Math Mastery — Algebra I & Geometry

Algebra I — 10 Questions

Q1 Algebra Medium Variable & Expression

🔑 KEY: variable = unknown box — a letter that holds a number

Which of the following is an algebraic expression (not an equation)?

Quick Example Equation: \( 3x + 2 = 11 \) ← has an "=" sign
Expression: \( 3x + 2 \) ← NO "=" sign

A \( 5x - 3 = 12 \)

B \( 2x^2 + 7x - 4 \)

C \( x = 9 \)

D \( 4x + 1 = 4x + 2 \)

Q2 Algebra Tricky Like Terms

🔑 KEY: like terms = same variable, same exponent

Simplify: \( 4x^2 + 3x - x^2 + 2 - 5x \)

Watch Out! \( 4x^2 \) and \( x^2 \) ARE like terms → combine them
\( 3x \) and \( 5x \) ARE like terms → combine them
\( 2 \) is a constant — stands alone

A \( 5x^2 - 2x + 2 \)

B \( 3x^2 + 8x + 2 \)

C \( 3x^2 - 2x + 2 \)

D \( 4x^2 - 2x + 2 \)

Q3 Algebra Medium Solving Equations

🔑 KEY: inverse operations — do the OPPOSITE to both sides

Solve for \( x \): \( \ 3x - 7 = 14 \)

Method Step 1: Add 7 to both sides → \( 3x = 21 \)
Step 2: Divide both sides by 3 → \( x = ? \)

A \( x = 5 \)

B \( x = 7 \)

C \( x = 9 \)

D \( x = 3 \)

Q4 Algebra Tricky Slope

🔑 KEY: slope = rise ÷ run → \(\dfrac{y_2 - y_1}{x_2 - x_1}\)

What is the slope of the line passing through \( (2, 5) \) and \( (6, 13) \)?

Formula \( m = \dfrac{13 - 5}{6 - 2} = \dfrac{?}{?} \)

Remember: Order matters — keep the same point "first" for both \( x \) and \( y \)

A \( m = 4 \)

B \( m = 2 \)

C \( m = 3 \)

D \( m = \dfrac{1}{2} \)

Q5 Algebra Tricky Inequalities

🔑 KEY: FLIP the sign when multiplying or dividing by a negative!

Solve: \( -4x + 8 > 20 \). Which is correct?

Trap Alert ⚠️ Step 1: \( -4x > 12 \)
Step 2: Divide by negative 4 → flip ">" to "<" !
Most students FORGET to flip!

A \( x > -3 \)

B \( x > 3 \)

C \( x < -3 \)

D \( x < 3 \)

Q6 Algebra Medium Function

🔑 KEY: function = each input → exactly ONE output

Which set of ordered pairs does NOT represent a function?

Vertical Line Test in list form If the same \( x \)-value appears with TWO different \( y \)-values → NOT a function
Example: \( (2, 3) \) and \( (2, 7) \) → x = 2 gives two outputs → ✗

A \( \{(1,2),\ (3,4),\ (5,6)\} \)

B \( \{(1,2),\ (1,5),\ (3,4)\} \)

C \( \{(2,1),\ (4,1),\ (6,1)\} \)

D \( \{(0,0),\ (1,1),\ (2,4)\} \)

Q7 Algebra Tricky Systems of Equations

🔑 KEY: substitution — solve one, plug into other

Solve the system: \( y = 2x + 1 \) and \( 3x + y = 16 \)

Substitution Steps Replace \( y \) in second equation: \( 3x + (2x + 1) = 16 \)
→ \( 5x + 1 = 16 \) → \( x = ? \) → then find \( y \)

A \( x = 2,\ y = 5 \)

B \( x = 4,\ y = 9 \)

C \( x = 3,\ y = 7 \)

D \( x = 5,\ y = 11 \)

Q8 Algebra Medium Exponent Rules

🔑 KEY: product rule — same base → ADD exponents: \(a^m \cdot a^n = a^{m+n}\)

Simplify: \( x^3 \cdot x^5 \)

Common Mistake ⚠️ WRONG: \( x^{15} \) ← multiplying exponents (that's the POWER rule)
RIGHT: Add exponents when multiplying same base → \( x^{3+5} \)

A \( x^{15} \)

B \( x^8 \)

C \( 2x^8 \)

D \( x^2 \)

Q9 Algebra Tricky Quadratic — Factoring

🔑 KEY: find two numbers that MULTIPLY to \(c\) and ADD to \(b\) in \(x^2+bx+c\)

Factor completely: \( x^2 - 5x + 6 \)

Think: × = 6, + = −5 Pairs that multiply to 6: (1×6), (2×3), (−2×−3), (−1×−6)
Which pair adds to −5? → \( -2 + (-3) = -5 \) ✓

A \( (x-2)(x-3) \)

B \( (x+2)(x+3) \)

C \( (x-1)(x-6) \)

D \( (x-2)(x+3) \)

Q10 Algebra Medium Polynomial — Degree

🔑 KEY: degree = highest exponent of the polynomial

What is the degree of the polynomial \( 4x^3 - 2x^5 + x - 7 \)?

Don't be fooled by order! Terms: \(4x^3\), \(-2x^5\), \(x^1\), \(-7\)
Exponents: 3, 5, 1, 0 → Highest = ?

