Tenth Grade (Grade 10) Algebraic Expressions Questions for Tests and Worksheets

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Grade 10 Algebraic Expressions

Factor by finding the GCF (Greatest Common Factor).

$3x+9y$

$3$
$3(x+3y)$
$12y$
$12xy$

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

$P(1+r/n)^(n \ t)$ , 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?

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.
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.
The final amount would be double if they invest $2,000.
It is not possible to say, without knowing the compounding period.

Grade 10 Algebraic Expressions

If c = 6 and d = 2, evaluate the expression.

$2c + c(d^2 - 6)$

Grade 10 Algebraic Expressions CCSS: HSA-SSE.A.2

Which of the expressions below is equivalent to

$(3x+y)^2$ ?

$9x^2+6xy+y^2$
$9x^2+3xy+y^2$
$9x^2+y^2$
$9x^2-y^2$

Grade 10 Algebraic Expressions CCSS: HSA-SSE.A.1, HSA-SSE.A.1b

The volume of a cone is given by the expression

$1/3 pi r^2 h$ , where

$r$ is the radius of the cone and

$h$ is the height of the cone. If one cone has a height of 10 cm, and a second cone has a height of 15 cm, how much larger is the volume of the second cone (assuming the radius is the same in each cone)?

The volume is $5 \ "cm"^3$ larger.
The volume is larger by a factor of 9/4.
The volume is larger by a factor of 1.5.
This cannot be determined without knowing the radius.

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

$2 pi sqrt(L/g)$ , 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?

It would increase it by a factor of $2.$
It would increase it by a factor of $4.$
It would increase it by a factor of $sqrt{2}$ .
It would increase it by a factor of $1/sqrt(2)$ .

Grade 10 Algebraic Expressions

Factor the following completely.

$6m^2+2mn-n^2-3mn$

$(3m-n)(n+2m)$
$(3n+m)(2m-n)$
$(3n+m)(2n-m)$
$(3m+n)(2m-n)$

Grade 10 Algebraic Expressions CCSS: HSA-SSE.A.1, HSA-SSE.A.1b

The surface area of a cone is given by the expression

$pi r(r+l)$ , 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?

The surface area would also double.
The surface area would increase by a factor of 4.
The surface area would increase by a factor of 3.
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

$v_0 t + 1/2 a t^2$ , where

$v_0$ 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?

No conclusion can be made without knowing for how long he walks.
That he stands still (does not walk).
That he will not walk very far.
That he walks at his initial speed the entire time.

Grade 10 Algebraic Expressions CCSS: HSA-SSE.A.1, HSA-SSE.A.1b

The magnitude of the gravitational force between two objects can be expressed by

$(Gm_1 m_2)/r^2$ , where

$G$ is the gravitational constant,

$m_1, m_2$ are the masses of the two objects, and

$r$ is the distance between them. If the distance between the objects decreases by a factor of 2, what happens to the magnitude of the gravitational force?

It decreases by a factor of $4.$
It decreases by a factor of $2.$
It decreases by a factor of $sqrt(2)$ .
It increases by a factor of $4.$

Grade 10 Algebraic Expressions CCSS: HSA-SSE.A.1, HSA-SSE.A.1b

For the expression

$((x^3-2)(3x-8)^3)/(y^2x^2)$ , what happens to the value of the expression when y increases?

The value decreases.
The value increases.
It is unaffected, since the x values are so much larger (y's impact is too small to affect it).
Without knowing what x is doing, it's impossible to tell.

Grade 10 Algebraic Expressions

Which of the following expressions correctly interprets the following phrase?

one less than two times a number, divided by three more than four times another number

$(3-2x)/(4y-1)$
$(2x)/(4y)-1$
$(1-2x)/(4y+3)$
$(2x-1)/(3+4y)$

Grade 10 Algebraic Expressions

Which of the following correctly interprets the expression

$(5x-1)/(4y)$ ?

One less than five times a number divided by four times a number
Five times a number minus one divided by four times another number
Five times a number divided by four times another number less one
One less than five times a number, divided by four times another number

Grade 10 Algebraic Expressions

Which of the following expressions correctly interprets the following phrase?

two less than three times a number, multiplied by three less than four times another number

$(3x-2)(4y-3)$
$(3x-2)/(4y-3)$
$(3x-3)(4y-2)$
$(3x-3)/(4y-2)$

Grade 10 Algebraic Expressions CCSS: HSA-SSE.A.2

Which of the expressions below is equivalent to

$5(x+1)(3x-8)$ ?

$(x+1)(3x-8)$
$(5x+1)(15x-8)$
$3x^2-5x-8$
$15x^2-25x-40$

Grade 10 Algebraic Expressions

Which of the following correctly interprets the expression

$(5x)/(3y-2)$ ?

Five times a number divided by two less than three times another number
Five times a number divided by 3 times another number minus two
Five times a number divided by 3 times a number less two
Five times a number divided by two less than three times a number

Grade 10 Algebraic Expressions CCSS: HSA-SSE.A.2

Which of the expressions below is equivalent to

$9x^2+12x+4$ ?

$(3x+2)^2$
$(3x+6)(3x+2)$
$(3x-2)^2$
$4(2x^2+6x+1)$

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

$(x_A,y_A), (x_B, y_B), (x_C, y_C)$ , the location of its centroid can be expressed as

$((x_A + x_B + x_C)/3, (y_A + y_B + y_C)/3 )$ . If vertex A of this triangle were moved 1 unit right and 1 unit up, how would this affect the location of the centroid?

The centroid would move 1 unit up and 1 unit right.
The centroid would move 1/3 of a unit up and 1/3 of a unit right.
The centroid would move 3 units up and 3 units right.
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 the expression

$(m v) / (sqrt(1-v^2//c^2))$ , which is the best explanation for why, when

$v$ is much smaller than

$c$ (

$v \ "<<" \ c$ ), the expression is very close to

$mv ?$

If $v \ "<<" \ c$ , $v$ becomes almost zero and it cancels out, and only $c$ is left.
Looking at the factor $sqrt(1-v^2/c^2)$ , if $v \ "<<" \ c$ , then $v^2/c^2$ is close to zero, and so this factor is very close to being equal to one.
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.
Because, if $v \ "<<" \ c$ , all parts of the expression with $v$ can be ignored.

Grade 10 Algebraic Expressions

Which of the following expressions correctly interprets the following phrase?
6 less than 3 times a number, times 4 more than two times another number

$3x-6*2y+4$
$6-3x-4+2y$
$(3x-6)(2y+4)$
$6-3x*4y+4$

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Tenth Grade (Grade 10) Algebraic Expressions Questions