Representing Other Algebraic Relationships — Drills
Representing Other Algebraic Relationships has 6 drill skills. Each one generates fresh questions every time, with a hint and full worked steps, so you can keep practising a single skill until it settles.
What these drills cover
These questions use 5 ideas from the course. Follow any of them for a definition, where it is taught, and what it leads to.
- Rate — A ratio of two different units, like miles per hour or dollars per pound.
- Proportional — Two quantities with a constant ratio: yx = k always.
- Like terms — Terms with exactly the same variable part; only these can be combined.
- Distribute — Multiply a bracket out: 3(x + 4) = 3x + 12.
- Sequence — An ordered list of numbers. The nth one is an.
Combine
Unlimited questions of this kind are generated in the app. Two examples:
Problem 1
Simplify 8n + 3 + 6n - 9.
Worked answer
14n-6
8n + 6n = 14n
3 - 9 = -6
Answer: 14n - 6
Problem 2
Simplify 2y + 8 + 5y - 7.
Worked answer
7y+1
2y + 5y = 7y
8 - 7 = 1
Answer: 7y + 1
Distribute
Unlimited questions of this kind are generated in the app. Two examples:
Problem 1
Expand 7(4x - 4).
Worked answer
28x-28
7 × 4x = 28x
7 × (-4) = -28
28x - 28
Problem 2
Expand -2(8y + 3).
Worked answer
-16y-6
-2 × 8y = -16y
-2 × (3) = -6
-16y - 6
Evaluating
Unlimited questions of this kind are generated in the app. Two examples:
Problem 1
Evaluate 6x + 12 when x = 8.
Worked answer
60
6 × 8 = 48
48 + 12 = 60
Problem 2
Evaluate 8x + 9 when x = 1.
Worked answer
17
8 × 1 = 8
8 + 9 = 17
Pattern
Unlimited questions of this kind are generated in the app. Two examples:
Problem 1
A pattern goes 8, 16, 24, 32, …. Find the 12th term.
Worked answer
96
Step = 8
Rule: 8n + 0 (check n = 1 gives 8)
8(12) + 0 = 96
Problem 2
A pattern goes 6, 8, 10, 12, …. Find the 25th term.
Worked answer
54
Step = 2
Rule: 2n + 4 (check n = 1 gives 6)
2(25) + 4 = 54
Custom
Unlimited questions of this kind are generated in the app. Two examples:
Problem 1
Define a ★ b = 2a - 4b. Compute 6 ★ 5.
Worked answer
-8
2(6) - 4(5)
= 12 - 20 = -8
Problem 2
Define a ★ b = 3a - 3b. Compute 2 ★ 3.
Worked answer
-3
3(2) - 3(3)
= 6 - 9 = -3
Inverses
Unlimited questions of this kind are generated in the app. Two examples:
Problem 1
6 workers finish a job in 12 days. At the same rate, how many days would 18 workers take?
Worked answer
4
Total work: 6 × 12 = 72 worker-days
72 ÷ 18 = 4 days
Notice the product stays constant: xy = 72.
Problem 2
3 workers finish a job in 18 days. At the same rate, how many days would 9 workers take?
Worked answer
6
Total work: 3 × 18 = 54 worker-days
54 ÷ 9 = 6 days
Notice the product stays constant: xy = 54.