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Common Core Standard HSA-SSE.A.1b Questions

Interpret complicated expressions by viewing one or more of their parts as a single entity. For example, interpret P(1+r)n as the product of P and a factor not depending on P.

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Grade 10 Algebraic Expressions CCSS: HSA-SSE.A.1, HSA-SSE.A.1b
The centroid of a triangle is the intersection of the triangle's three medians. For triangle ABC, whose vertices are represented by (xA,yA),(xB,yB),(xC,yC), the location of its centroid can be expressed as (xA+xB+xC3,yA+yB+yC3). If vertex A of this triangle were moved 1 unit right and 1 unit up, how would this affect the location of the centroid?
  1. The centroid would move 1 unit up and 1 unit right.
  2. The centroid would move 1/3 of a unit up and 1/3 of a unit right.
  3. The centroid would move 3 units up and 3 units right.
  4. This cannot be determined without knowing the numerical coordinates of the three vertices.
Grade 10 Algebraic Expressions CCSS: HSA-SSE.A.1, HSA-SSE.A.1b
For a pendulum of length L, its period of oscillation can be modeled by the expression 2π√Lg, where g is the acceleration due to gravity. How would increasing the length of the pendulum by a factor of 2 affect the period of oscillation?
  1. It would increase it by a factor of 2.
  2. It would increase it by a factor of 4.
  3. It would increase it by a factor of √2.
  4. It would increase it by a factor of 1√2.
Grade 10 Algebraic Expressions CCSS: HSA-SSE.A.1, HSA-SSE.A.1b
One way the rate of population growth (how fast or slowly a population is growing) can be modeled is by the expression rN(K-NK), where N is the size of the population, K is a constant which describes the maximum population that a certain geographic region can support, and r is a positive constant that relates to the maximum growth rate. If the population of a certain species is growing and becomes very close to the carrying capacity, what will happen to the rate of growth and why?
  1. The growth rate of the population will diminish, because N≈K, and so K-NK will approach zero.
  2. The population will grow more rapidly, since both N and K become large.
  3. The population growth rate will remain the same, since the parameter K is found in both the numerator and denominator, and thus any increase or decrease in its value will cancel out.
  4. This cannot be determined without knowing specific numerical values for r,K, and N.
Grade 10 Algebraic Expressions CCSS: HSA-SSE.A.1, HSA-SSE.A.1b
The value of someone's money in an account that earns compound interest can be modeled by the expression P(1+rn)n t, where P is the original amount invested, r is the annual interest rate, n is the compounding period (for example, if it is monthly, then n=12), and t is the amount of time the money has been in the account. If someone wants to invest their money in an account that has compound interest, how would their balance in their account differ after 3 years if they invested $1,000 vs $2,000?
  1. If they invest $2,000 and the interest rate is less than 1%, the investment will be less than double. If the interest rate is 1% or more, the end balance will be more than double.
  2. The final amount would be 8 times as large if they invest $2,000, since all the other variables cancel out, and just the exponent of 3 is left.
  3. The final amount would be double if they invest $2,000.
  4. It is not possible to say, without knowing the compounding period.
Grade 10 Algebraic Expressions CCSS: HSA-SSE.A.1, HSA-SSE.A.1b
For the expression mv√1-v2/c2, which is the best explanation for why, when v is much smaller than c (v << c), the expression is very close to mv?
  1. If v << c, v becomes almost zero and it cancels out, and only c is left.
  2. Looking at the factor √1-v2c2, if v << c, then v2c2 is close to zero, and so this factor is very close to being equal to one.
  3. Since v is in the denominator, if it is much smaller than c the entire denominator becomes close to zero, then this part of the expression is undefined and can be ignored.
  4. Because, if v << c, all parts of the expression with v can be ignored.
Grade 10 Algebraic Expressions CCSS: HSA-SSE.A.1, HSA-SSE.A.1b
For the expression (x3-2)(3x-8)3y2x2, what happens to the value of the expression when y increases?
  1. The value decreases.
  2. The value increases.
  3. It is unaffected, since the x values are so much larger (y's impact is too small to affect it).
  4. Without knowing what x is doing, it's impossible to tell.
Grade 10 Algebraic Expressions CCSS: HSA-SSE.A.1, HSA-SSE.A.1b
The surface area of a cone is given by the expression πr(r+l), where r is the radius of the cone and l is the slant height of the cone (the length from the edge of the base to the vertex). If the radius of a cone doubled, what would happen to the volume?
  1. The surface area would also double.
  2. The surface area would increase by a factor of 4.
  3. The surface area would increase by a factor of 3.
  4. Not enough information to determine.
Grade 10 Algebraic Expressions CCSS: HSA-SSE.A.1, HSA-SSE.A.1b
Caleb is walking in a straight line. The distance he travels can be expressed by v0t+12at2, where v0 is his initial speed, t is the amount of time he walks, and a is how much he accelerates in the direction he is walking. If Caleb does not accelerate at all, what does this imply?
  1. No conclusion can be made without knowing for how long he walks.
  2. That he stands still (does not walk).
  3. That he will not walk very far.
  4. That he walks at his initial speed the entire time.

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