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Eleventh Grade (Grade 11) Function and Algebra Concepts Questions

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Grade 11 Complex Numbers CCSS: HSN-CN.A.2
Add the complex numbers. [math](-3+7i) + (3 - i)[/math]
  1. [math]6i[/math]
  2. [math]6 + 8i[/math]
  3. [math]-6 + 6i[/math]
  4. [math]6 + 6i[/math]
Grade 11 Polynomials and Rational Expressions CCSS: HSN-CN.C.9
Looking at the graph of a quadratic polynomial, roots or zeros correspond to where the graph crosses the x-axis. When the graph just touches the x-axis, this corresponds to a double root. The Fundamental Theorem of Algebra states that a quadratic polynomial will always have 2 roots. How is this reconciled with a quadratic polynomial whose graph does not intersect the x-axis?
  1. Quadratic polynomials always intersect the x-axis.
  2. If a quadratic polynomial doesn't cross the x-axis it is no longer a polynomial, and the Fundamental Theorem of Algebra no longer applies.
  3. When a quadratic polynomial doesn't cross the x-axis, this simply implies that its roots are complex with non-zero imaginary parts.
  4. Simply translate the quadratic polynomial till it does cross the x-axis.
Grade 11 Polynomials and Rational Expressions CCSS: HSN-CN.C.9
Jeremy is working with the Fundamental Theorem of Algebra, and thinks he's found an exception. Looking at [math]f(x) = 4(x-1)^2[/math], this will result in only one root, [math]x=1[/math]. Therefore, despite this being a second degree polynomial, there is only one root. Is this correct?
  1. Yes, this is a known exception.
  2. No, this is not a polynomial, it is a quadratic function.
  3. No, if the quadratic formula is used, the other root is found.
  4. No, this root has multiplicity of 2, which means it counts as two roots.
Grade 11 Complex Numbers CCSS: HSN-CN.A.2
Evaluate. [math](5 - 6i) - (-3 + 9i)[/math]
  1. [math]2 + 3i[/math]
  2. [math]2 - 3i[/math]
  3. [math]8 - 15i[/math]
  4. [math]8 + 3i[/math]
Grade 11 Complex Numbers CCSS: HSN-CN.A.3
Divide the complex numbers. [math](-13+i) / (4+4i[/math]
  1. [math]"Undefined"[/math]
  2. [math]-13/4 + 1/4 i[/math]
  3. [math]- 3/2 + 7/4 i[/math]
  4. [math] -7/4 + 7/4 i[/math]
Grade 11 Vectors CCSS: HSN-VM.B.4, HSN-VM.B.4c
For vectors [math]vec{v}[/math] and [math]vec{w}[/math], if one were to find [math]vec{w} - vec{v}[/math] graphically, which of the following could be true? Choose all that apply.
  1. The heads of the vectors would be touching.
  2. The tails of the vectors would be touching.
  3. The head of vector [math]vec{w}[/math] would touch the tail of vector [math]vec{v}[/math].
  4. The head of vector [math]vec{v}[/math] would touch the tail of vector [math]vec{w}[/math].
Grade 11 Complex Numbers CCSS: HSN-CN.A.3
Evaluate. [math](9-3i) / (-6-3i)[/math]
  1. [math]0[/math]
  2. [math]-1+i[/math]
  3. [math]1-i[/math]
  4. [math]-5/3 + 5/3 i[/math]
Grade 11 Complex Numbers CCSS: HSN-CN.B.6
What is the distance between the complex numbers [math]2-4i[/math] and [math]-3/2 - 1/2 i[/math] in the complex plane?
  1. [math]7/2 sqrt(2)[/math]
  2. [math]1/2sqrt(130)[/math]
  3. [math]5/2 sqrt(2)[/math]
  4. [math]1/8 sqrt(82)[/math]
Grade 11 Complex Numbers CCSS: HSN-CN.A.3
Divide the complex numbers. [math](8-8i) / (2-2i)[/math]
  1. [math]"Undefined"[/math]
  2. [math]0[/math]
  3. [math]4[/math]
  4. [math]4-4i[/math]
Grade 11 Complex Numbers CCSS: HSN-CN.A.3
Evaluate. [math]3/(6i)[/math]
  1. [math]1/2 i[/math]
  2. [math]1+1/2 i[/math]
  3. [math]-1/2[/math]
  4. [math]-1/2 i[/math]
Grade 11 Complex Numbers CCSS: HSN-CN.A.2
Write the expression as a complex number in standard form.

[math](3 - 5i)(1 + 3i)[/math]
  1. [math]3 - 15i[/math]
  2. [math]-2i + 4i[/math]
  3. [math]18 + 4i[/math]
  4. [math]15 - 2i[/math]
Grade 11 Polynomials and Rational Expressions CCSS: HSA-APR.A.1
What is the product [math](x + 5)(x^3 - 2x -3)?[/math]
  1. [math]x^4 + 5x^3 - 2x^2 - 7x -15[/math]
  2. [math]x^4 + 5x^3 - 2x^2 - 13x - 15[/math]
  3. [math]x^4 + 5x^3 - 2x^2 - 10x - 15[/math]
  4. [math]x^4 + 5x^3 - 2x^2 - 3x - 15[/math]
Grade 11 Exponents CCSS: HSN-RN.A.2
Evaluate. [math](1/27)^(-2/3)[/math]
  1. -3
  2. 9
  3. [math]1/3[/math]
  4. [math]-1/9[/math]
Grade 11 Complex Numbers CCSS: HSN-CN.B.6
Find the distance between [math]z = 6 + 7i[/math] and [math]w = -2 - 3i[/math] in the complex plane.
  1. [math]4sqrt(2)[/math]
  2. [math]18[/math]
  3. [math]2sqrt(2)[/math]
  4. [math]2sqrt(41)[/math]
Grade 11 Quadratic Equations and Expressions
What is the simplified form of [math](3x^3y^-4)^-2?[/math]
Exponent answers must have positive exponents in them.
  1. [math]y^8/(6x^-2)[/math]
  2. [math](9y^8)/(x^6)[/math]
  3. [math](y^8)/(9x^6)[/math]
  4. [math](y^8)/(9x^-6)[/math]
Grade 11 Systems of Equations CCSS: HSA-REI.C.6
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