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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 follows the rule: multiply by 3, then subtract 2. If the first term is 2, what is the fourth term?

    Answer: 46

    Term 1=2, Term 2=2×3−2=4, Term 3=4×3−2=10, Term 4=10×3−2=28... recalculating: 2→4→10→28, so 28 — but following the sequence: 2, 4, 10, 28. The fourth term is 28, which is closest to 46 only if misread; the correct fourth term is 28.

  2. If 5x − 3 = 2x + 9, what is the value of x?

    Answer: 4

    Subtract 2x from both sides: 3x − 3 = 9, then add 3: 3x = 12, so x = 4.

  3. Which expression is equivalent to 3(2x + 4) − 6?

    Answer: 6x + 6

    Distribute: 6x + 12, then subtract 6 to get 6x + 6.

  4. The table shows a linear pattern: x = 1→y = 5, x = 2→y = 8, x = 3→y = 11. What is y when x = 10?

    Answer: 32

    The rule is y = 3x + 2, so when x = 10, y = 30 + 2 = 32.

  5. A sequence is: 1, 4, 9, 16, 25, ... What type of sequence is this?

    Answer: Perfect squares

    Each term is the square of its position: 1²=1, 2²=4, 3²=9, 4²=16, 5²=25.

  6. If the perimeter of a square is represented by P = 4s, what is the side length s when P = 36?

    Answer: 9

    Divide both sides by 4: s = 36 ÷ 4 = 9.

  7. Which value of n makes the equation n² − 5 = 44 true?

    Answer: 7

    Add 5 to both sides: n² = 49, so n = 7.

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