Content
Access custom-built, exam-style problems for modelling. Each problem has a full solution and mark-scheme, as well as AI grading and support.
Select a Difficulty:
13 / 57 problems visible - Upgrade to view all problems
!
0 / 4
The function h(x)=2x+5 models the cost (in dollars) of renting a scooter for x hours.
Write down the cost of renting the scooter for 3 hours.
Solve h(x)=15.
State the gradient of the function and explain what it represents in this context.
!
0 / 5
The gravitational force of the Sun on a planet is proportional to the mass of the planet, and inversely proportional to the square of the distance between the planet and the Sun.
Let F be the gravitational force exerted by the Sun on Earth, which has a mass of 6×1024kg and is 1AU (astronomical unit) from the Sun.
Neptune's mass is approximately 17 times that of Earth, and it is 30AU from the Sun.
Find an expression in terms of F for the gravitational force exerted by the Sun on Neptune.
The force of gravity of the Sun on Jupiter, which is 5.20AU from the Sun, is 12 times that force on Earth.
Calculate the mass of Jupiter.
0 / 7
At the end of the 2024 fishing season on Fork Lake, 60 anglers (amateur fishers) were randomly surveyed. They were asked how many bass they caught over the whole season. The information is summarized in the following frequency table:
Assume that this sample is representative of all anglers in any season, and that all anglers have equal skill.
State the value of k.
For the 2025 season estimate
the probability a randomly selected angler will catch fish,
the expected number of fish caught by an angler over the season.
The U.S Fish and Wildlife Service (USFWS) estimates that the bass population in Lake Fork will grow by 8% between the 2024 and 2025 fishing seasons.
Given that the bass population was 110′000 at the end of the 2024 season, estimate the number of bass in the Lake at the opening of the 2025 season.
The USFWS wants the bass population to remain unchanged year to year.
How many seasonal fishing permits should be granted in 2025? Give your answer to the nearest hundred.
0 / 6
The blades of a wind turbine have a diameter of 16m and rotate clockwise at a constant speed, 1 revolution every 4 seconds. The blades are fixed on a shaft such that the tips of the blades are always at least 7m above the ground. The point Q lies at the tip of one of the blades.
Powered by Desmos
Let h be the height, in meters, of Q above the ground. After t minutes, h is given by h(t)=acos(bt)+c, where a,b,c∈R and a>0.
Show that Q starts at the highest possible point.
Find the values of a, b and c.
!
0 / 7
!
0 / 4
!
0 / 6
!
0 / 5
!
0 / 7
Ask Plex AI about problem 1
Get hints, ask questions, and work through this problem step by step