Sequences and Series
Financial Maths
Geometry
Modelling
Acosta Trivia
100
Alex is training for a marathon and runs 10 miles the first week. He runs 10% more each week. What type of sequence is this?
Geometric
100
$20,000 is invested at 4.8% p.a. interest compounded quarterly. Find the value of this investment after 3 years.
$23,077.89
100
100. ft^2
100
A plumber charges a $60 deposit and then $45 per hour of work. Write a linear model connecting C, cost in dollars, to t, time in hours.
C=45t+60
100
What other subject besides math has Ms. Acosta taught at St. George's?
CSC
200
A factory makes 100 shoes this week. Each week they make 12 more than the previous week. Write a formula to find the number of shoes produced in n weeks.
100+(n-1)*12
200
How much would need to be invested now to get a maturing value of $20,000 in 4 years' time, given the money will be invested at a fixed interest rate of 7.5% p.a. compounded annually? Round your answer up to the next dollar.
$14,977
200
The height of a cylinder is the same as its diameter. The volume of the cylinder is given below. Find the radius.
Volume = 16pi
r = 2
200
The cost of renting a bike (charged per hour) and a helmet (one time fee) is represented by the following equation: C = 5h+10
Isaiah paid $30. How many hours did he rent the bike for?
2
200
In which U.S. state was Ms. Acosta born?
Illinois
300
A population has 100,000 people. It's population is expected to increase by 2% each year. Find the population in 15 years.
134,587
300
George receives a loan of $12,000 at an interest rate of 4.3% per year, compounded annually. He agrees to pay back the loan in installments of $1500 made at the end of each year. Find the number of years it will take to repay the loan.
10 years
300
An ice cream cone has a vertical height of 20 cm and a volume of 950 cm^3. Find the radius of the cone.
6.73 cm
300
The profit made by a baker making x homemade pies can be modelled by the function below. Find the number of pies he should make to maximize profit.
P=-0.05x^2+9x-60
90 pies
300
How many siblings does Ms. Acosta have?
3 (2 brothers and 1 sister)
400
A carpenter builds 2 shelves his first month at work. Each month he increases the number of shelves he can build by 3. Find the total amount of shelves he built in one year.
222 shelves
400
Joe deposits $500,000 into an annuity fund which earns 4.5% interest per year, compounded monthly. Joe wants the money to last for 20 years. How much can he afford to withdraw each month?
$282.60
400
Daniel has two water tanks with fish inside. The first is in the shape of a cylinder with diameter 40cm and height 45 cm. The second tank is a cuboid with length 40cm, width 32 cm, and height 42 cm. Each fish requires 15,000 cm^3 water to live comfortably. Calculate the number of fish Daniel can have in his fish tanks total.
6 fish
400
The entrance to a tunnel can be modelled using the quadratic below. Where h is the height of the tunnel in cm and x is the horizontal distance from the bottom left corner of the tunnel (0,0) given in cm. Find the equation of the axis of symmetry of the model of the tunnel.
h(x)=-0.6x^2+3.12x
x=2.6
400
Ms. Acosta is planning to move to which city in the U.S.?
Boulder, Colorado
500
Reed and Casey both run 5 kilometers in Week 1. Reed increases the amount he runs each week by 20%. Casey increases the amount he runs each week by 2 kilometers. At which week will Reed surpass Casey in number of kilometers run that week?
Week 9
500
Sara takes out a loan of $32,000. She will repay the loan over 5 years at an interest rate of 5.29% p.a., compounded monthly. She will pay the loan back in equal installments at the end of each month. After four years of repaying the loan, she decides she wants to pay the rest off in one payment. How much will she need to pay for this final payment?
$7092.82
500
A cone has a volume of 150 cm^3 and a vertical height of 14cm. Find the curved surface area of the cone.
145 cm^2
500
The path of an owl can be modelled by the function below where s(t) is the height of the owl in meters and t is the time after it leaves the branch in seconds. The owl is initially 12 meters above the ground. After 1 second the owl is 19.8 m above the ground. After 2 seconds, 34.5 m. After 4 seconds, 22.8 m. Solve for the values of a, b, c, and d.
s(t)=at^3+bt^2+ct+d
a = -2.58
b = 11.2
c = -0.8
d = 12
500
Ms. Acosta will be celebrating her ___ wedding anniversary this year?
Third