Pre-Algebra
10 Problems
Q01
Order of Operations · PEMDAS
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Quick Recall
PEMDAS: Parentheses → Exponents → Multiply/Divide → Add/Subtract
Evaluate:
3 + 4 × 2² − (6 ÷ 3)
Q02
Integer Operations · Negative Numbers
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Quick Recall
Subtracting a negative = ADDING a positive: a − (−b) = a + b
Simplify:
−8 + 3 − (−5) + (−2)
Q03
One-Step Equations · Word Problems
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Quick Recall
ISOLATE x: apply the inverse operation to BOTH sides equally
A bag of apples costs $x. After buying 3 bags, you spent $19.50. Which equation is correct, and what is x?
Q04
Fractions · Division (Keep-Change-Flip)
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Quick Recall
Dividing fractions: KEEP the first · CHANGE ÷ to × · FLIP the second
Simplify completely:
(3/4) ÷ (9/16)
Q05
Ratios & Proportions · Cross-Multiply
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Quick Recall
CROSS-MULTIPLY: a/b = c/d means a × d = b × c
A recipe uses 2 cups of flour for every 3 cups of milk. How many cups of milk are needed for 5 cups of flour?
Q06
Percents · Percent Discount
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Quick Recall
35% OFF → Sale price = original × 0.65 (not × 0.35 — that's just the discount!)
A jacket originally costs $120. It is on sale for 35% off. What is the sale price?
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Quick Recall
UNDO in REVERSE order: undo + or − first, THEN undo × or ÷
Solve for n:
4n − 7 = 21
Q08
Exponent Rules · Product & Quotient
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Quick Recall
Same base: MULTIPLY → ADD exponents · DIVIDE → SUBTRACT exponents
Simplify (x ≠ 0):
x⁵ × x³ ÷ x⁴
Q09
Inequalities · Flip the Sign Rule
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Quick Recall
FLIP the inequality sign when you MULTIPLY or DIVIDE by a NEGATIVE number!
Solve:
−3x + 2 ≤ 14
Q10
Distributive Property · Combining Like Terms
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Quick Recall
DISTRIBUTE first → then COLLECT like terms (same variable + same power)
Simplify:
3(2x − 4) + 5x − 6
Geometry
10 Problems
Q11
Triangle Angle Sum Theorem
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Quick Recall
TRIANGLE SUM = 180° — always, for every triangle, no exceptions!
A triangle has angles (3x + 5)°, (x − 5)°, and 60°. Find x, then find the measure of the largest angle.
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Quick Recall
a² + b² = c² — c is ALWAYS the hypotenuse (longest side, opposite the right angle)
A ladder leans against a wall. The base is 6 ft from the wall and it reaches 8 ft up the wall. How long is the ladder?
Q13
Area of a Circle · Radius vs. Diameter
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Quick Recall
Area = πr² · Circumference = 2πr — always use RADIUS (half the diameter)!
A circular pizza has a diameter of 14 inches. What is its area? (Use π ≈ 3.14)
Q14
Complementary & Supplementary Angles
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Quick Recall
COMPLEMENTARY = 90° (2 angles) · SUPPLEMENTARY = 180° (2 angles)
Angles A and B are supplementary. Angle A = (3x + 15)°, Angle B = (x + 5)°. Find the measure of Angle B.
Q15
Volume of a Rectangular Prism
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Quick Recall
Volume = l × w × h — multiply all 3 dimensions, then apply any percentage
A fish tank is 40 cm long, 25 cm wide, and 30 cm tall. If filled to 80% capacity, how many cm³ of water are inside?
Q16
Similar Figures · Area Scale Factor
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Quick Recall
AREA scales by the SQUARE of the side ratio: sides 3:5 → areas 9:25
Two similar triangles have sides in ratio 3:5. The smaller triangle has area 27 cm². What is the area of the larger?
Q17
Parallel Lines & Transversals
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Quick Recall
ALTERNATE interior angles = EQUAL · CO-INTERIOR (same-side) angles = 180°
Two parallel lines are cut by a transversal. Two co-interior angles measure (5x − 10)° and (3x + 30)°. Find x.
Q18
Perimeter of Composite (L-Shape) Figures
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Quick Recall
L-shape perimeter = FULL rectangle perimeter! The cut removes 2 sides but adds 2 equal sides back.
An L-shape is made by removing a 3 m × 4 m corner from a 10 m × 8 m rectangle. What is the perimeter?
Full rect: 10 m wide, 8 m tall · Corner removed: 3 m wide, 4 m tall (top-right)
Q19
Coordinate Geometry · Distance Formula
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Quick Recall
Distance = √[(x₂−x₁)² + (y₂−y₁)²] — Pythagorean Theorem applied to a coordinate grid
Find the distance between A(1, 2) and B(4, 6).
Q20
Surface Area of a Cylinder
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Quick Recall
SA = 2πr² + 2πrh → 2 circles (top + bottom) + 1 rectangle (lateral face)
A cylindrical can has radius 4 cm and height 10 cm. What is the total surface area? (π ≈ 3.14)