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Common Core Standard HSA-APR.C.5 Questions

(+) Know and apply the Binomial Theorem for the expansion of (x + y)n in powers of x and y for a positive integer n, where x and y are any numbers, with coefficients determined for example by Pascal’s Triangle.1

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Grade 11 Polynomials and Rational Expressions CCSS: HSA-APR.C.5
Find the 4th term in the expansion[math](1 + 5x)^8[/math].
  1. [math]17500x^3[/math]
  2. [math]4375x^3[/math]
  3. [math]7000x^3[/math]
  4. [math]3500x^3[/math]
Grade 11 Polynomials and Rational Expressions CCSS: HSA-APR.C.5
Expand the binomial [math](p−2q)^4[/math] using Pascal's Triangle.
  1. [math]p^4 − 8p^3q + 24p^2q^2 − 32pq^3 + 16q^4[/math]
  2. [math]p^4 − 4p^3q + 12p^2q^2 − 16pq^3 + 16q^4[/math]
  3. [math]p^4 − 8p^3q + 16p^2q^2 − 32pq^3 + 16q^4[/math]
  4. [math]p^4 − 8p^3q + 20p^2q^2 − 32pq^3 + 16q^4[/math]
Grade 11 Polynomials and Rational Expressions CCSS: HSA-APR.C.5
For the expansion of [math](x+y)^n[/math], the coefficient of the term [math]x^k y^(n-k)[/math] represents which of the following?
  1. The number of distinct sequences of k x’s and (n-k) y’s
  2. The sum of the exponents
  3. The number of ways to choose k positions for x out of n positions
  4. The combination value [math]((n), (k))[/math]
Grade 11 Polynomials and Rational Expressions CCSS: HSA-APR.C.5
Find the 3rd term in the expansion of [math]((1/2​)x−4)^5[/math].
  1. [math]−80x^3[/math]
  2. [math]20x^3[/math]
  3. [math]−40x^3[/math]
  4. [math]10x^3[/math]
Grade 11 Polynomials and Rational Expressions CCSS: HSA-APR.C.5
Expand the binomial [math](x+5)^3[/math] using Pascal's Triangle.
  1. [math]x³^3+ 15x^2 + 75x + 125[/math]
  2. [math]x³^3+ 10x^2 + 25x + 125[/math]
  3. [math]x³^3+ 15x^2 + 50x + 125[/math]
  4. [math]x³^3+ 5x^2 + 25x + 125[/math]
Grade 11 Polynomials and Rational Expressions CCSS: HSA-APR.C.5
Find the 3rd term in the expansion [math](1 - 2x)^7[/math].
  1. [math]84x^2[/math]
  2. [math]-84x^2[/math]
  3. [math]168x^2[/math]
  4. [math]-168x^2[/math]
Grade 11 Polynomials and Rational Expressions CCSS: HSA-APR.C.5
Find the 4th term in the expansion [math](2a - 5)^6[/math]
  1. [math]20000a^3[/math]
  2. -[math]20000a^3[/math]
  3. [math]15000a^3[/math]
  4. -[math]15000a^3[/math]
Grade 11 Polynomials and Rational Expressions CCSS: HSA-APR.C.5
Expand the binomial [math](1+2x)^5[/math] using Pascal's Triangle.
  1. [math]1 + 10x + 40x^2 + 80x^3 + 80x^4 + 32x^5[/math]
  2. [math]1 + 5x + 20x^2 + 40x^3 + 40x^4 + 32x^5[/math]
  3. [math]1 + 10x + 20x^2 + 80x^3 + 80x^4 + 32x^5[/math]
  4. [math]1 + 10x + 40x^2 + 80x^3 + 40x^4 + 32x^5[/math]
Grade 11 Polynomials and Rational Expressions CCSS: HSA-APR.C.5
Expand the binomial [math](x^2-1)^3[/math] using Pascal's Triangle.
  1. [math]x^6 - 3x^4 + 3x^2 - 1[/math]
  2. [math]x^6 + 3x^4 + 3x^2 + 1[/math]
  3. [math]x^6 - x^4 + x^2 - 1[/math]
  4. [math]x^6 - 3x^4 + x^2 - 1[/math]
Grade 11 Polynomials and Rational Expressions CCSS: HSA-APR.C.5
Expand the binomial [math](x-3)^4[/math] using Pascal's Triangle.
  1. [math]x^4+12x^3+54x^2+108x+81[/math]
  2. [math]x^4-12x^3+54x^2-108x+81[/math]
  3. [math]x^4-12x^3-54x^2-108x-81[/math]
  4. [math]x^4-12x^3+18x^2-36x+81[/math]
Grade 11 Polynomials and Rational Expressions CCSS: HSA-APR.C.5
Expand the binomial [math](4x+y)^3[/math] using Pascal's Triangle.
  1. 64x³ + 48x²y + 16xy² + y³
  2. 64x³ + 32x²y + 8xy² + y³
  3. 16x³ + 12x²y + 3xy² + y³
  4. 64x³ + 48x²y + 12xy² + y³
Grade 11 Polynomials and Rational Expressions CCSS: HSA-APR.C.5
Find the 3rd term in expansion [math](2x-3)^5[/math].
  1. [math]720x^3[/math]
  2. [math]80x^3[/math]
  3. [math]72x^3[/math]
  4. [math]120x^3[/math]
Grade 11 Polynomials and Rational Expressions CCSS: HSA-APR.C.5
Find the 7th term in expansion [math](x+y)^8[/math].
  1. [math]8x^2y^6[/math]
  2. [math]28x^2y^6[/math]
  3. [math]70x^2y^6[/math]
  4. [math]56x^2y^6[/math]
Grade 11 Polynomials and Rational Expressions CCSS: HSA-APR.C.5
Estimate [math]2.001^6[/math] using the Binomial Theorem with the first 3 terms, where 2.001 = 2+0.001.
  1. 64.192
  2. 64.192016
  3. 64.192096
  4. 64.192096016
Grade 11 Polynomials and Rational Expressions CCSS: HSA-APR.C.5
Which of the following are true about the general term in the expansion of [math](x+y)^n[/math]? The (k+1)th term is:
  1. [math]((n), (k)) x^(n-k)y^k[/math]
  2. [math] (n!) / (k!) x^(n-k) y^k[/math]
  3. The term where the exponents of x and y add to n
  4. Found using values from the (n+1)th row of Pascal’s Triangle
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