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Algebra and Patterns Flashcards

7 cards from real ICAS practice questions. Tap to flip, then mark Knew It or Still Learning — missed cards come back until you master them.

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  1. A pattern of dots forms rows: row 1 has 1 dot, row 2 has 3 dots, row 3 has 5 dots. How many dots are in row 10?

    Answer: 19

    The nth row has 2n − 1 dots; for row 10: 2(10) − 1 = 19.

  2. Which pair of values (x, y) satisfies both equations: y = 2x and y = x + 5?

    Answer: (5, 10)

    Set 2x = x + 5, so x = 5 and y = 10; check: 10 = 5 + 5 ✓.

  3. The expression 5x − 2(x − 3) simplifies to:

    Answer: 3x + 6

    Distribute −2: 5x − 2x + 6 = 3x + 6.

  4. A sequence is defined by: T(1) = 5 and T(n) = T(n−1) + 4. What is T(6)?

    Answer: 25

    T(1)=5, T(2)=9, T(3)=13, T(4)=17, T(5)=21, T(6)=25.

  5. If the area of a rectangle is A = lw and l = 2w, which equation represents the area in terms of w only?

    Answer: A = 2w²

    Substitute l = 2w into A = lw: A = (2w)(w) = 2w².

  6. What is the next term in the pattern: 1, 1, 2, 3, 5, 8, 13, ___?

    Answer: 21

    Each term is the sum of the two preceding terms (Fibonacci): 8 + 13 = 21.

  7. If 2(3x + 1) = 4x + 10, what is x?

    Answer: 4

    Expand: 6x + 2 = 4x + 10, subtract 4x: 2x + 2 = 10, so 2x = 8 and x = 4.

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