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

1 Exponent rules / 4 pts

Simplify. In part d, write the answer with positive exponents.

1. \(n^8\cdot n^5\)
2. \((4b^3)^2\)
3. \(\dfrac{28p^9}{7p^4}\)
4. \(3k^{-4}m\)

2 Scientific notation / 3 pts

1. Write 0.000062 in scientific notation.
2. Write 83,000,000 in scientific notation.
3. Compute \((2.5\times 10^6)(4\times 10^2)\) and give the result in scientific notation.

3 Classifying a polynomial / 3 pts

Consider \(3x - 8 + 5x^3\).

1. Write it in standard form.
2. Give its degree and its leading coefficient.
3. Is it a monomial, a binomial or a trinomial?

4 Adding and subtracting / 3 pts

Let \(A = 5x^2 - 2x + 1\) and \(B = x^2 + 6x - 4\). Compute

1. \(A + B\)
2. \(A - B\)

5 Multiplying polynomials / 4 pts

Expand and simplify.

1. \(3x(2x^2 + x - 6)\)
2. \((x+8)(x-3)\)
3. \((x-1)(x^2 + 2x + 3)\)

6 Special products / 3 pts

Expand using a special product.

1. \((x+10)^2\)
2. \((3x-4)^2\)
3. \((6x+5)(6x-5)\)