Practice Maths

Modelling Relationships 1 — Solutions

  1. Complete Tables of Values

    1. y = 0, 2, 4, 6, 8 ▶ View Solution
    2. y = 5, 6, 7, 8, 9 ▶ View Solution
    3. y = −2, 1, 4, 7, 10 ▶ View Solution
    4. y = 1, 5, 9, 13, 17 ▶ View Solution
    5. y = 3, 3.5, 4, 4.5, 5 ▶ View Solution
    6. y = 5, 4, 3, 2, 1 ▶ View Solution
    7. y = 4, 6, 8, 10, 12 ▶ View Solution
    8. y = 10, 7, 4, 1, −2 ▶ View Solution

  2. Is It Linear?

    1. y: 1, 3, 5, 7, 9: Linear — constant difference of 2 ▶ View Solution
    2. y: 0, 1, 4, 9, 16: Non-linear — differences 1, 3, 5, 7 are not constant ▶ View Solution
    3. y: 10, 8, 6, 4, 2: Linear — constant difference of −2 ▶ View Solution
    4. y: 3, 6, 12, 24, 48: Non-linear — differences double each time; this is exponential ▶ View Solution
    5. y: 5, 5, 5, 5, 5: Linear — constant difference of 0; horizontal line y = 5 ▶ View Solution
    6. y: 2, 5, 9, 14, 20: Non-linear — differences are 3, 4, 5, 6 — not constant ▶ View Solution

  3. Find the Rule

    1. y = 4x ▶ View Solution
    2. y = 2x + 3 ▶ View Solution
    3. y = −3x + 10 ▶ View Solution
    4. y = 3x + 1 ▶ View Solution
    5. y = 6 ▶ View Solution
    6. y = 1.5x ▶ View Solution

  4. Real-World Modelling

      1. C = 40t + 60 ▶ View Solution
      2. $60, $100, $140, $180, $220 ▶ View Solution
      3. $180 ▶ View Solution
      4. 5 hours ▶ View Solution
      1. F = 2.20d + 3.50 ▶ View Solution
      2. $3.50, $5.70, $7.90, $10.10, $12.30 ▶ View Solution
      3. $21.10 ▶ View Solution
      1. C = 50 − 3d ▶ View Solution
      2. Day 16 (≈ 16.7 days) ▶ View Solution
      1. V = 200t ▶ View Solution
      2. 15 minutes ▶ View Solution

  5. Substituting into Rules

    1. 0, 12, 24 ▶ View Solution
    2. 7, 13, 19 ▶ View Solution
    3. 10, 4, −2 ▶ View Solution
    4. 1, 2.5, 4 ▶ View Solution
    5. −3, 6, 15 ▶ View Solution
    6. 20, 11, 2 ▶ View Solution

  6. Rate of Change

    1. 5; increasing ▶ View Solution
    2. −3; decreasing ▶ View Solution
    3. 1; increasing ▶ View Solution
    4. −1; decreasing ▶ View Solution
    5. 0; constant (neither increasing nor decreasing) ▶ View Solution
    6. 0.5; increasing ▶ View Solution
    7. −10; decreasing ▶ View Solution
    8. 4; increasing ▶ View Solution

  7. Proportional Relationships

    1. Yes — k = 3 ▶ View Solution
    2. No — does not pass through the origin (y-intercept = 2) ▶ View Solution
    3. Yes — y = 3x; k = 3 ▶ View Solution
    4. No — not proportional; rule: y = 3x + 1 ▶ View Solution
    5. Same rate of change (4); y = 4x starts at 0, y = 4x + 5 starts at 5 when x = 0 ▶ View Solution
    6. Yes — d = 80t; k = 80 km/h (speed) ▶ View Solution

  8. Interpreting Tables and Rules

    1. 10 = fixed monthly fee; 2 = cost per GB of data ▶ View Solution
    2. Equal at x = 1; y = 5x + 3 gives larger y for x > 1 ▶ View Solution
    3. y = 3x + 8 ▶ View Solution
    4. y = −2x + 6 and y = 8 − 3x ▶ View Solution

  9. Creating Tables from Contexts

    1. H = 20 − 2t; table: 20, 18, 16, 14, 12, 10; burns out at t = 10 hours ▶ View Solution
    2. M = 12b; table: 0, 12, 24, 36, 48, 60; 5 batches for 60 muffins ▶ View Solution
    3. D = 5 − 3t; home at t ≈ 1 h 40 min ▶ View Solution
    4. A: W = 4t; B: W = 2t + 6; equal at t = 3 hours ▶ View Solution

  10. Modelling Extended Contexts

    1. D = 12t + 10; at t = 1.5 h: 28 km; reaches 46 km at t = 3 hours ▶ View Solution
    2. Deposit: B = 200 + 50w; reaches $700 after 10 weeks  |  Withdrawal: B = 200 − 30w; hits $0 after approx. 7 weeks ▶ View Solution
    3. C = 15n + 300; max 30 students; cost per student = $25 ▶ View Solution
    4. Equal at 150 texts; Plan Y cheaper for 200 texts ▶ View Solution