IB MYP Mathematics

Core Concepts
Year 9 – 10

20 exam-style questions across all major units. Study the concepts, then test yourself.

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6
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40
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📚 Concepts
✏️ Quiz
📋 Answers
1. Algebra
2. Functions
3. Geometry
4. Trigonometry
5. Statistics
6. Number
Unit 1 — Algebra

Solving equations, quadratics, systems of equations, exponents, and sequences.

Quadratic Formula
x = (−b ± √(b²−4ac)) / 2a
Difference of Squares
a²−b² = (a+b)(a−b)
Perfect Square
(a±b)² = a²±2ab+b²
Exponent Laws
aᵐ·aⁿ = aᵐ⁺ⁿ, (aᵐ)ⁿ = aᵐⁿ
Arithmetic Sequence
aₙ = a₁ + (n−1)d
Geometric Sequence
aₙ = a₁ · rⁿ⁻¹
⭐ Must Memorise
  • Discriminant: b²−4ac > 0 → two real roots; = 0 → one root; < 0 → no real roots
  • Zero product property: if ab = 0, then a = 0 or b = 0
  • a⁰ = 1 for any a ≠ 0; a⁻ⁿ = 1/aⁿ
  • Sum of arithmetic series: Sₙ = n/2 · (a₁ + aₙ)
📝 Worked Example

Solve: x² − 5x + 6 = 0

Factor: (x−2)(x−3) = 0 → x = 2 or x = 3 ✓
Check: 4−10+6=0 ✓ and 9−15+6=0 ✓

Unit 2 — Functions

Linear, quadratic, exponential functions; domain/range; transformations; inverse functions.

Slope-Intercept
y = mx + b
Vertex Form (Quadratic)
y = a(x−h)² + k
Slope Formula
m = (y₂−y₁)/(x₂−x₁)
Exponential Growth/Decay
y = a · bˣ (b > 0, b ≠ 1)
Axis of Symmetry
x = −b / 2a
Inverse Function
Swap x ↔ y, solve for y
⭐ Must Memorise
  • Domain: all valid x-inputs; Range: all possible y-outputs
  • Vertex form: (h, k) is the vertex of the parabola
  • b > 1 → exponential growth; 0 < b < 1 → exponential decay
  • Vertical shift: y=f(x)+k; Horizontal shift: y=f(x−h)
📝 Worked Example

Find the vertex of y = 2x² − 8x + 5

x = −(−8)/(2·2) = 8/4 = 2; y = 2(4)−8(2)+5 = 8−16+5 = −3
Vertex: (2, −3) ✓

Unit 3 — Geometry

Circle theorems, similarity, congruence, coordinate geometry, surface area and volume.

Circle Area / Circumference
A = πr², C = 2πr
Sphere
V = 4/3·πr³, SA = 4πr²
Cone
V = 1/3·πr²h
Distance Formula
d = √((x₂−x₁)²+(y₂−y₁)²)
Midpoint
M = ((x₁+x₂)/2, (y₁+y₂)/2)
Similar Triangles
a/a' = b/b' = c/c'
⭐ Must Memorise
  • Angle in semicircle = 90° (Thales' theorem)
  • Angles in same segment are equal
  • Opposite angles in cyclic quadrilateral sum to 180°
  • Perpendicular from centre bisects the chord
📝 Worked Example

A cone has radius 3 cm and height 4 cm. Find its volume.

V = 1/3 · π · 3² · 4 = 1/3 · π · 9 · 4 = 12π ≈ 37.7 cm³ ✓

Unit 4 — Trigonometry

SOH-CAH-TOA, sine rule, cosine rule, Pythagorean theorem, angles of elevation/depression.

SOH-CAH-TOA
sin=O/H, cos=A/H, tan=O/A
Sine Rule
a/sinA = b/sinB = c/sinC
Cosine Rule
c² = a²+b²−2ab·cosC
Area of Triangle
Area = 1/2·ab·sinC
Pythagorean Theorem
a² + b² = c²
Key Values
sin30°=1/2, sin45°=√2/2, sin60°=√3/2
⭐ Must Memorise
  • Use sine rule when given: angle-angle-side (AAS) or angle-side-side (ASS)
  • Use cosine rule when given: SAS or SSS
  • Angle of elevation: looking UP; Angle of depression: looking DOWN
  • cos90° = 0, sin90° = 1, tan45° = 1
📝 Worked Example

In triangle ABC, AB = 7, BC = 5, angle B = 60°. Find AC.

AC² = 7²+5²−2(7)(5)cos60° = 49+25−70(0.5) = 74−35 = 39
AC = √39 ≈ 6.24 cm ✓

Unit 5 — Statistics & Probability

Descriptive statistics, probability rules, normal distribution, scatter plots, correlation.

