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MYP 3

Year 9 — All Learning Objectives

Developing the mathematician's toolkit

9.1 Surds and Pythagoras

Term 1

Surds

  1. 1. Differentiate between rational and irrational numbers.
  2. 2. Understand the concept of surds and their approximate values.
  3. 3. Simplify surds by extracting the largest square factor.
  4. 4. Multiply and divide surds, and add/subtract like surds.
  5. 5. Rationalise a denominator of the form 1/√a.

Pythagoras' Theorem

  1. 6. Apply Pythagoras' theorem to find a missing side in a right-angled triangle.
  2. 7. Use the converse of Pythagoras' theorem to test whether a triangle is right-angled.
  3. 8. Use Pythagoras' theorem to find distances between two points in 2D.
  4. 9. Use Pythagoras' theorem to find lengths in 3D solids (space diagonals, slant heights).
  5. 10. Give Pythagoras answers in surd form where appropriate.
  6. 11. Apply Pythagoras' theorem to practical problems (ladders, ziplines, triangles in real contexts).

9.2 Mensuration

Term 1

Mensuration

  1. 1. Use vocabulary for 3D shapes: vertex, edge, face.
  2. 2. Classify 3D shapes and identify their properties.
  3. 3. Draw and interpret nets of 3D solids.
  4. 4. Calculate the volume of prisms (including cylinders).
  5. 5. Calculate the volume of pyramids and cones (V = ⅓ × base area × height).
  6. 6. Calculate the volume of a sphere (V = ⁴⁄₃ π r³).
  7. 7. Calculate the surface area of prisms and cylinders.
  8. 8. Calculate the surface area of a sphere (SA = 4πr²).
  9. 9. Convert between units of capacity, area and volume.
  10. 10. Substitute values into mensuration formulae.
  11. 11. Rearrange mensuration formulae to make a different variable the subject.

9.3 Right-angle Trigonometry

Term 1–2

Trigonometric Ratios

  1. 1. Identify and name the sides of a right-angled triangle (opposite, adjacent, hypotenuse).
  2. 2. Define the sine, cosine and tangent ratios (SOH CAH TOA).
  3. 3. Use trigonometric ratios to find a missing side in a right-angled triangle.
  4. 4. Use inverse trigonometric ratios to find a missing angle in a right-angled triangle.
  5. 5. Use exact values of sin, cos and tan at 30°, 45° and 60°.
  6. 6. Apply right-angle trigonometry to angles of elevation and depression.
  7. 7. Apply right-angle trigonometry to problems set inside 3D solids.

9.4 Transformations, Congruence and Similarity

Term 2

Transformations

  1. 1. Perform translations, rotations and reflections of shapes.
  2. 2. Perform enlargements from a given centre with a positive whole-number or fractional scale factor.
  3. 3. Transform individual coordinates and rigid figures on the Cartesian plane.
  4. 4. Describe transformations fully (type + parameters).
  5. 5. Perform and describe compound transformations.

Congruence and Similarity

  1. 6. Understand definitions and notation for congruence (≡) and similarity (∼).
  2. 7. Identify congruent figures using SSS, SAS, ASA and RHS.
  3. 8. Identify similar figures using matching angle criteria.
  4. 9. Find missing sides or angles in similar figures using the linear scale factor.
  5. 10. Understand that area scales by the square of the scale factor (k²).
  6. 11. Understand that volume scales by the cube of the scale factor (k³).

9.5 Coordinate Geometry

Term 2

Coordinate Geometry

  1. 1. Understand gradient as angles and ratios.
  2. 2. Calculate the gradient of a line through two points.
  3. 3. Calculate the distance between two points on a Cartesian plane.
  4. 4. Calculate the midpoint between two points.
  5. 5. Understand the properties of parallel and perpendicular lines.
  6. 6. Determine the equation of a line in slope-intercept form (y = mx + c).
  7. 7. Graph lines from given equations and read intercepts.
  8. 8. Find the equation of a line given a point and gradient or two points.
  9. 9. Discuss the rate of change of one variable in relation to another.

9.6 Simultaneous Equations

Term 2–3

Simultaneous Equations

  1. 1. Solve simultaneous equations graphically.
  2. 2. Solve simultaneous equations numerically using tables.
  3. 3. Solve simultaneous equations algebraically using the equal value (y = y) method.
  4. 4. Solve simultaneous equations by substitution.
  5. 5. Solve simultaneous equations by elimination.
  6. 6. Recognise systems with no solution or infinitely many solutions.
  7. 7. Model real-world word problems with a pair of simultaneous equations and solve them.

9.7 Indices and Scientific Notation

Term 3

Indices

  1. 1. Evaluate numerical expressions involving positive integer indices.
  2. 2. Apply the index laws for multiplication, division and power of a power.
  3. 3. Evaluate expressions with zero and negative integer indices.
  4. 4. Evaluate expressions with fractional indices (e.g. a^(1/2), a^(1/3)).
  5. 5. Simplify algebraic expressions using the index laws.

Scientific Notation

  1. 6. Convert between ordinary numbers and scientific (standard) form.
  2. 7. Multiply and divide numbers in standard form.
  3. 8. Apply compound percentage change to numbers in standard form.

9.8 Sets, Probability and Games

Term 3

Sets and Venn Diagrams

  1. 1. Understand the definition of a set including finite, infinite and universal sets, and use interval notation.
  2. 2. Perform set operations: complement, union, intersection and subset.
  3. 3. Identify and represent the special number sets (N, Z, Q, Q', R) using Venn diagrams.
  4. 4. Use 2-set Venn diagrams to represent relationships and solve count problems.
  5. 5. Use 3-set Venn diagrams and the inclusion-exclusion principle.

Probability and Games

  1. 6. Define experimental and theoretical probability and represent it as a fraction, decimal or percentage.
  2. 7. Determine sample spaces using lists, tables, 2D grids and tree diagrams.
  3. 8. Calculate probabilities for compound events including "and" and "or".
  4. 9. Calculate probabilities for events without replacement (using tree diagrams).
  5. 10. Calculate expected values for multi-event experiments.
  6. 11. Determine whether games are fair using expected value.