Topic Review — Patterns & Algebra

Review Questions

1. Write algebraic expressions for each of the following: Fluency

   1. 5 more than x
   2. 3 times x minus 7
   3. x divided by 4 plus 2
   4. double n plus 9

2. Evaluate each expression when y = 4: Fluency

   1. 3y + 2
   2. y² − 1
   3. 10 − 2y
   4. 5y ÷ 2
   5. 4y + 3y

3. Complete the table for the rule y = 2x + 3: Fluency

   x	1	2	3	4	5
   y

4. Find the rule for this input/output table: Understanding

   Input (x)	1	2	3	4	10
   Output (y)	4	7	10	13

   1. Describe the pattern of output numbers in words.
   2. Write an algebraic rule for y in terms of x.
   3. What is the output when x = 10?

5. Fence post pattern: 1 panel needs 2 posts, 2 panels need 3 posts, 3 panels need 4 posts. Understanding

   1. Complete the table for t = 1 to 5 panels:

      Panels (t)	1	2	3	4	5
      Posts (p)

   2. Write a rule for the number of posts p in terms of the number of panels t.
   3. How many posts are needed for 20 panels?

6. Taxi fare: a taxi charges a $3.50 flat fee plus $1.80 per kilometre. Problem Solving

   1. Write an expression for the total cost C in terms of the number of kilometres k.
   2. What is the cost for an 8 km trip?
   3. What is the maximum number of whole kilometres you can travel for $30?

7. Simplify each expression by collecting like terms: Fluency

   1. 3x + 5x
   2. 7y − 2y + y
   3. 4a + 3b + 2a − b
   4. 5m − 3m + 6

8. Evaluate each expression when a = 3 and b = 5: Fluency

   1. 2a + b
   2. ab − 4
   3. 3b − 2a
   4. a² + b

9. Tile pattern: each new row of a tile arrangement adds 4 tiles to the previous row. The first row has 3 tiles. Understanding

   1. How many tiles are in the 2nd, 3rd, and 4th rows?
   2. Write a rule for the number of tiles T in the nth row.
   3. Which row has exactly 27 tiles?

10. Mobile phone plan: a plan charges a $20 monthly fee plus $0.05 per text message. Understanding

    1. Write an expression for the monthly cost C in terms of the number of texts t.
    2. What is the cost if you send 300 texts in a month?
    3. A student has a budget of $35 per month. What is the maximum number of texts they can send?

11. Two patterns: Pattern A starts at 10 and increases by 3 each step. Pattern B starts at 2 and increases by 5 each step. Problem Solving

    1. Write a rule for each pattern in terms of the step number n.
    2. At which step number do the two patterns give the same value?
    3. Which pattern grows faster? How can you tell from the rules?