Roots and Rational Exponents
A student is editing audio files for a fan edit and sees the volume is scaled by a factor of:
v= 161/4
What is the simplified value of this expression?
A. 2
B. 4
C. 8
D. 16
A.2
Which of the following is not a possible answer for 4x
a. x = 3
b. x = 0
c. x = -14
d. x = 56
Which of the following trinomials can be factored using the decomposition method?
a. x2−16x2
b. x2+8x+16
c. x2+5x+6
d. x2−49
c. x2+5x+6
Simplify (x2-9)/(x2-x-6)
a. (x+3)/(x+2)
b. (x-3)/(x+2)
c. (x-3)/(x-3)
d. (x+3)/(x-3)
a a. (x+3)/(x+2)
Multiple Choice #2
An Indigenous canoe builder is carving two traditional canoes. One has a length of:
L=√144 and the other L=1441/2
What can you say about the two expressions?
A. The second is twice the first.
B. They are equal.
C. The first is a simplified form of the second.
D. They can’t be compared without a calculator.
B. They are equal.
Evaluate: 3∛(x7y12z2)
a. (2x)y4 ∛(3xz2)
b. x2y4 ∛(xz2)
c. (2x)(4y)∛(xz2)
d. x2y4∛z2
b. x2y4 ∛(xz2)
Which of the following is the correct factored form of the expression 4x2−20x+25
a. (2x−5)2
b. (4x−5)(x−5)
c. (2x+5)2
d. (4x+5)(x−5)
a. (2x−5)2
A student simplified (2x2-8)/(x-2) to 2x-4. Is this correct? Why or why not?
The student is incorrect. It should have simplified to 2(x+2). Likely caused by an error of not factoring or cancelling out the wrong factors.
An Indigenous artist carves a special totem pole whose height ℎ (in meters) follows the formula: h =(811/4x3/2)÷ 91/2
where 𝑥 is the base width of the totem in meters.
If the base width 𝑥 is 16 meters, simplify the expression and find the height ℎ.
Solve (y3z)/√(x3y4)
yz/√x
Explain how you can tell if a trinomial is a perfect square trinomial, including examples in your explanation.
A perfect square trinomial has the form a2±2ab+b2 = (a±b)2, where both the first and last terms are perfect squares, while the middle term is twice the product of their square roots.
Eg. x2+6x+9 = (x+3)2
A member of the Haida tribe, a First Nations community in the pacific northwest coast is trying to create a sign that spans the width w, across 2 adjacent Indigenous reserves. Determine a simplified expression for the length of the sign if A1=x2+4x+4, L1=x2-4, A2=2x2-8x-8, L2=2x2-8
(2x2+8)/(x-2)(x+2) x≠2,-2
Mia simplified 163/4 and wrote:
“I took the cube root of 16 and then raised it to the 4th power, so I got (∛16)4 .”
Is the student’s method correct? If it is wrong, explain the mistake and show the right way to simplify.
Mia’s method is incorrect, she mixed up the numerator and denominator of the exponent.
A functions student, Remi, solved a question like this:
In a close-knit Indigenous community, Tayen and Awena are preparing for the annual Elders and Youth Gathering, where young people learn from their elders and carry on important cultural teachings.
Tayen is learning to make traditional tools, while Awena is helping prepare food using recipes passed down from their grandparents. As part of a math challenge at the gathering, an Elder shares this puzzle:
If you add Tayen’s and Awena’s ages, the total is 34, and if you square Tayen’s age and add twice Awena’s age, the total is 292. Solve for Tayens and Awenas' age.
Awena's age: 18
Tayen's age: 16
Researchers have determined that the effect of being in a math class on 16 year olds can be modelled by the question, where y is the heart rate in beats per minute and x is the hours spent in a math classroom:
y=(x2-36)/(√3-4)
Is there a limit to how long students can spend doing math questions in a classroom? (Hint: How long does it take before students' hearts stop beating?)
a. x≠6
b. x≥6
c. 0≤x≤6
d. No limit
c. 0≤x≤6