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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 12 Polynomials and Rational Expressions CCSS: HSA-APR.C.5
Use Pascal's triangle to expand $(x+y)^3$.
1. $(x+y)^3=x^3+y^3$
2. $(x+y)^3=x^1+x^2+x^3+y^1+y^2+y^3$
3. $(x+y)^3=x^3+3x^2y+3xy^2+y^3$
4. $(x+y)^3=xy+3x^2y^2+9x^3y^3$
Grade 12 Combinations and Permutations CCSS: HSS-CP.B.9
If a coin is flipped 15 times, how many ways can you get 8 heads?
1. $6","435$
2. $5.27*10^27$
3. $32","432","400$
4. $3.24*10^5$
Grade 12 Polynomials and Rational Expressions CCSS: HSA-APR.C.5
Use Pascal's triangle to expand $(x+y)^5$.
1. $(x+y)^5=x^5+5x^4y+10x^3y^2+10x^2y^3+4xy^4+y^5$
2. $(x+y)^5=x^1+x^2+x^3+x^4+x^5+y^1+y^2+y^3+y^4+y^5$
3. $(x+y)^5=x^5+y^5$
4. $(x+y)^5=xy+5x^2y^2+10x^3y^3+15x^4y^4+20x^5y^5$
Grade 12 Combinations and Permutations CCSS: HSS-CP.B.9
If a coin is flipped 5 times how many ways can you get 4 tails?
1. $20$
2. $1$
3. $2880$
4. $5$
Grade 12 Combinations and Permutations CCSS: HSS-CP.B.9
If a coin is flipped 18 times how many ways can you get 2 tails?
1. $1.28*10^16$
2. $153$
3. $3.2*10^15$
4. $306$
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