angles (also called consecutive interior) always add up to 180°.
Alternate interior angles are equal. Corresponding angles are equal. Trap: Students confuse alternate interior (equal) with co-interior (supplementary).
✓ CORRECT
Co-interior (same-side interior) angles are supplementary: they add to 180°. So \(180 - 115 = 65°\). If the question asked for alternate interior, the answer would be 115°.
Q·17Hard
SIMILAR TRIANGLES → RATIOS OF SIDES ARE EQUAL
Two similar triangles have sides in a ratio of \(2:5\). The smaller triangle has a base of \(8\). What is the base of the larger triangle?
Quick Example
Ratio 1:3, smaller side = 4 → larger = \(4 \times 3 = 12\). Or set up a proportion: \(\dfrac{1}{3} = \dfrac{4}{x}\) → \(x = 12\). Trap: Adding the difference instead of using the ratio multiplier.
✓ CORRECT
Set up proportion: \(\dfrac{2}{5} = \dfrac{8}{x}\). Cross-multiply: \(2x = 40\) → \(x = 20\). The scale factor from small to large is \(\dfrac{5}{2}\), so \(8 \times \dfrac{5}{2} = 20\).
Q·18Easy
PERIMETER = SUM OF ALL SIDES
A rectangle has length \(12\) cm and width \(7\) cm. What is its perimeter?
Quick Example
Rectangle \(l=5, w=3\): \(P = 2(5+3) = 2(8) = 16\) Trap: Forgetting rectangles have 2 lengths and 2 widths — only adding them once.
✓ CORRECT
\(P = 2(l + w) = 2(12 + 7) = 2 \times 19 = 38\) cm. Option C (19) is the trap — that's just \(l+w\), not the full perimeter.
Q·19Hard
EXTERIOR ANGLE = SUM OF THE TWO NON-ADJACENT INTERIOR ANGLES
In triangle \(ABC\), \(\angle A = 40°\) and \(\angle B = 75°\). An exterior angle is drawn at vertex \(C\). What is its measure?
Quick Example
Interior angles 30° and 50° → exterior angle at third vertex = \(30 + 50 = 80°\). Trap: Students find the interior angle at C (65°) and stop. The exterior is its supplement, OR just add the remote interior angles.
✓ CORRECT
Exterior angle = sum of remote interior angles = \(40 + 75 = 115°\). Or: \(\angle C = 180 - 40 - 75 = 65°\); exterior = \(180 - 65 = 115°\). Both methods give 115°.
Q·20Hard
MIDPOINT = AVERAGE THE COORDINATES: ((x₁+x₂)/2, (y₁+y₂)/2)
Point \(M\) is the midpoint of segment \(\overline{AB}\). \(A = (2, -4)\) and \(M = (5, 1)\). Find the coordinates of \(B\).
Quick Example
\(A=(0,0)\), \(M=(3,2)\) → \(B=(6,4)\). Each coordinate of M is the average of A and B's coordinates. Trap: Students think B = M + M instead of using algebra to back-solve.