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NY Regents Algebra II Mathematics — practice by topic

Browse 44 questions across 11 Mathematics topics. Choose what you want to revise, then open a question to check its answer and worked solution.

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Mathematics topics

Complex Numbers (6)Exponential and Logarithmic Models (5)Graphs of Polynomial Functions (5)Power and Polynomial Functions (5)Rational Functions (5)Zeros of Polynomial Functions (5)Properties of Logarithms (4)Quadratic Functions (4)Dividing Polynomials (3)Exponential and Logarithmic Equations (3)Fitting Exponential Models to Data (1)

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The imaginary unit i is defined as the square root of which number?Read the answer and worked solution →In the complex number 7 + 4i, which part is the real part?Read the answer and worked solution →For f(x) = a(x - h) squared + k, what does a size of a above 1 do to the graph?Read the answer and worked solution →What is the degree of a polynomial function?Read the answer and worked solution →

Worked practice questions

The imaginary unit i is defined as the square root of which number?

  1. Negative one
  2. Positive one
  3. Negative four
  4. Positive four
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Correct answer: A. Negative one

1. Square roots of negative numbers are not real numbers. 2. To handle them, one new number is defined as the square root of negative 1, and it is named i. 3. Squaring that definition gives i squared equal to negative 1, which is what makes the system work. _Source: OpenStax Precalculus (CC BY 4.0), section 3.1 Complex Numbers_

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In the complex number 7 + 4i, which part is the real part?

  1. The number 4i
  2. The number 7
  3. The number 4
  4. The number 11
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Correct answer: B. The number 7

1. Standard form for a complex number is a + bi. 2. In that form a is the real part and bi is the imaginary part. 3. Matching 7 + 4i against a + bi gives a equal to 7, so the real part is 7. _Source: OpenStax Precalculus (CC BY 4.0), section 3.1 Complex Numbers_

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For f(x) = a(x - h) squared + k, what does a size of a above 1 do to the graph?

  1. The graph becomes wider
  2. The graph shifts upward
  3. The graph becomes narrower
  4. The graph shifts sideways
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Correct answer: C. The graph becomes narrower

1. The number a in front of the squared bracket controls a vertical stretch. 2. A size above 1 pulls every point further from the horizontal axis. 3. So the parabola looks narrower, while a size below 1 makes it look wider. _Source: OpenStax Precalculus (CC BY 4.0), section 3.2 Quadratic Functions_

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