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Common Core Standard HSA-SSE.A.1 Questions

Interpret expressions that represent a quantity in terms of its context.

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Grade 10 Algebraic Expressions CCSS: HSA-SSE.A.1, HSA-SSE.A.1b
Grade 10 Algebraic Expressions CCSS: HSA-SSE.A.1, HSA-SSE.A.1b
Grade 9 Algebraic Expressions CCSS: HSA-SSE.A.1, HSA-SSE.A.1a
Grade 10 Algebraic Expressions CCSS: HSA-SSE.A.1, HSA-SSE.A.1b
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 2πLg, 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 12.
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 NK, 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 9 Algebraic Expressions CCSS: HSA-SSE.A.1, HSA-SSE.A.1a
Beth wants to go on a road trip this summer. She will be taking her car, which gets an average of 19 miles per gallon in fuel economy. Beth creates an expression to calculate the total cost of gas for her trip, 119xy, where x is the typical price of gas (in dollars per gallon) where she will be driving. What does the factor y represent?
  1. The number of miles she expects to drive.
  2. The total cost of gas, for one fill up.
  3. The number of times she expects she will have to stop to fill up her car with gas.
  4. The total amount of gas, in gallons, needed to fill her car's gas tank.
Grade 9 Algebraic Expressions CCSS: HSA-SSE.A.1, HSA-SSE.A.1a
Jake and Will work at a bakery. If J represents the number of cakes Jake can bake per day, W represents the number of cakes Will can bake per day, x represents the number of days Jake works in a week, and y represents the number of days Will works in a week, what does the expression xJ+yW represent?
  1. The number of hours Jake and Will work in a week.
  2. The number of cakes made by Jake and Will in a week.
  3. The total number of cakes both Jake and Will could bake per day.
  4. The combined number of days Jake and Will work in a week.
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 mv1-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.
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