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Common Core Standard HSF-LE.A.2 Questions

Construct linear and exponential functions, including arithmetic and geometric sequences, given a graph, a description of a relationship, or two input-output pairs (include reading these from a table).

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Grade 10 Sequences and Series CCSS: HSF-IF.A.3, HSF-BF.A.2, HSF-LE.A.2
Which formula represents the general term of the following sequence? [math]1/2, -1, 2, -4, ...[/math]
  1. [math]a_n = 1/2 * 2^n[/math]
  2. [math]a_n = 1/2 * (-2)*(n-1)[/math]
  3. [math]a_n = 1/2 * -2^(n-1)[/math]
  4. [math]a_n = 1/2 * (-2)^(n-1)[/math]
Grade 10 Sequences and Series CCSS: HSF-BF.A.1, HSF-BF.A.1a, HSF-LE.A.2
Which recursive function defines the sequence [math]0, 2, 2, 10, 18, 58, 130, ...[/math] for [math]n in N ?[/math]
  1. [math]t(1) = 0; \ \ t(n) = t(n-1) + n-2, \ n>1[/math]
  2. [math]t(1)=0, \ t(2)=2; \ \ t(n) = t(n-1) + 4t(n-2), \ n>2[/math]
  3. [math]t(1)=0, \ t(2)=2; \ \ t(n) = t(n-1) + 2t(n-2), \ n>2[/math]
  4. [math]t(1)=0, \ t(2)=2; \ \ t(n) = t(n-1) + 4(n-2), \ n>2[/math]
Grade 11 Exponents CCSS: HSF-LE.A.2
Grade 10 Sequences and Series CCSS: HSF-BF.A.1, HSF-BF.A.1a, HSF-BF.A.2, HSF-LE.A.2
Which of the following recursive functions defines the sequence [math]5,8,11,14,... ?[/math] Assume [math]n in NN[/math].
  1. [math]t(1) = 3; \ \ t(n) = t(n-1) + 5, \ n>1[/math]
  2. [math]t(1) = 5, \ \ t(n) = t(n-1) - 3, \ n>1[/math]
  3. [math]t(1) = 5, \ \ t(n) = t(n-1) + 3, \ n>1[/math]
  4. [math]t(2) = 8, \ \ t(n) = t(n-2) + 6, \ n>2[/math]
Grade 10 Sequences and Series CCSS: HSF-BF.A.1, HSF-BF.A.1a, HSF-BF.A.2, HSF-LE.A.2
Given the sequence [math]1,4,16,64,256,...[/math], which of the following correctly defines this sequence in a recursive form? Assume that [math]n in NN[/math].
  1. [math]t(1) = 1; \ \ t(n) = 4t(n-1), \ n>1[/math]
  2. [math]t(1) = 4; \ \ t(n) = 4t(n-1), \ n>1[/math]
  3. [math]t(1) = 1; \ \ t(n) = 1/4 t(n-1), \ n>1[/math]
  4. [math]t(1) = 1; \ \ t(n) = 2^(2(n-1)), n>1[/math]
Grade 10 Sequences and Series CCSS: HSF-BF.A.1, HSF-BF.A.1a, HSF-BF.A.2, HSF-LE.A.2
Find the recursive form of the sequence [math]10, 5, 0, -5, -10,...[/math] Assume [math]n in NN[/math].
  1. [math]t(1) = 10; \ \ t(n) = -t(n-1) + 5, \ n>1[/math]
  2. [math]t(1) = 10; \ \ t(n) = -5 + t(n-1), \ n>1[/math].
  3. [math]t(1) = 10; \ \ t(n) = 10 - t(n-1), \ n>1[/math].
  4. [math]t(1) = 10; \ \ t(n) = t(n-1) - 5, n>1[/math]
Grade 10 Sequences and Series CCSS: HSF-BF.A.1, HSF-BF.A.1a, HSF-BF.A.2, HSF-LE.A.2
Given the sequence [math]128, 64, 32, 16, 8, ...[/math] which of the following functions describes it? Assume [math]n in NN[/math].
  1. [math]t(1) = 128; \ \ t(n) = 2 t(n-1), \ n>1[/math]
  2. [math]t(1) = 128; \ \ t(n) = 128 - t(n-1), \ n>1[/math]
  3. [math]t(1) = 128; \ \ t(n) = t(n) - 1/2t(n-1), n>1[/math]
  4. [math]t(1) = 128; \ \ t(n) = 1/2 t(n-1), \ n>1[/math]
Grade 10 Sequences and Series CCSS: HSF-BF.A.1, HSF-BF.A.1a, HSF-BF.A.2, HSF-LE.A.2
Which of the following functions describes the sequence [math]18, 31/2, 13, 21/2, 8, ... ?[/math] Assume that [math]n in NN[/math].
  1. [math] t(1) = 18; \ \ t(n) = 43/50 t(n-1), n>1[/math]
  2. [math]t(1) = 18; \ \ t(n) = t(n-1) - 5/2, n>1[/math]
  3. [math]t(1) = 18; \ \ t(n) = t(n-2) - 5, n>2[/math]
  4. [math]t(1) = 18; \ \ t(n) = 5/2 - t(n-1), t>1[/math]
Grade 9 Linear Equations CCSS: HSF-LE.A.2
Create a linear function, given the points [math](-2,5)[/math] and [math](1,-2)[/math].
  1. [math]f(x) = 7/3 x - 13/3[/math]
  2. [math]f(x) = -3/7 x - 11/7[/math]
  3. [math]f(x) = 3/7 x - 17/7[/math]
  4. [math]f(x) = -7/3 x + 1/3[/math]
Grade 10 Sequences and Series CCSS: HSF-BF.A.1, HSF-BF.A.1a, HSF-LE.A.2
Which of the following functions correctly describes the sequence [math]1,3,5,9,13,21,...?[/math] Assume that [math]n in NN[/math].
  1. [math] t(1) = 1, t(2) = 3; \ \ t(n) = 2t(n-2) + 3, n>2[/math]
  2. [math]t(1) = 1; \ \ t(n) = t(n-1) + 2, n>1[/math]
  3. [math]t(1)=1, t(2)=3; \ \ t(n) = t(n-2) + t(n-1) + 1, n>2[/math]
  4. [math]t(1) = 1; \ \ t(n) = t(n-1) + 2^(n-1), \ n>1[/math]
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