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Maths 1 Specification

7 sections · comprehensive exam board content overview

  • Standard units: mass (kg), length (m), time (s), money (€, $)
  • Compound units: speed (m s⁻¹), density (kg m⁻³), pressure (Pa = N m⁻²)
  • Convert freely between related units, using decimal quantities when appropriate

  • Ordering: Order integers, decimals, fractions; use symbols <, >, =
  • Operations: Apply +, −, ×, ÷ to integers, decimals, proper/improper fractions, mixed numbers (including negatives)
  • Factors & Multiples: Prime numbers, divisors, common factors, HCF, LCM, prime factorisation
  • Inverse Operations: Use cancellation; priority: brackets → powers → roots → reciprocals
  • Counting Strategies: If m ways for task A and n ways for task B, total ways = m × n
  • Roots: Square, cube, and their positive/negative roots
  • Indices: Laws for integer, fractional, negative powers; simplify expressions
  • Standard form: Write numbers as a × 10ⁿ with 1 ≤ a < 10
  • Decimals ↔ Fractions ↔ Percentages: Convert; recurring decimals ↔ fractions
  • Exact calculations: Work with surds, multiples of π; rationalise denominators
  • Bounds & Rounding: Use upper/lower bounds; express error intervals with inequality notation
  • Approximations: Estimate expressions involving π or surds

  • Scale factors & maps – interpret diagrams using ratios
  • Express quantities as fractions or percentages; find percentage changes
  • Direct proportion: y = kx
  • Inverse proportion: y = k/x
  • Use ratio notation to compare lengths, areas, volumes; link to similarity and trigonometric ratios
  • Solve growth/decay problems (compound interest) via iterative formulas

  • Notation: = (equals), ≠ (not equal), ≈ (approximately equal), ≡ (identity)
  • Substitution: Insert numerical values into formulae (including scientific ones)
  • Expanding & Factoring: Expand (a + b)(c + d); factor; factor trinomials
  • Rational Expressions: Cancel common factors; apply four rules for simplification
  • Rearranging: Change the subject of a formula
  • Equations vs. Identities: Demonstrate equivalence algebraically
  • Coordinate Geometry: Work in all four quadrants; calculate gradients m = (y₂ − y₁)/(x₂ − x₁) and intercepts for y = mx + c
  • Lines: Find equation through two points; determine parallel (same gradient) and perpendicular (product = −1) lines
  • Quadratics: Identify roots, turning points; complete the square; use quadratic formula
  • Graph Types: Linear, quadratic, cubic, reciprocal (y = 1/x), exponential (y = aˣ), trigonometric (sin, cos, tan)
  • Interpretation: Use graphs to solve kinematic problems, estimate areas under curves, find gradients
  • Simultaneous Equations: Solve algebraically (substitution/elimination) or graphically; include linear–quadratic pairs
  • Inequalities: Solve and represent on number lines/graphs
  • Sequences: Generate terms; deduce nth term for linear (aₙ = a + (n−1)d) or quadratic sequences

  • Basic terminology: points, lines, planes, angles, polygons, regular polygons, symmetries
  • Angle properties: sum of interior/exterior angles; parallel line angle relationships
  • Quadrilateral families: square, rectangle, parallelogram, trapezium, kite, rhombus – state defining properties
  • Triangle congruence: SSS, SAS, ASA, RHS
  • Similarity: Maintain shape, scale factor; use proportion of corresponding sides
  • Transformations: Rotation, reflection, translation (vectors), enlargement (including negative/fractional scales)
  • Pythagoras: a² + b² = c² in 2-D and 3-D contexts
  • Circle terminology: Centre, radius, diameter, chord, arc, sector, segment; minor/major distinctions
  • Circle theorems:
    • Angle at centre = 2 × angle at circumference
    • Angle in a semicircle = 90°
    • Angles in the same segment are equal
    • Tangent–chord theorem (alternate segment)
    • Radius ⟂ tangent at point of contact
    • Cyclic quadrilateral opposite angles sum to 180°
  • Coordinate geometry: solve problems using 2-D planes
  • 3-D shapes: faces, edges, vertices; cubes, prisms, cylinders, cones, spheres
  • Area & Volume Formulas:
    • Triangle: A = ½bh
    • Parallelogram: A = bh
    • Trapezium: A = ½(a + b)h
    • Circle: A = πr²
    • Cylinder: Surface = 2πr² + 2πrh; Volume = πr²h
    • Sphere: Surface = 4πr²; Volume = ⁴⁄₃πr³
    • Cone: Surface = πr² + πrl; Volume = ⅓πr²h
  • Sector calculations: Arc length l = rθ (θ in radians); sector area A = ½r²θ
  • Trigonometric ratios (right-angled triangles): sin = opp/hyp, cos = adj/hyp, tan = opp/adj
  • Exact values for 30°, 45°, 60° (e.g., sin 45° = 1/√2)
  • Vectors: Addition, scalar multiplication, diagrammatic representation; use for geometric arguments and proofs

  • Representation:
    • Two-way tables, bar charts, pie charts, pictograms – categorical data
    • Vertical line charts – ungrouped discrete numerical data
    • Line graphs – time-series data
    • Histograms (equal/unequal classes) – grouped discrete or continuous data
    • Cumulative frequency graphs – cumulative distributions (frequency density)
  • Descriptive measures: mean, median, mode, range; for grouped data compute estimates (modal class, estimated mean/median)
  • Quartiles & IQR: use to compare distributions
  • Scatter graphs: identify correlation (not causation); draw line of best fit; interpolate/extrapolate with caution

  • Frequency trees & tables to analyse outcomes
  • Equally likely events → calculate expected frequencies
  • Probability scale: 0 ≤ P(A) ≤ 1
  • Additive rule for mutually exclusive events; multiplicative rule for independent events
  • Conditional probability: P(A|B) = P(A ∩ B) / P(B)
  • Set & Venn diagrams to visualise relationships; systematic enumeration via tables, grids, and tree diagrams
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