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Spacecraft Algebraic Patterns
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Spacecraft Algebraic Patterns
A spacecraft design team is testing patterns to predict how many parts they will need. In each rule, n is the stage number. Read each mission carefully, show your thinking, and use Australian dollars where needed.
Mission 1: Decode the patterns
The design team records parts by stage number. Use the stage number n to describe each pattern.
1.A spacecraft gains 4 solar panels at each stage. The first three counts are 6, 10, 14. What is the common difference?
2.The number of solar panels at stage n follows the pattern 6, 10, 14, 18, ... Which rule gives the number of panels, p?
- p = 4n + 2
- p = 6n + 4
- p = 2n + 4
- p = 4n + 6
3.A robot arm uses 7 bolts for each module. If b = 7n, how many bolts are needed for 8 modules?
4.Match each spacecraft part pattern to its algebraic rule. The first term is the count at stage 1.
- Fuel cells: 5, 8, 11, 14, ...
- Windows: 4, 8, 12, 16, ...
- Warning lights: 7, 9, 11, 13, ...
- 2n + 5
- 3n + 2
- 4n
5.A trainee says the rule 2n + 3 makes the sequence 5, 7, 9, 11, ... Is the claim true or false? Explain using the first two stages.
Mission 2: Predict and design
The team needs reliable predictions before building the next spacecraft.
6.A pattern follows the rule t = 3n + 1, where t is the number of thrusters. Complete the missing values for stages 1, 2, 3 and 6.
7.A probe carries 2, then 5, then 8, then 11 sample containers at stages 1 to 4. Use the grid to find the rule and the number of containers at stage 10. Write both answers on the answer lines.
Stage n
1
2
3
4
Containers c
2
5
8
11
8.A station’s inspection queue drops by 3 tasks each stage: 18, 15, 12, 9, ... Write a rule for the number of tasks, q, at stage n. Then find q at stage 6.
9.Each module needs 4 bolts, so the total for n modules is b = 4n. Bolts cost $2.50 each. What is the total bolt cost for 8 modules?
10.Invent a growing spacecraft-part pattern that starts with 3 parts at stage 1 and increases by 2 parts each stage. Write the first four terms, give a rule using n, and predict the count at stage 9.
Draw a small spacecraft component that shows your rule from the previous question. Label the stage number and part count.
3 printable pages
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