A 3

B 4

C 5

D 7

Geometry — 10 Questions

Q11 Geometry Medium Supplementary Angles

🔑 KEY: Supplementary = Straight line = 180° | Complementary = Corner = 90°

Two angles are supplementary. One angle measures \( 63° \). What is the measure of the other angle?

Formula Supplementary: \( \angle A + \angle B = 180° \)
→ \( \angle B = 180° - 63° = ? \)

A \( 27° \)

B \( 107° \)

C \( 117° \)

D \( 127° \)

Q12 Geometry Tricky Triangle Angles

🔑 KEY: Triangle Angle Sum = 180° always, no exceptions!

In a triangle, two angles measure \( 47° \) and \( 85° \). What is the third angle?

Formula \( \angle A + \angle B + \angle C = 180° \)
→ \( 47° + 85° + \angle C = 180° \) → \( \angle C = ? \)

A \( 38° \)

B \( 48° \)

C \( 58° \)

D \( 132° \)

Q13 Geometry Tricky Pythagorean Theorem

🔑 KEY: \(a^2 + b^2 = c^2\) — \(c\) is ALWAYS the hypotenuse (longest side)

A right triangle has legs of length \( 6 \) and \( 8 \). What is the length of the hypotenuse?

Classic 3-4-5 Family \( 6^2 + 8^2 = 36 + 64 = 100 \)
\( c = \sqrt{100} = ? \) ← Memorize: 6-8-10 is a Pythagorean triple!

A \( c = 7 \)

B \( c = 9 \)

C \( c = 10 \)

D \( c = 14 \)

Q14 Geometry Medium Area — Circle

🔑 KEY: Area = πr² | Circumference = 2πr — r is radius, NOT diameter!

A circle has a diameter of \( 10 \). What is its area? (Use \( \pi \approx 3.14 \))

Trap: diameter ≠ radius! Diameter = 10 → Radius = \( 10 \div 2 = 5 \)
Area = \( \pi r^2 = 3.14 \times 5^2 = 3.14 \times 25 = ? \)

A \( 31.4 \)

B \( 78.5 \)

C \( 314 \)

D \( 62.8 \)

Q15 Geometry Tricky Congruence & Similarity

🔑 KEY: Congruent (≅) = same shape AND size | Similar (~) = same shape, different size

Two triangles have all three corresponding angles equal, but different side lengths. These triangles are ___.

Memory Trick: AA = Similar Same angles → same shape → Similar (∼)
Same angles AND same sides → Congruent (≅)
Which applies here?

A Congruent

B Similar

C Neither congruent nor similar

D Identical

Q16 Geometry Medium Parallel Lines & Transversal

🔑 KEY: alternate interior = equal | co-interior (same-side) = 180°

Two parallel lines are cut by a transversal. One co-interior (same-side interior) angle is \( 72° \). What is the other co-interior angle?

Co-interior Angles Co-interior angles are supplementary → they add up to \(180°\)
(Also called "consecutive interior" or "same-side interior" angles)

A \( 72° \)

B \( 18° \)

C \( 108° \)

D \( 90° \)

Q17 Geometry Tricky Volume — Rectangular Prism

🔑 KEY: Volume = length × width × height — use cubic units!

A rectangular prism has length \( 5 \) cm, width \( 4 \) cm, and height \( 3 \) cm. What is its volume?

Formula \( V = l \times w \times h = 5 \times 4 \times 3 = ? \) cm³

Always write the unit as cm³ (cubic centimeters)!

A \( 47 \text{ cm}^3 \)

B \( 60 \text{ cm}^3 \)

C \( 94 \text{ cm}^3 \)

D \( 12 \text{ cm}^3 \)

Q18 Geometry Tricky Quadrilateral — Interior Angles

🔑 KEY: Sum of interior angles = (n−2) × 180°, where n = number of sides

What is the sum of the interior angles of a hexagon?

Formula Hexagon has 6 sides → \( n = 6 \)
Sum = \( (6 - 2) \times 180° = 4 \times 180° = ? \)

A \( 540° \)

B \( 900° \)

C \( 720° \)

D \( 1080° \)

Q19 Geometry Medium Midpoint Formula

🔑 KEY: Midpoint = average the x's, average the y's → \(\left(\dfrac{x_1+x_2}{2},\ \dfrac{y_1+y_2}{2}\right)\)

Find the midpoint of the segment with endpoints \( (2, 6) \) and \( (8, 4) \).

Calculate \( x\text{-midpoint} = \dfrac{2+8}{2} = 5 \)
\( y\text{-midpoint} = \dfrac{6+4}{2} = ? \)

A \( (5, 6) \)

B \( (5, 5) \)

C \( (4, 5) \)

D \( (6, 4) \)

Q20 Geometry Tricky Transformation — Reflection

🔑 KEY: reflect over x-axis → flip y sign | reflect over y-axis → flip x sign

Point \( P(3, -5) \) is reflected over the y-axis. What are the new coordinates?

Rule for y-axis reflection \( (x, y) \rightarrow (-x, y) \) — only the x-coordinate changes sign
So \( (3, -5) \rightarrow (?, ?) \)

A \( (3, 5) \)

B \( (-3, 5) \)

C \( (-3, -5) \)

D \( (5, -3) \)

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