IB MYP Mathematics 9–10 | Core Concepts Quiz

Study Guide

Core Concepts & Formulas

Review key ideas and memorize essential formulas before the quiz

Algebra & Equations

Q1 – Q4

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📐 Key Concepts

Quadratic equation: ax² + bx + c = 0

Quadratic formula: x = (−b ± √(b²−4ac)) / 2a

Discriminant: Δ = b² − 4ac → Δ>0: two roots, Δ=0: one root, Δ<0: no real roots

Factoring: look for two numbers that multiply to ac and add to b

⭐ Memorize

x = (−b ± √(b²−4ac)) / 2a (a+b)² = a²+2ab+b² | (a−b)² = a²−2ab+b² (a+b)(a−b) = a²−b²

✏️ Example

Solve: x² − 5x + 6 = 0

Factor: (x−2)(x−3) = 0 → x = 2 or x = 3

✓ Answer: x = 2 or x = 3

Functions & Graphs

Q5 – Q7

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📐 Key Concepts

Linear function: y = mx + c (m = slope, c = y-intercept)

Slope formula: m = (y₂−y₁)/(x₂−x₁)

Quadratic function: y = ax² + bx + c — vertex at x = −b/(2a)

Exponential function: y = aˣ — domain all reals, range y>0

⭐ Memorize

Slope: m = (y₂−y₁) / (x₂−x₁) Vertex x-coord: x = −b/(2a) Parallel lines: same slope | Perpendicular: m₁·m₂ = −1

✏️ Example

Find slope through (1, 3) and (4, 9)

m = (9−3)/(4−1) = 6/3 = 2

✓ Answer: m = 2

Geometry & Trigonometry

Q8 – Q11

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📐 Key Concepts

Pythagorean theorem: a² + b² = c² (c = hypotenuse)

SOH-CAH-TOA: sin θ = opp/hyp, cos θ = adj/hyp, tan θ = opp/adj

Area of circle: A = πr² | Circumference: C = 2πr

Sum of interior angles of polygon: (n−2)×180°

⭐ Memorize

a² + b² = c² sin θ = O/H | cos θ = A/H | tan θ = O/A Area triangle = ½ × base × height Interior angle sum = (n−2) × 180°

✏️ Example

Right triangle: legs 3 and 4. Find hypotenuse.

c² = 3² + 4² = 9 + 16 = 25 → c = 5

✓ Answer: c = 5

Number & Indices

Q12 – Q14

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📐 Key Concepts

Index laws: aᵐ × aⁿ = aᵐ⁺ⁿ, aᵐ ÷ aⁿ = aᵐ⁻ⁿ, (aᵐ)ⁿ = aᵐⁿ

Negative exponent: a⁻ⁿ = 1/aⁿ

Fractional exponent: a^(1/n) = ⁿ√a

Scientific notation: a × 10ⁿ where 1 ≤ a < 10

⭐ Memorize

aᵐ × aⁿ = aᵐ⁺ⁿ | aᵐ ÷ aⁿ = aᵐ⁻ⁿ (aᵐ)ⁿ = aᵐⁿ | a⁰ = 1 | a⁻¹ = 1/a a^(1/2) = √a | a^(m/n) = ⁿ√(aᵐ)

✏️ Example

Simplify: (2³)² × 2⁻⁴

= 2⁶ × 2⁻⁴ = 2²= 4

✓ Answer: 4

Statistics & Probability

Q15 – Q18

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📐 Key Concepts

Mean: sum of all values ÷ number of values

Median: middle value when sorted; if even, average of two middle values

Probability: P(A) = favourable outcomes / total outcomes

P(A or B) = P(A) + P(B) − P(A and B)

Independent events: P(A and B) = P(A) × P(B)

⭐ Memorize

Mean = Σx / n P(A∪B) = P(A) + P(B) − P(A∩B) P(A∩B) = P(A) × P(B) [if independent]

✏️ Example

Find the mean of: 4, 7, 9, 6, 4

Sum = 4+7+9+6+4 = 30. Mean = 30/5 = 6

✓ Answer: 6

Sequences & Patterns

Q19 – Q20

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📐 Key Concepts

Arithmetic sequence: aₙ = a₁ + (n−1)d (d = common difference)

