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CAEC: Math: patterns and algebra

Extending patterns, writing and solving linear equations from word problems, rearranging and using formulas, and logical number reasoning.

  • 16 questions
  • Topic drill
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Math: patterns and algebra · Question 1Score 0/0

Kai has $36 saved and adds $12 each week. After how many weeks will he have $120?

Study reference: CAEC Test Outcomes and Evaluation Plan by Subject (Alberta.ca, 2024), Ch. 4 Mathematics — Part II: Patterns and relations, outcomes 2.1–2.4 (p. 4)

All 16 questions in this test

Every question and its answer choices. The correct answers and explanations appear when you take the test above.

  1. Kai has $36 saved and adds $12 each week. After how many weeks will he have $120?

    1. 13
    2. 7
    3. 10
    4. 4

  2. Which equation describes: "Four less than twice a number is 18"?

    1. 2n + 4 = 18
    2. 4 − 2n = 18
    3. 2n − 4 = 18
    4. 2(n − 4) = 18

  3. Evaluate 4a − 2b when a = 3 and b = −5.

    1. -22
    2. 2
    3. 1
    4. 22

  4. A taxi charges $12 plus $0.25 per minute of waiting. Which expression gives the cost for m minutes?

    1. 0.25(12 + m)
    2. 12m + 0.25
    3. 12 + 0.25m
    4. 12.25m

  5. Solve the linear equation 3x + 25 = 85.

    1. x = 36.7
    2. x = 30
    3. x = 60
    4. x = 20

  6. Figure 1 uses 4 toothpicks, figure 2 uses 7 and figure 3 uses 10. How many toothpicks are in figure 6?

    1. 16
    2. 22
    3. 19
    4. 24

  7. Two numbers add to 48. One is 6 more than the other. What is the smaller number?

    1. 42
    2. 21
    3. 27
    4. 24

  8. A pattern starts at 5 and adds 3 each time. Which rule gives the nth term?

    1. 5n + 3
    2. n + 3
    3. 3n + 5
    4. 3n + 2

  9. A table shows x = 1, 2, 3 and y = 7, 9, 11. Which rule fits?

    1. y = 7x
    2. y = x + 6
    3. y = 2x + 5
    4. y = 3x + 4

  10. Find the missing term in the doubling pattern 3, 6, 12, 24, ___.

    1. 27
    2. 36
    3. 30
    4. 48

  11. Phone plan A costs $30 plus $5 per GB. Plan B costs $50 plus $1 per GB. At how many GB do they cost the same?

    1. 10 GB
    2. 20 GB
    3. 5 GB
    4. 4 GB

  12. What is the next number in the pattern 7, 11, 15, 19, …?

    1. 23
    2. 27
    3. 24
    4. 21

  13. Use F = 9/5 C + 32 to convert 25 °C to degrees Fahrenheit.

    1. 59 °F
    2. 45 °F
    3. -3.9 °F
    4. 77 °F

  14. Use P = 2(l + w) to find the perimeter of a rectangle 14 m long and 9 m wide.

    1. 46 m
    2. 126 m
    3. 23 m
    4. 32 m

  15. A plumber charges a $40 call-out fee plus $15 per half-hour. The bill is $115. How many half-hours did she work?

    1. 10
    2. 7.7
    3. 5
    4. 3

  16. Rearrange the formula d = st to make t the subject.

    1. t = d − s
    2. t = d ÷ s
    3. t = s ÷ d
    4. t = d × s

Math: patterns and algebra: key rules to remember

Our summary of what the official handbook says on this topic, in our own words. Read it before or after the practice questions above, then check the original chapter. Read the official chapter ↗

Part II Patterns and relations (10–20 %)

  • 2.1 interpret and extend patterns and relationships.
  • 2.2 write and solve linear equations that model real situations.
  • 2.3 apply and manipulate a given equation or formula.
  • 2.4 analyze and solve problems with numerical and logical reasoning.

Method notes

  • Arithmetic pattern: constant difference d; nth term = d·n + (first term − d).
  • Geometric pattern: multiply by a constant ratio.
  • Equation from words: fixed fee + rate × quantity = total.
  • Solve by undoing operations in reverse order; check by substitution.
  • Rearranging d = st gives t = d ÷ s; F = 9/5 C + 32.

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