Mathematics Standard • Year 11 • Module 1 • Lesson 9
Coordinates, Tables and Linear Patterns
Practise HSC-style writing on tables, ordered pairs and linearity — three multi-mark short answers and one extended response with marking criteria.
1. Short-answer questions
1.1 Write the ordered pairs for inputs 0, 1, 2, 3 and outputs 8, 13, 18, 23. Show that the table is linear and state the constant difference. 3 marks Band 3
1.2 A savings table is $50, $65, $80, $95 for weeks 0, 1, 2, 3. (a) Write the ordered pairs. (b) Predict the savings at week 4. (c) Predict the savings at week 10. 3 marks Band 3-4
1.3 Outputs 1, 4, 9, 16 correspond to inputs 1, 2, 3, 4.
(a) Calculate the differences between consecutive outputs.
(b) Explain whether this table is linear, justifying with the differences.
(c) Describe in one sentence what kind of pattern is producing these outputs. 4 marks Band 4
2. Extended response
2.1 A water-tank fill is monitored at a Sydney depot. The table records litres in the tank at minute readings 0, 1, 2, 3 and the manager is unsure if the pump's flow rate is constant.
Time (min): 0, 1, 2, 3, 4
Volume (L): 200, 245, 290, 335, 380
(a) Write the five ordered pairs in the form (time, volume).
(b) Calculate the four minute-to-minute differences in volume.
(c) State whether the pump's flow is constant (linear) and quote the per-minute rate as part of your justification.
(d) The tank's capacity is 600 L. Use the constant rate to predict at what time (in minutes from start) the tank reaches 600 L, and write a one-sentence operations message the manager could send to the staff. 7 marks Band 5-6
Explicit marking criteria
Part (a) — 1 mark
• 1 mark — all five pairs correct: (0, 200), (1, 245), (2, 290), (3, 335), (4, 380).
Part (b) — 1 mark
• 1 mark — all four differences +45 L each.
Part (c) — 2 marks
• 1 mark — states linear because all four differences are equal.
• 1 mark — names the rate as 45 L/min (with units).
Part (d) — 3 marks
• 1 mark — sets up the equation 200 + 45t = 600 (or equivalent).
• 1 mark — solves to t = 400/45 ≈ 8.89 min (accept 8.9 or 8 min 53 s).
• 1 mark — clear operations message stating when the tank will be full.
Your response:
Stuck on (d)? Capacity minus starting volume = 600 − 200 = 400 L still needed. At 45 L/min that takes 400/45 minutes.How did this worksheet feel?
What I'll revisit before next class:
1.1 — Pairs, linearity and rate (3 marks)
Sample response.
Pairs: (0, 8), (1, 13), (2, 18), (3, 23).
Differences: +5, +5, +5 — all equal, so the table is linear with a constant difference of +5 per input step.
Marking notes. 1 mark — pairs correct. 1 mark — differences calculated. 1 mark — explicit conclusion "linear, +5/step".
1.2 — Savings predictions (3 marks)
Sample response.
(a) (0, 50), (1, 65), (2, 80), (3, 95). (Differences +15 each step, so linear at +$15/week.)
(b) Week 4: 95 + 15 = $110.
(c) Week 10: 50 + 10(15) = 50 + 150 = $200.
Marking notes. 1 mark — pairs correct. 1 mark — week 4 prediction. 1 mark — week 10 prediction using the rate, not 7 more adds.
1.3 — Square-number table (4 marks)
(a) Sample response. Differences: 4 − 1 = +3, 9 − 4 = +5, 16 − 9 = +7.
(b) Sample response. Differences are +3, +5, +7 — NOT equal, so the table is not linear. Linear requires a single constant difference.
(c) Sample response. The outputs are square numbers (1², 2², 3², 4²), so this is a quadratic pattern, not linear.
Marking notes. 1 mark — all three differences correct. 1 mark — clear statement that not equal → not linear. 1 mark — quadratic / square-number identification. 1 mark — overall justification ties the differences to the conclusion.
2.1 — Sydney depot tank fill (7 marks): sample Band-6 response with annotations
Sample Band-6 response.
(a) Ordered pairs.
(0, 200), (1, 245), (2, 290), (3, 335), (4, 380). [1 mark.]
(b) Minute-to-minute differences.
245 − 200 = +45, 290 − 245 = +45, 335 − 290 = +45, 380 − 335 = +45. All four differences are +45 L. [1 mark.]
(c) Constant rate?
Because all four minute-to-minute differences are equal, the table is linear, so the pump's flow rate is constant. [1 mark — linearity statement.]
The rate is 45 L per minute. [1 mark — rate with units.]
(d) Predicting full tank.
Set 200 + 45t = 600. [1 mark — correct equation.]
45t = 400 → t = 400/45 ≈ 8.89 minutes (about 8 min 53 s). [1 mark — correct value.]
Operations message: "Tank started at 200 L at time 0. Pumping continues at 45 L/min, so it will reach the 600 L capacity at about 8 min 53 s — please prepare to switch off the pump." [1 mark — clear message including time and capacity.]
Total: 7/7.
Band descriptors for marker.
Band 3: Writes the pairs and identifies "going up by 45" but does not link to "linear" or include units in the rate. ≈ 2-3 marks.
Band 4: (a)-(c) fully correct but (d) attempts only one calculation without the equation. ≈ 4-5 marks.
Band 5: (d) equation set up; t calculated correctly but no operations message. ≈ 5-6 marks.
Band 6: All parts complete with a clear, contextual operations message. 7/7.