# Worksheet: Evaluating Higher-Degree Algebraic Expressions

In this worksheet, we will practice evaluating algebraic expressions of more than one degree with one or multiple variables and applying this in real-world problems.

Q1:

Find the value of given and .

Q2:

Given that and , find the value of .

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• B
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• E

Q3:

The formula to calculate the volume of a sphere is .

Make the subject.

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• E

Find the radius of a sphere with a volume of 900 cubic centimeters. Give your answer accurate to two decimal places.

Q4:

Evaluate for .

Q5:

Given that , , and , evaluate .

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• B
• C84
• D
• E

Q6:

Given that , find when , , and .

Q7:

Given that and , find the numerical value of .

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• E

Q8:

Given that and , evaluate .

Q9:

Given that , what is the value of ?

Q10:

Given that , , and , determine the numerical value of the expression .

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• D

Q11:

Evaluate , given that and .

Q12:

Given that , , and , evaluate when .

Q13:

Given that and , which of the following choices is a negative number?

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• B
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• D

Q14:

Given that and , find the value of .

Q15:

Given that and , evaluate .

• A
• B16
• C
• D2

Q16:

Given that and , find the value of .

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• E

Q17:

If and , what is the value of ?

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• D1

Q18:

Evaluate for and .

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• E

Q19:

Given that and , evaluate .

Q20:

The height of an object dropped from the top of a 150-foot-tall building can be described by the expression , where is the time in seconds during which the object is falling. Determine the height of the object 2 seconds after it has been dropped.

Q21:

The distance, in feet, an object falls seconds after it is released is given by the expression , where is the acceleration due to gravity. Determine how many feet a stone will fall 5 seconds after it is released from the top of a cliff. Assume feet per second squared.

Q22:

The expression can be used to determine the surface area of a cube, where is the edge length of the cube. Determine the surface area of a cube whose edge is 11 centimeters long.

Q23:

Evaluate for .

Q24:

The surface area, , of a cube of edge is given by . What is the surface area of a cube of edge 9 length units?

Q25:

If and , evaluate .