Sum of arithmetic sequence: Sₙ = n/2 × (a₁ + aₙ)

Geometric sequence: aₙ = a₁ × rⁿ⁻¹ (r = common ratio)

To find common difference: d = a₂ − a₁

⭐ Memorize

Arithmetic: aₙ = a₁ + (n−1)d Sum: Sₙ = n/2 × (a₁ + aₙ) Geometric: aₙ = a₁ × rⁿ⁻¹

✏️ Example

Arithmetic sequence: a₁ = 3, d = 4. Find a₅.

a₅ = 3 + (5−1)×4 = 3 + 16 = 19

✓ Answer: 19

Examination

20 Core Questions

Choose the best answer for each question

Progress — 0 / 20

Score

30:00

Unit 1 · Algebra

★ Easy

Solve for x: 2x + 5 = 17

Unit 1 · Algebra

★★ Medium

Which expression is equivalent to (x + 3)²?

Unit 1 · Quadratics

★★ Medium

What are the solutions of x² − 7x + 12 = 0?

Unit 1 · Discriminant

★★★ Hard

For 2x² − 4x + 2 = 0, the discriminant Δ = b² − 4ac equals:

Unit 2 · Functions

★ Easy

Find the slope of the line through points (2, 1) and (6, 9).

Unit 2 · Graphs

★★ Medium

The vertex of the parabola y = x² − 6x + 5 has x-coordinate:

Unit 2 · Linear Functions

★★ Medium

Line L has equation y = 3x − 2. What is the y-intercept?

Unit 3 · Pythagoras

★ Easy

A right triangle has legs of length 5 and 12. What is the length of the hypotenuse?

Unit 3 · Trigonometry

★★ Medium

In a right triangle, the opposite side = 4 and hypotenuse = 5. What is sin θ?

Unit 3 · Circle

★★ Medium

A circle has radius r = 7 cm. What is its area? (Use π ≈ 3.14)

Unit 3 · Angles

★★ Medium

What is the sum of interior angles of a regular hexagon (6 sides)?

Unit 4 · Indices

★ Easy

Simplify: x³ × x⁵

Unit 4 · Indices

★★ Medium

What is the value of 27^(1/3)?

Unit 4 · Scientific Notation

★★★ Hard

Express 0.0000456 in scientific notation.

Unit 5 · Statistics

★ Easy

What is the mean of the data set: 8, 12, 5, 15, 10?

Unit 5 · Statistics

★★ Medium

What is the median of: 3, 7, 1, 9, 4, 6?

Unit 5 · Probability

★★ Medium

A bag has 4 red, 3 blue, and 3 green marbles. What is the probability of picking a red marble?

Unit 5 · Probability

★★★ Hard

Two fair coins are flipped. What is the probability of getting exactly one head?

Unit 6 · Sequences

★★ Medium

An arithmetic sequence has first term a₁ = 5 and common difference d = 3. What is the 10th term?

Unit 6 · Sequences

★★★ Hard

A geometric sequence starts: 2, 6, 18, 54, … What is the 6th term?

Grade 9–10
Core Concepts

Core Concepts & Formulas

📐 Key Concepts

⭐ Memorize

✏️ Example

📐 Key Concepts

⭐ Memorize

✏️ Example

📐 Key Concepts

⭐ Memorize

✏️ Example

📐 Key Concepts

⭐ Memorize

✏️ Example

📐 Key Concepts

⭐ Memorize

✏️ Example

📐 Key Concepts

⭐ Memorize

✏️ Example

20 Core Questions

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Full Solutions & Explanations

Grade 9–10Core Concepts

Core Concepts & Formulas

📐 Key Concepts

⭐ Memorize

✏️ Example

📐 Key Concepts

⭐ Memorize

✏️ Example

📐 Key Concepts

⭐ Memorize

✏️ Example

📐 Key Concepts

⭐ Memorize

✏️ Example

📐 Key Concepts

⭐ Memorize

✏️ Example

📐 Key Concepts

⭐ Memorize

✏️ Example

20 Core Questions

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Full Solutions & Explanations

Grade 9–10
Core Concepts