Practice Maths

Modelling Relationships — Review Answers

  1. Rules and Tables:

    1. y = 3x + 4 ▶ View Solution
    2. 2, 7, 12, 17, 22 ▶ View Solution
    3. y = 7x ▶ View Solution
    4. y = 3x: Yes — passes through origin; y = 3x + 2: No — y-intercept ≠ 0 ▶ View Solution

  2. Linear or Non-Linear:

    1. Linear — constant difference of 4 ▶ View Solution
    2. Non-linear — differences 1, 3, 5 are not constant ▶ View Solution
    3. Linear — constant difference of 2 ▶ View Solution
    4. Non-linear — values double each time ▶ View Solution

  3. Gradient and y-intercept:

    1. 4x − 3: gradient = 4; −2x + 8: gradient = −2 ▶ View Solution
    2. 4x − 3: y-intercept = −3; −2x + 8: y-intercept = 8 ▶ View Solution
    3. 4x − 3: y = 9; −2x + 8: y = 2 ▶ View Solution
    4. 4x − 3: x = ¾; −2x + 8: x = 4 ▶ View Solution

  4. Writing Rules from Context:

    1. V = 200t; after 15 minutes: 3 000 litres ▶ View Solution
    2. C = 0.25k + 50; cost for 120 km: $80 ▶ View Solution
    3. E = 12h; to earn $90: 7.5 hours ▶ View Solution
    4. H = −2t + 20; burns out at t = 10 hours ▶ View Solution

  5. Problem Solving:

    1. 100 texts: Plan A ($40) cheaper; 200 texts: equal ($55 each); equal at 200 texts per month ▶ View Solution
    2. a = 3, b = 5; rule: y = 3x + 5; y = 35 when x = 10 ▶ View Solution
    3. Parallel lines (same gradient 3); y = 3x + 5 is higher; at x = 4: y = 17 and y = 10 ▶ View Solution
    4. x = 4: y = 16; x = 5: y = 25; non-linear; rule: y = x² ▶ View Solution

  • Read Values from a Rule:

    1. C = 10 ▶ View Solution
    2. C = 34 ▶ View Solution
    3. n = 10 ▶ View Solution
    4. The 10 represents the fixed base cost (flat fee regardless of items bought) ▶ View Solution

  • Direct Proportion:

    1. k = 7; y = 7x ▶ View Solution
    2. y = 49 ▶ View Solution
    3. S = 0.3F ▶ View Solution
    4. 225 g ▶ View Solution

  • Comparing Linear Rules:

    1. A: C = 80h + 60; B: C = 60h + 100 ▶ View Solution
    2. A: $300; B: $280 ▶ View Solution
    3. Equal at h = 2 hours ▶ View Solution
    4. Choose B (5 hours: A = $460, B = $400) ▶ View Solution

  • Interpret a Graph:

    1. Gradient = 30 ▶ View Solution
    2. Speed = 30 km/h ▶ View Solution
    3. d = 30t ▶ View Solution
    4. 195 km ▶ View Solution

  • Graph Features:

    1. y-intercept = 8 (initial water level); x-intercept = 4 (tank empty at t = 4 hours) ▶ View Solution
    2. Parallel lines (same gradient 2); they never intersect ▶ View Solution
    3. y = −3x + 15; x-intercept = 5 ▶ View Solution