Student Review Jeopardy Board

Quadratic Equations

100

What is the standard form of a quadratic equation?

ax^2+bx+c=0

200

Factor the quadratic equation x^2−5x+6=0

(x−2)(x−3)=0

300

A school music club offers to cover $50 of each student’s Spotify Premium subscription. If the club has $1000 in total funding, how many students can get their subscription covered?

1000÷50=20
20 students can receive help

400

A dancer’s jump is modeled by the quadratic function h(t) = −5t² + 20t, where h(t) represents height in meters and t represents time in seconds.
When does the dancer reach their highest point in the jump?

The maximum occurs at t=−b/2a or -20/2(-5)
The plant reaches max height after 2 seconds.

500

A school wants a curved accessibility ramp modeled by h(x)=−1/2 (x²)+3x+2 What are the possible x-values for the ramp’s start and end?

Using the quadratic formula, the possible x-values for the ramp's start and end are approximately x=-0.61m and x=6.61m. 

Trigonometry

100

What is the sine ratio in a right triangle?

sinθ=hyp/opp

200

Solve for x in a right triangle where sin⁡30=x/10

x=10×sin30=5

300

Professional climber Magnus Midtbo is setting up a beginner-friendly training wall with a gentle incline of 4° to help new climbers practice technique (forms a right triangle). If the climbing wall is 5 meters long, how high does the wall reach?

Sinθ = Opp/Hyp

sin⁡4^∘=h/5

height = 5 x sin4^∘ = 0.35m (approximately)

400

Baker Duff Goldman stacks a 3-meter-long ramp to roll a tray cart up to a shelf that’s 2 meters high.
To make sure the ramp isn’t too steep, he wants to find out what angle it makes with the floor.
What is the angle of the ramp to the ground?

Let θ be the angle. 

tanθ = opp/adj

tan(θ)=2/3. 

θ=arctan(2/3)≈33.69∘. 

The board should be tilted approximately 33.69 degrees.

500

During a Katy Perry concert, she stands on a 1.5 m stage while the audience (where Justin Trudeau is attending) is 20m away. What is the angle of elevation from the audience to the singer?

tan = opp/adj . 

tan⁡θ=1.5/20 

so θ=tan^-1(1.5/20). 

θ= 4.29^o (Approximately)

Linear Systems

100

What are three ways to solve a system of equations?

Graphing, substitution, elimination.

200

Solve using substitution: y=2x+3y and y=-x+6

x=1 and y=5

300

A school gym orders 10 new pieces of fitness equipment costing $2,300 in total.
Each treadmill costs $300, and each yoga mat set costs $200.
How many of each did the gym purchase?

300T+200Y=2,300,  --> T+Y=10  ---> Let Y= 10-T

300T + 200(10-T) = 2,300

300T +2000 - 200T = 2,300 (collect like terms)

100T=300.   -->    T=3 --> sub T=3 into either equation to find Y ---> Y=10 - (3) = 7

3 treadmills and 7 Yoga mats were purchased.

400

A school’s coding lab buys two types of keyboards for the computer science room. Type A costs $15, and Type B costs $25. They order 20 keyboards in total and spend $400. How many of each type did they order?

a+b=20  and 15a+25b=400

Let b=(20 - a)  ---> 15a +25(20-a) = 400

15a +500- 25a = 400 ---> -10a = -100 --> a=10

b=(20-10) so b=10

They ordered 10 of each type a=10 and b=10

500

A high school is designing an accessibility improvement project. The school allocates $10,000 for three major initiatives:

• Automatic doors installation (x)
• Braille signs for classrooms (y)
• Adjustable desks for students with mobility needs (z)

The costs for each initiative are:

• Each automatic door costs $1,200
• Each Braille sign costs $75
• Each adjustable desk costs $250

Given the following conditions:

1. The school buys a total of 35 items across all three initiatives.
2. The number of adjustable desks is twice the number of automatic doors.
3. The total budget of $10,000 is fully spent.

Set up a system of equations and solve for x, y, and z

x+y+z=35                                     (total items)

z=2x                                      (desks twice doors)

1200(x)+75(y)+250(z)=10000           (budget)

Sub (z=2x) & (y=35-x-z) to get y=(35-3x)

1200x + 75(35-3x) +250(2x) =10000   ---> x=5

plug x=5 into z=2x --> z=2(5) = 10

Plug x=5 into y=35-3x --> y=35-3(5) = 20

x=5, y=20, z=10

Exponents & Radicals

100

Simplify (y³x²)(yx⁴)

x⁶y⁴

200

Simplify 4³/4²

4

300

A dance instructor teaches exponents by doubling the number of dancers in each round from the previous (starting with 2 dancers 2ⁿ). Round one starts with 2¹ dancers. How many dancers will there be in round five?

Round 5, so n=5

2⁵ =32 Blocks would be needed

400

A film student starts a small movie collection with 10 movies. Each year, their collection triples from the last as they buy, stream, or trade for more movies. After 4 years, they decide to donate 25% of their collection to the school film club. How many movies remain in their personal library?

The number of movies follows an exponential growth pattern:

N=P×r^t

N= total number of movies after t years. 

P = starting number of movies

r=growth rate, t= time

Starting number of movies = 10

Growth rate = triples every year → multiply by 3 each year.

Time = 4 years

Donation = 25% of total (so they keep 75%)

B=10×3⁴ =810 movies before donation.

They donate 25% of the movies:

Donation=0.25×810=202.5

Since movies must be whole, they donate 203 movies.

The number of books left:

810−203=607 books remain

500

A school is providing adaptive communication devices for non-verbal students. These devices have a battery that lasts 24 hours when fully charged, but due to wear and tear, the battery life decreases by 20% each year. After 5 years, how long will a fully charged battery last? (Round to the nearest hour.)

Exponential decay: Battery life after t years: A=P(1−r)^t

^{A = battery life after t years
P= initial value
r= rate of decrease
t= time in years} 

B=B₀ x (1-r)^t

B₀=24hrs initial battery life

r=0.20 (20% decay)

t=5 years

B= approx 8 hrs

Wildcard Questions

100

What is the mean of {4, 6, 8, 10, 12}

8

200

A teacher is analyzing data on the effectiveness of different learning strategies for students with IEP's. They find that Strategy A works for 70% of the students, and Strategy B works for 80% of the students. Assuming the strategies are independent, what is the probability that both strategies together will work for all students with IEP's?

Probability of both being successful: 

0.70 * 0.80 = 0.56 or 56%.

300

A school is installing an escalator for those who struggle to walk up stairs or need minor assistance to walk up stairs. The escalator rises 6 meters to the second floor and extends 11 meters horizontally. 

What is the length of the escalator?

Pythagorean theorem:

a²+b²=c²

6²+11²=c²

c=sqrt(157) or 12.53

400

A school provides tablets to support students with learning disabilities. A total of 20 tablets were purchased at a cost of $400 each. However, if the school had purchased more, the supplier would have given a discount of $5 per additional tablet beyond 20. Let x be the number of extra tablets purchased beyond 20. The total cost, C(x), can be modeled by:

C(x)=(20+x)(400−5x)

How many tablets should the school buy to minimize total cost?

Expand Equation: -5x²+300x+8000

Use vertex formula: -b/2a to find the minimum

20+x = 20+(30) = 50 tablets

C(30) = 12500 (minimizing the cost)

500

A school subscribes to an AI-powered reading tool that costs $100/month, doubling every 6 months:

C(t) = 100(2)^t/6 

When will the cost exceed $5,000?  

100(2)^t/6 > 5000

2^t/6 > 50

t>6log₂(50) which is approximately 34 months