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# Common Core Standard HSF-BF.A.1a Questions

Determine an explicit expression, a recursive process, or steps for calculation from a context.

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Grade 10 Sequences and Series
Given the sequence defined by $a(n) = 3 + 5*2^n, \ n in NN, n >=1$, which of the following recursive formulas defines the same sequence? Assume for all sequences that $n in NN$.
1. $t(1) = 13; \ \ t(n) = 3 + 5*2^(n-1), n>1$
2. $t(1) = 13; \ \ t(n) = 2 t(n-1), \ n>1$
3. $t(1) = 13; \ \ t(n) = 13 + t(n-1), \ n>1$
4. $t(1) = 13; \ \ t(n) = -3 + 2t(n-1), \ n >1$
Grade 11 Functions and Relations CCSS: HSF-BF.A.1, HSF-BF.A.1a
Grade 10 Sequences and Series
Which of the following recursive functions defines the sequence $5,8,11,14,... ?$ Assume $n in NN$.
1. $t(1) = 3; \ \ t(n) = t(n-1) + 5, \ n>1$
2. $t(1) = 5, \ \ t(n) = t(n-1) - 3, \ n>1$
3. $t(1) = 5, \ \ t(n) = t(n-1) + 3, \ n>1$
4. $t(2) = 8, \ \ t(n) = t(n-2) + 6, \ n>2$
Grade 10 Sequences and Series
Given the sequence $1,4,16,64,256,...$, which of the following correctly defines this sequence in a recursive form? Assume that $n in NN$.
1. $t(1) = 1; \ \ t(n) = 4t(n-1), \ n>1$
2. $t(1) = 4; \ \ t(n) = 4t(n-1), \ n>1$
3. $t(1) = 1; \ \ t(n) = 1/4 t(n-1), \ n>1$
4. $t(1) = 1; \ \ t(n) = 2^(2(n-1)), n>1$
Grade 10 Functions and Relations CCSS: HSF-BF.A.1, HSF-BF.A.1a
What is the function rule of the total cost T(x) of x books, if each book costs $11.95? 1. T(x) = 11.95x 2. T(x) = 11.95 - x 3. T(x) = x + 11.95 4. T(x) = x - 11.95 Grade 10 Sequences and Series Find the recursive form of the sequence $10, 5, 0, -5, -10,...$ Assume $n in NN$. 1. $t(1) = 10; \ \ t(n) = -t(n-1) + 5, \ n>1$ 2. $t(1) = 10; \ \ t(n) = -5 + t(n-1), \ n>1$. 3. $t(1) = 10; \ \ t(n) = 10 - t(n-1), \ n>1$. 4. $t(1) = 10; \ \ t(n) = t(n-1) - 5, n>1$ Grade 10 Functions and Relations CCSS: HSF-BF.A.1, HSF-BF.A.1a Grade 10 Sequences and Series Given the sequence $128, 64, 32, 16, 8, ...$ which of the following functions describes it? Assume $n in NN$. 1. $t(1) = 128; \ \ t(n) = 2 t(n-1), \ n>1$ 2. $t(1) = 128; \ \ t(n) = 128 - t(n-1), \ n>1$ 3. $t(1) = 128; \ \ t(n) = t(n) - 1/2t(n-1), n>1$ 4. $t(1) = 128; \ \ t(n) = 1/2 t(n-1), \ n>1$ Grade 10 Sequences and Series Grade 10 Sequences and Series Which of the following functions describes the sequence $18, 31/2, 13, 21/2, 8, ... ?$ Assume that $n in NN$. 1. $t(1) = 18; \ \ t(n) = 43/50 t(n-1), n>1$ 2. $t(1) = 18; \ \ t(n) = t(n-1) - 5/2, n>1$ 3. $t(1) = 18; \ \ t(n) = t(n-2) - 5, n>2$ 4. $t(1) = 18; \ \ t(n) = 5/2 - t(n-1), t>1$ Grade 11 Functions and Relations Grade 10 Sequences and Series Grade 10 Sequences and Series Which of the following functions correctly describes the sequence $1,3,5,9,13,21,...?$ Assume that $n in NN$. 1. $t(1) = 1, t(2) = 3; \ \ t(n) = 2t(n-2) + 3, n>2$ 2. $t(1) = 1; \ \ t(n) = t(n-1) + 2, n>1$ 3. $t(1)=1, t(2)=3; \ \ t(n) = t(n-2) + t(n-1) + 1, n>2$ 4. $t(1) = 1; \ \ t(n) = t(n-1) + 2^(n-1), \ n>1$ Grade 9 Functions and Relations CCSS: HSF-BF.A.1, HSF-BF.A.1a Troy wants to join Universal Gym. The gym charges a one-time membership fee of$50 and \$24.50 per month. Write a function that represents this situation.
1. $f(m) = 50m+24.50$
2. $f(m) = 50+24.50m$
3. $f(m) = 50m+24.50m$
4. $f(m) = 50+24.50$
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