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Exponent Rules and Polynomials: math test solutions, Grade 9 – download the PDF

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Test solutions Grade 9 : Exponent Rules and Polynomials — Zyro the alien explorer of Planète Maths

Test solutions with the detailed point scale. Add up your points and spot what to review.

Suggested time: 45 minutes. Out of 20 points. Calculator allowed only when the problem says so.

1 Exponent rules / 4 pts

  1. \(n^{13}\) (1 pt)
  2. \(16b^6\) (1 pt)
  3. \(4p^5\) (1 pt)
  4. \(\dfrac{3m}{k^4}\) (1 pt)

2 Scientific notation / 3 pts

  1. \(6.2\times 10^{-5}\) (1 pt)
  2. \(8.3\times 10^{7}\) (1 pt)
  3. \(2.5\cdot 4 = 10\), so \(10\times 10^{8} = 1\times 10^{9}\) (1 pt)

3 Classifying a polynomial / 3 pts

  1. \(5x^3 + 3x - 8\) (1 pt)
  2. Degree 3, leading coefficient 5 (1 pt)
  3. Three terms: a trinomial (1 pt)

4 Adding and subtracting / 3 pts

  1. \(6x^2 + 4x - 3\) (1 pt)
  2. \(5x^2 - 2x + 1 - x^2 - 6x + 4 = 4x^2 - 8x + 5\) (2 pts: 1 for the sign change, 1 for the result)

5 Multiplying polynomials / 4 pts

  1. \(6x^3 + 3x^2 - 18x\) (1 pt)
  2. \(x^2 - 3x + 8x - 24 = x^2 + 5x - 24\) (1 pt)
  3. \(x^3 + 2x^2 + 3x - x^2 - 2x - 3 = x^3 + x^2 + x - 3\) (2 pts: 1 for the distribution, 1 for combining like terms)

6 Special products / 3 pts

  1. \(x^2 + 20x + 100\) (1 pt)
  2. \(9x^2 - 24x + 16\) (1 pt)
  3. \(36x^2 - 25\) (1 pt)
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