Algebra: Test 1

10 questions · 15 minutes · scoring and calculator rules shown before you begin

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Algebra Test 1: questions and answers

Take the test first if you want an honest score. The answers and solutions below are folded away until you open them.

  1. 1. If 6x + 6 = 72, find x.
    1. 12
    2. 8
    3. 9
    4. 11

    Reference: q-8ab4389a-24 · Report this question

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    Answer: D. 11

    6x = 72 − 6 = 66, so x = 11.
  2. 2. Find (6 + 5)² − (6 − 5)².
    1. 120
    2. 126
    3. 122
    4. 114

    Reference: q-901be797-26 · Report this question

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    Answer: A. 120

    Use (a+b)² − (a−b)² = 4ab = 4×6×5 = 120.
  3. 3. If x = 3 and y = 2, find x² + 2xy + y².
    1. 23
    2. 31
    3. 19
    4. 25

    Reference: q-dcea9106-40 · Report this question

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    Answer: D. 25

    x² + 2xy + y² = (x + y)² = (3 + 2)² = 25.
  4. 4. If x/3 = 9, find x.
    1. 29
    2. 30
    3. 28
    4. 27

    Reference: q-83643e1-20 · Report this question

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    Answer: D. 27

    Multiply both sides by 3: x = 3 × 9 = 27.
  5. 5. Which is the factorisation of x² − 9?
    1. x(3 − x)
    2. (x − 3)(x + 3)
    3. (x − 3)²
    4. (x + 3)²

    Reference: q-b00d2810-38 · Report this question

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    Answer: B. (x − 3)(x + 3)

    x² − a² = (x − a)(x + a), so the factorisation is (x − 3)(x + 3).
  6. 6. If 8x + 6 = 46, find x.
    1. 5
    2. 2
    3. 3
    4. 8

    Reference: q-d94e90d1-24 · Report this question

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    Answer: A. 5

    8x = 46 − 6 = 40, so x = 5.
  7. 7. Find (5 + 2)² − (5 − 2)².
    1. 34
    2. 36
    3. 40
    4. 42

    Reference: q-b733268f-26 · Report this question

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    Answer: C. 40

    Use (a+b)² − (a−b)² = 4ab = 4×5×2 = 40.
  8. 8. If x = 6 and y = 4, find x² + 2xy + y².
    1. 98
    2. 106
    3. 100
    4. 96

    Reference: q-6d224c5d-40 · Report this question

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    Answer: C. 100

    x² + 2xy + y² = (x + y)² = (6 + 4)² = 100.
  9. 9. If x/6 = 11, find x.
    1. 64
    2. 65
    3. 63
    4. 66

    Reference: q-552c3f-21 · Report this question

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    Answer: D. 66

    Multiply both sides by 6: x = 6 × 11 = 66.
  10. 10. Which is the factorisation of x² − 64?
    1. (x + 8)²
    2. (x − 8)²
    3. (x − 8)(x + 8)
    4. x(8 − x)

    Reference: q-73b40c43-39 · Report this question

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    Answer: C. (x − 8)(x + 8)

    x² − a² = (x − a)(x + a), so the factorisation is (x − 8)(x + 8).

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