Number Sense & Equations
Q1–10If x + 7 = 3, what is the value of x?
Memory Point
ISOLATE — move everything away from the variable. Do the opposite operation to both sides.
x + 7 − 7 = 3 − 7 → x = −4
Many students write +4 because they add instead of subtract. Remember: INVERSE operation.
Simplify: 3(x + 4) − 2x
Memory Point
DISTRIBUTE first, then COMBINE like terms. Order: D → C.
3(x+4) − 2x = 3x + 12 − 2x = x + 12
Trap: students forget to distribute 3 to both x AND 4, or they forget to subtract 2x properly. Answer: B.
What is the value of −3²? (Note: the negative sign is outside)
Memory Point
PARENTHESES matter: (−3)² = +9 but −3² = −9. Exponent applies only to 3, not the minus.
−(3²) = −(9) = −9
If it were (−3)², the answer would be +9. This is one of the most commonly missed questions. Answer: B.
Evaluate: 2 + 3 × 4 − 1
Memory Point
PEMDAS — Parentheses, Exponents, Multiply/Divide (left→right), Add/Subtract (left→right). Multiply BEFORE you add!
2 + (3 × 4) − 1 = 2 + 12 − 1 = 13
Many students compute left-to-right: (2+3)×4−1 = 19. That's wrong! Multiplication first. Answer: B.
A car travels 120 miles in 2 hours. At the same rate, how many miles will it travel in 5 hours?
Memory Point
UNIT RATE first: miles ÷ hours = miles per hour. Then multiply by new time.
Rate = 120 ÷ 2 = 60 mph → 60 × 5 = 300 miles
Answer: C.
Solve: −2x < 8. What is the correct answer?
Memory Point
FLIP the sign when multiplying or dividing by a negative number. This is the #1 inequality mistake.
−2x < 8 → divide by −2 → FLIP sign → x > −4
Students commonly forget to flip the inequality sign when dividing by negative. Answer: C.
What is ¾ + ⅔?
Memory Point
LCD — Least Common Denominator. Find a common bottom, then add tops. Never add denominators!
3/4 = 9/12 and 2/3 = 8/12
9/12 + 8/12 = 17/12
Answer: C. Trap B is adding 3+2=5 and 4+3=7. Never do that!
A shirt costs $40. It is on sale for 25% off. What is the sale price?
Memory Point
PERCENT → DECIMAL: divide by 100. Then: Sale price = Original × (1 − rate). Or find discount first, then subtract.
Discount = $40 × 0.25 = $10 → Sale price = $40 − $10 = $30
Trap A: students give the discount amount, not the final price. Answer: C.
Evaluate: (−4) × (−3) + (−5)
Memory Point
SIGN RULES: (−) × (−) = (+). Same signs → positive. Different signs → negative.
(−4) × (−3) = +12 (negative × negative = positive)
12 + (−5) = 12 − 5 = 7
Answer: B.
Solve for x: 2x − 5 = 11
Memory Point
TWO-STEP rule: ① Undo addition/subtraction first. ② Then undo multiplication/division. Work outside-in.
Step 1: 2x − 5 + 5 = 11 + 5 → 2x = 16
Step 2: 2x ÷ 2 = 16 ÷ 2 → x = 8
Answer: B.
Shapes, Angles & Space
Q11–20Two angles of a triangle are 55° and 70°. What is the third angle?
Memory Point
TRIANGLE SUM = 180°. Always. Add the two known angles, subtract from 180. Done.
180° − 55° − 70° = 55°
Answer: B. The triangle would actually be isosceles since two angles are equal!
A rectangle has length 9 cm and width 4 cm. What is its area?
Memory Point
AREA = multiply (×). PERIMETER = add all sides. Area = l × w. Perimeter = 2(l + w).
Area = 9 × 4 = 36 cm²
Trap A: 26 cm is the perimeter (2×9 + 2×4). Trap C: same number but wrong units — area needs cm². Answer: B.
A right triangle has legs of 3 and 4. What is the length of the hypotenuse?
Memory Point
a² + b² = c² — c is always the hypotenuse (longest side, opposite right angle). Memorize 3-4-5 triangle!
3² + 4² = c² → 9 + 16 = 25 → c = √25 = 5
Trap D: 25 is c², not c. Don't forget to take the square root! Answer: A.
A circle has a radius of 6 cm. What is its circumference? (Use π ≈ 3.14)
Memory Point
C = 2πr (circumference). A = πr² (area). Confusing these is the #1 circle error.
C = 2 × π × r = 2 × 3.14 × 6 = 37.68 cm
Trap A: that's the area (πr² = 3.14 × 36 = 113.04). Trap B: used diameter (12) instead of 2r... wait, 2×3.14×3 = 18.84 — that's r=3. Answer: C.
Angles A and B are supplementary. Angle A = 112°. What is angle B?
Memory Point
SUPPLEMENTARY = 180° (straight line). COMPLEMENTARY = 90° (right angle). S comes before C, 180 > 90.
B = 180° − 112° = 68°
Trap A: 90°−68° = 22° — that's complementary math applied to supplementary. Answer: B.
A triangle has a base of 10 cm and a height of 6 cm. What is its area?
Memory Point
A = ½ × b × h — triangle is half a rectangle. Always divide by 2! Students forget the ½.
A = ½ × 10 × 6 = ½ × 60 = 30 cm²
Trap A: forgot the ½. Answer: B.
A rectangular box (cuboid) has length 5, width 3, and height 4. What is its volume?
Memory Point
V = l × w × h for rectangular prism. Think: "how many unit cubes fit inside?" Multiply all 3 dimensions.
V = 5 × 3 × 4 = 60 units³
Trap B: correct number but wrong unit (units² is area, volume needs units³). Answer: C.
Two parallel lines are cut by a transversal. One angle is 65°. What is its alternate interior angle?
Memory Point
Z-shape = ALTERNATE INTERIOR = EQUAL. F-shape = CORRESPONDING = EQUAL. Co-interior (C-shape) = 180°.
Alternate interior angle = 65°
The "Z" pattern: imagine the letter Z between two parallel lines. The angles at each end of the Z are equal. Answer: C.
A circle has a diameter of 14 cm. What is the area? (Use π ≈ 3.14)
Memory Point
r = d ÷ 2. Always halve the diameter before plugging into A = πr². Using d instead of r is the top circle mistake.
r = 14 ÷ 2 = 7 cm
A = π × 7² = 3.14 × 49 = 153.86 cm²
Trap A: used d=14 instead of r=7: 3.14 × 196 = 615.44. Answer: B.
What is the sum of interior angles of a hexagon (6-sided polygon)?
Memory Point
Sum = (n − 2) × 180°. Where n = number of sides. Triangle: (3−2)×180 = 180°. Square: (4−2)×180 = 360°.
n = 6 → (6 − 2) × 180° = 4 × 180° = 720°
Trap A: (5−2)×180 = 540° — that's a pentagon. Answer: B.