Mean
x̄ = Σx / n
Probability
P(A) = favourable / total
P(A or B)
P(A)+P(B)−P(A∩B)
P(A and B) independent
P(A) × P(B)
IQR
IQR = Q3 − Q1
Standard Deviation (σ)
σ = √(Σ(x−x̄)²/n)
⭐ Must Memorise
  • Median: middle value when data is sorted
  • Mode: most frequently occurring value
  • Outlier: below Q1−1.5×IQR or above Q3+1.5×IQR
  • Correlation: r close to ±1 = strong; r close to 0 = weak
📝 Worked Example

A bag has 3 red, 5 blue balls. One is drawn, not replaced, then another. Find P(both red).

P(1st red) = 3/8; P(2nd red | 1st red) = 2/7
P(both red) = 3/8 × 2/7 = 6/56 = 3/28 ✓

Unit 6 — Number Systems

Surds, rational/irrational numbers, scientific notation, percentage, ratio, indices.

Surd Simplification
√(ab) = √a · √b
Rationalise Denominator
1/√a = √a/a
Scientific Notation
a × 10ⁿ, 1 ≤ a < 10
% Change
(new−old)/old × 100%
Compound Interest
A = P(1 + r/n)ⁿᵗ
Fractional Exponent
a^(m/n) = ⁿ√(aᵐ)
⭐ Must Memorise
  • √2 ≈ 1.414, √3 ≈ 1.732, √5 ≈ 2.236
  • Irrational: cannot be written as p/q (e.g. π, √2, e)
  • a^(1/2) = √a; a^(1/3) = ∛a
  • Multiplying by (a−b)/(a−b): conjugate surd rationalisation
📝 Worked Example

Simplify: √48

√48 = √(16×3) = √16 · √3 = 4√3 ✓

Practice Questions

01
Unit 1 · Algebra
Easy
Which of the following is a root of the equation x² − 7x + 12 = 0?
02
Unit 1 · Algebra
Medium
The discriminant of 2x² − 3x + 5 = 0 is:
03
Unit 1 · Algebra — Exponents
Medium
Simplify: (2³ × 2⁵) ÷ 2⁶
04
Unit 2 · Functions
Medium
The vertex of the parabola y = x² − 6x + 11 is:
05
Unit 2 · Functions
Easy
The function f(x) = 3 · 2ˣ is an example of:
06
Unit 2 · Functions — Linear
Medium
A line passes through the points (1, 3) and (4, 9). What is its equation?
07
Unit 3 · Geometry
Medium
A cylinder has radius 4 cm and height 10 cm. Its volume is (use π ≈ 3.14):
08
Unit 3 · Geometry — Circle Theorems
Hard
In a circle, an inscribed angle that subtends a diameter must equal:
09
Unit 3 · Geometry — Coordinate
Medium
What is the distance between points (−1, 2) and (3, 5)?
10
Unit 4 · Trigonometry
Easy
In a right triangle, the side opposite to the 30° angle is 5 cm. What is the hypotenuse?
11
Unit 4 · Trigonometry — Cosine Rule
Hard
In triangle PQR, PQ = 6, QR = 8, and angle Q = 90°. What is cos P (to 3 significant figures)?
12
Unit 4 · Trigonometry — Sine Rule
Hard
In triangle ABC, angle A = 40°, angle B = 75°, and side a = 10 cm. Using the sine rule, side b ≈ (sin 40° ≈ 0.643, sin 75° ≈ 0.966):
13
Unit 5 · Statistics
Easy
The data set is: 4, 7, 2, 9, 7, 3, 7. What is the mode?
14
Unit 5 · Statistics — IQR
Medium
For the data: 3, 5, 7, 9, 11, 13, 15, the interquartile range (IQR) is:
15
Unit 5 · Probability
Medium
A fair die is rolled twice. What is the probability of getting a 6 on both rolls?
16
Unit 6 · Number — Surds
Medium
Simplify: √75 − √27
17
Unit 6 · Number — Indices
Hard
Evaluate: 27^(2/3)
18
Unit 1 · Algebra — Sequences
Medium
The 10th term of the arithmetic sequence 3, 7, 11, 15, ... is:
19
Unit 6 · Number — Percentage
Medium
A price increases from $80 to $100. The percentage increase is:
20
Unit 3 · Geometry — Similar Triangles
Hard
Two similar triangles have sides in the ratio 3:5. If the area of the smaller triangle is 27 cm², the area of the larger triangle is:

Answer Key & Solutions

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