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Math 7

Math 7 · Worksheets

Patterns and expressions

Ten questions of mixed difficulty, covering Patterns and expressions. Print it, or work through it on screen — the answer key starts on its own page.

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Patterns and expressions

Math 7 · maddyhelps.com

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Circle the best answer for each question. Show your work in the space provided.

  1. A pattern has 3, 5, 7 and 9 squares in figures 1, 2, 3 and 4. How many squares are in figure 6?

    1. a) 15
    2. b) 13
    3. c) 11
    4. d) 18

  2. Evaluate 4n − 3 when n = 5.

    1. a) 42
    2. b) 17
    3. c) 8
    4. d) 6

  3. A table of values has x = 2, 4, 6, 8 and y = 7, 13, 19, 25. What is y when x = 20?

    1. a) 61
    2. b) 70
    3. c) 121
    4. d) 97

  4. In a table of values, y goes up by 4 each time x goes up by 1, and y = 3 when x = 0. What is y when x = 10?

    1. a) 13
    2. b) 40
    3. c) 43
    4. d) 70

  5. A table of values has x = 1, 2, 3, 4 and y = 5, 8, 11, 14. Which equation matches the table?

    1. a) y = 5x
    2. b) y = 3x + 5
    3. c) y = 3x + 2
    4. d) y = x + 4

  6. Which of these is an equation?

    1. a) 3x + 2 = 11
    2. b) 3x + 2 + 11
    3. c) 5 + 2y − 8
    4. d) 4n − 7 + n

  7. Evaluate n/4 + 5 when n = 12.

    1. a) 4.25
    2. b) 17
    3. c) 8
    4. d) 53

  8. Which expression means 'seven less than three times a number n'?

    1. a) 7 − 3n
    2. b) 3n − 7
    3. c) 3n + 7
    4. d) 3(n − 7)

  9. A bowling alley charges $3 to rent shoes plus $6 for each game. Which expression gives the cost, in dollars, of g games?

    1. a) 9g
    2. b) g + 9
    3. c) 3g + 6
    4. d) 6g + 3

  10. Which statement about 2x + 5 and 2x + 5 = 17 is true?

    1. a) Both are equations, because both of them contain the variable x.
    2. b) Both are expressions, because neither one gives a value for x.
    3. c) The first is an expression; the second is an equation with one solution.
    4. d) The first can be solved for x; the second can only be evaluated.

Answer key · Patterns and expressions

Math 7 · maddyhelps.com

  1. b) 13 — The pattern adds 2 squares each time, so figure 5 has 11 and figure 6 has 13 — or use the rule 2n + 1: 2 × 6 + 1 = 13. Answering 18 multiplies figure 1's 3 squares by 6, but the pattern grows by 2 each time, not 3.
  2. b) 17 — 4n means 4 × n, so 4 × 5 − 3 = 20 − 3 = 17. Writing the 5 next to the 4 gives 45 − 3 = 42; the variable stands for a number that is multiplied by 4, not a missing digit.
  3. a) 61 — x goes up by 2 each time, not 1, so y goes up 6 for every 2 — that is 3 for each 1 — and the relation is y = 3x + 1: 3 × 20 + 1 = 61. Treating the 6 as the change for each 1 gives y = 6x + 1 and 121, or 97 if you keep adding 6 from x = 8.
  4. c) 43 — Start at 3 and add 4 ten times: 3 + 4 × 10 = 43, so the relation is y = 4x + 3. 40 forgets the starting value of 3. 70 multiplies the value at x = 1, which is 7, by 10 — that only works when the graph goes through (0, 0).
  5. c) y = 3x + 2 — y goes up 3 each time x goes up 1, so the equation has 3x, and when x = 1, 3 × 1 = 3 needs 2 more to make 5. y = x + 4 and y = 5x work for the first row only — check every row, not just one. y = 3x + 5 gives 8 when x = 1.
  6. a) 3x + 2 = 11 — An equation says two things are equal, so it has an equal sign, and you can solve it: here x = 3. The others are expressions — they have no equal sign, and you evaluate them for a value of the variable instead of solving them.
  7. c) 8 — Divide first: 12 ÷ 4 = 3, then add 5 to get 8. 53 multiplies by 4 instead of dividing, and 4.25 adds before dividing, (12 + 5) ÷ 4 — but here the 4 divides only the n.
  8. b) 3n − 7 — Three times the number is 3n, and seven less than that takes 7 away from it: 3n − 7. Writing 7 − 3n follows the order of the words, but 'seven less than' means take 7 away from the other amount — just as 7 less than 10 is 10 − 7 = 3.
  9. d) 6g + 3 — The $6 is paid for every game, so it multiplies g; the $3 for shoes is paid once, so it is added on its own. Swapping them gives 3g + 6, and 9g charges for shoes again with every game.
  10. c) The first is an expression; the second is an equation with one solution. — 2x + 5 has no equal sign, so it is an expression, with a value for any x you choose — 7 when x = 1, 15 when x = 5. Adding = 17 makes an equation, which is true only when x = 6. A variable does not make something an equation; the equal sign does.