Pre-Algebra · Geometry · Self-Study Edition
20 Problems · Interactive · Self-Check
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Pre-Algebra
Problems 1 – 10
PROBLEM 01
Order of Operations
Evaluate the expression.
★ Most missed: forgetting to do multiplication before addition!
$3 + 4 \times 2 - 2 + 1$
🧠PEMDAS — Parentheses → Exponents → Multiply/Divide → Add/Subtract (left to right)
Answer
PROBLEM 02
Integer Operations
Simplify.
★ Two negatives multiplied = positive!
$-3 \times (-4) \div (-2) + (-4)$
🧠SAME signs → (+), DIFFERENT signs → (−)
Answer
PROBLEM 03
Solving One-Step Equations
Solve for \(x\).
★ Do the SAME thing to both sides.
$3x - 4 = 11$
🧠BALANCE — whatever you do to one side, do to the other
x =
PROBLEM 04
Ratios & Proportions
Solve the proportion.
★ Cross-multiply, then divide!
$\dfrac{4}{x} = \dfrac{2}{30}$
🧠CROSS-MULTIPLY — \(a/b = c/d \Rightarrow ad = bc\)
x =
PROBLEM 05
Percentages
Find the value.
★ Percent means "per hundred." Change % → decimal first.
What is 15% of 200?
🧠IS / OF — "is" = \(=\), "of" = \(\times\), "%" = ÷ 100
Answer
PROBLEM 06
Inequalities
Solve for \(x\).
★ When you multiply/divide by a negative, FLIP the inequality sign!
$-2x \leq 4$
🧠FLIP rule — divide by negative → flip \(\leq\) to \(\geq\)
x ≥
PROBLEM 07
Distributive Property / FOIL
Expand and simplify.
★ Students forget the middle terms of FOIL most often.
$(x + 2)(x - 3)$
🧠FOIL — First · Outer · Inner · Last
Answer
PROBLEM 08
Exponent Rules
Simplify.
★ Zero exponent is always 1 (except 0⁰). Negative exponent flips to denominator.
$2^3 \times 2^{-1}$
🧠SAME base → ADD exponents: \(a^m \cdot a^n = a^{m+n}\)
Answer
PROBLEM 09
GCF & Factoring
Find the GCF.
★ List ALL factors of both, pick the GREATEST one in common.
GCF of 12 and 15
🧠GCF = Greatest Common Factor — biggest number that divides BOTH evenly
GCF =
PROBLEM 10
Graphing & Slope
Find the slope of the line through two points.
★ The most common mistake: dividing \(\Delta x\) by \(\Delta y\) (upside down!).
Points: \((1, 3)\) and \((3, 7)\)
🧠RISE over RUN: \(m = \dfrac{y_2 - y_1}{x_2 - x_1}\)
slope =
Geometry
Problems 11 – 20
PROBLEM 11
Complementary Angles
Find the missing angle.
★ Complementary = adds up to 90°. Supplementary = adds up to 180°. Don't mix them up!
Two angles are complementary. One angle is 40°. Find the other.
🧠Complementary = Corner (90°) · Supplementary = Straight (180°)
Answer
PROBLEM 12
Triangle Angle Sum
What is the sum of all interior angles of a triangle?
★ This is a theorem — true for EVERY triangle, always.
$\angle A + \angle B + \angle C = ?°$
🧠TRIANGLE SUM — always 180°, no exceptions
Answer
PROBLEM 13
Pythagorean Theorem
Find the hypotenuse.
★ \(c\) is always the LONGEST side, opposite the right angle.
Right triangle: legs \(a = 3\), \(b = 4\). Find \(c\).
🧠a² + b² = c² — "3-4-5" is the classic triple!
c =
PROBLEM 14
Perimeter
Find the perimeter of the rectangle.
★ Perimeter = total distance AROUND the shape (add all sides).
Rectangle: length \(= 10\), width \(= 4\)
🧠P = 2l + 2w — "two lengths + two widths"
P =
PROBLEM 15
Area of Triangle
Find the area.
★ Don't forget to divide by 2! Triangles = half a rectangle.
Triangle: base \(= 8\), height \(= 6\)
🧠A = ½ bh — half times base times height
A =
PROBLEM 16
Quadrilateral Angles
What is the sum of interior angles in a quadrilateral?
★ Each time you add a side to a polygon, add 180° to the total.
Square, rectangle, trapezoid — what's the angle sum?
🧠(n − 2) × 180° — n = number of sides · quad: (4−2)×180
Sum =
PROBLEM 17
Circumference of Circle
Find the circumference. Use \(\pi \approx 3.14\).
★ C uses diameter (full width); Area uses radius (half width). Confusing these = #1 mistake!
Circle with diameter \(d = 24\)
🧠C = πd (diameter) or C = 2πr (radius)
C ≈
PROBLEM 18
Congruence vs. Similarity
Choose the correct word:
Two triangles have exactly the same shape AND the same size. They are _____.
★ Similar = same shape, different size. Congruent = same shape AND size.
Same shape + Same size = ?
🧠≅ CONGRUENT (identical) · ~ SIMILAR (proportional copy)
Word
PROBLEM 19
Parallel Lines & Transversals
Find the missing angle.
★ Alternate interior angles are EQUAL. Co-interior (same-side) angles add to 180°.
Two parallel lines cut by a transversal.
One alternate interior angle = 70°.
Find its alternate interior partner.
🧠ALT. INTERIOR = equal · CO-INTERIOR = supplementary (180°)
Angle =
PROBLEM 20
Volume of Rectangular Prism
Find the volume.
★ Volume = 3D space inside. Always in cubic units (cm³, m³).
Rectangular prism: \(l = 5\), \(w = 6\), \(h = 5\)
🧠V = l × w × h — length times width times height
V =