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Tenth Grade (Grade 10) Algebraic Expressions Questions

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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 [math]P(1+r/n)^(n \ t)[/math], where [math]P[/math] is the original amount invested, [math]r[/math] is the annual interest rate, [math]n[/math] is the compounding period (for example, if it is monthly, then [math]n=12[/math]), and [math]t[/math] 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
Factor by finding the GCF (Greatest Common Factor).

[math]3x+9y[/math]
  1. [math]3[/math]
  2. [math]3(x+3y)[/math]
  3. [math]12y[/math]
  4. [math]12xy[/math]
Grade 10 Algebraic Expressions CCSS: HSA-SSE.A.1, HSA-SSE.A.1b
For a pendulum of length [math]L[/math], its period of oscillation can be modeled by the expression [math]2 pi sqrt(L/g)[/math], where [math]g[/math] 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 [math]2.[/math]
  2. It would increase it by a factor of [math]4.[/math]
  3. It would increase it by a factor of [math]sqrt{2}[/math].
  4. It would increase it by a factor of [math]1/sqrt(2)[/math].
Grade 10 Algebraic Expressions CCSS: HSA-SSE.A.2
Which of the expressions below is equivalent to [math](3x+y)^2[/math] ?
  1. [math]9x^2+6xy+y^2[/math]
  2. [math]9x^2+3xy+y^2[/math]
  3. [math]9x^2+y^2[/math]
  4. [math]9x^2-y^2[/math]
Grade 10 Algebraic Expressions CCSS: HSA-SSE.A.1, HSA-SSE.A.1b
For the expression [math]((x^3-2)(3x-8)^3)/(y^2x^2)[/math], 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
Factor the following completely. [math]6m^2+2mn-n^2-3mn[/math]
  1. [math](3m-n)(n+2m)[/math]
  2. [math](3n+m)(2m-n)[/math]
  3. [math](3n+m)(2n-m)[/math]
  4. [math](3m+n)(2m-n)[/math]
Grade 10 Algebraic Expressions
Which of the following correctly interprets the expression [math](5x-1)/(4y)[/math]?
  1. One less than five times a number divided by four times a number
  2. Five times a number minus one divided by four times another number
  3. Five times a number divided by four times another number less one
  4. One less than five times a number, divided by four times another number
Grade 10 Algebraic Expressions
Grade 10 Algebraic Expressions
Grade 10 Algebraic Expressions CCSS: HSA-SSE.A.2
Which of the expressions below is equivalent to [math]5(x+1)(3x-8)[/math] ?
  1. [math](x+1)(3x-8)[/math]
  2. [math](5x+1)(15x-8)[/math]
  3. [math]3x^2-5x-8[/math]
  4. [math]15x^2-25x-40[/math]
Grade 10 Algebraic Expressions
Which of the following correctly interprets the expression [math](5x)/(3y-2)[/math]?
  1. Five times a number divided by two less than three times another number
  2. Five times a number divided by 3 times another number minus two
  3. Five times a number divided by 3 times a number less two
  4. Five times a number divided by two less than three times a number
Grade 10 Algebraic Expressions CCSS: HSA-SSE.A.1, HSA-SSE.A.1b
For the expression [math](m v) / (sqrt(1-v^2//c^2))[/math], which is the best explanation for why, when [math]v[/math] is much smaller than [math]c[/math] ([math]v \ "<<" \ c[/math]), the expression is very close to [math]mv ?[/math]
  1. If [math]v \ "<<" \ c[/math], [math]v[/math] becomes almost zero and it cancels out, and only [math]c[/math] is left.
  2. Looking at the factor [math]sqrt(1-v^2/c^2)[/math], if [math]v \ "<<" \ c[/math], then [math]v^2/c^2[/math] is close to zero, and so this factor is very close to being equal to one.
  3. Since [math]v[/math] is in the denominator, if it is much smaller than [math]c[/math] the entire denominator becomes close to zero, then this part of the expression is undefined and can be ignored.
  4. Because, if [math]v \ "<<" \ c[/math], all parts of the expression with [math]v[/math] can be ignored.
Grade 10 Algebraic Expressions
Grade 10 Algebraic Expressions CCSS: HSA-SSE.A.2
Which of the expressions below is equivalent to [math]9x^2+12x+4[/math] ?
  1. [math](3x+2)^2[/math]
  2. [math](3x+6)(3x+2)[/math]
  3. [math](3x-2)^2[/math]
  4. [math]4(2x^2+6x+1)[/math]
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 [math]r N ((K-N)/K)[/math], where [math]N[/math] is the size of the population, [math]K[/math] is a constant which describes the maximum population that a certain geographic region can support, and [math]r[/math] 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 [math]N~~K[/math], and so [math](K-N)/K[/math] will approach zero.
  2. The population will grow more rapidly, since both [math]N[/math] and [math]K[/math] become large.
  3. The population growth rate will remain the same, since the parameter [math]K[/math] 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 [math]r, K,[/math] and [math]N[/math].
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