Practice SL 2.1—Equations of a line with authentic IB Mathematics Applications & Interpretation (AI) exam questions for both SL and HL students. This question bank mirrors Paper 1, 2, 3 structure, covering key topics like core principles, advanced applications, and practical problem-solving. Get instant solutions, detailed explanations, and build exam confidence with questions in the style of IB examiners.
A manufacturing company observes that its profit increases by $500 for every 50 units sold.
Find the rate of change of the profit function.
If the company sells 200 units, calculate the total profit.
If the goal is to reach a profit of $3,000, determine how many units the company must sell.
In urban planning, architects must ensure that roofs have a sufficient slope to facilitate rainwater drainage. For effective drainage, a roof must have a slope of at least 15 degrees.
Convert this slope into a ratio.
If the width of the roof is 10 meters, calculate how much higher one side should be compared to the other to meet the 15-degree requirement.
A new eco-friendly transportation route is being constructed parallel to an existing highway to reduce traffic congestion. The highway follows the equation .
Find the equation of the new transportation route that runs parallel to the highway and maintains a distance of 5 kilometers from it.
Write the equation of the new route in intercept form.
Write the equation of the new route in normal form.
A new park is being designed, and the planners need to place a fountain at a specific point along the line segment connecting two landmarks, A(1, 4) and B(5, 6).
Find the coordinates of point P on the line segment such that it is twice as far from A as it is from B, on the same side of A as B
Find the coordinates of point P on the line segment such that it is twice as far from A as it is from B, on the opposite side of A from B
An electric airplane is making a sustainable descent towards an airport. The airplane starts its descent at a height of 10,000 meters, located 100 kilometers away from the airport, and lands directly at the airport.
Find the equation of the line that models the airplane's descent path, assuming a constant descent angle.
How high will the airplane be when it is 40 kilometers from the airport?
Consider the two lines and .
Find the acute angle between lines and .
Determine if the system of equations and is consistent.
Find the distance between the two given lines if they are parallel.
Sketch the lines and .
A ski resort is evaluating its beginner slope, which descends 120 meters over a horizontal distance of 500 meters.
Calculate the slope of the ski run. Give your answer as a decimal.
If a skier starts at the top of the slope and skis 200 meters horizontally, how much elevation will they lose?
If the resort classifies slopes with a gradient greater than 30% as intermediate, would this slope be classified as beginner or intermediate? Show your working.
A ramp is being designed to provide wheelchair access to a public building. The ramp must comply with the standard that requires a maximum slope of 1:12.
Calculate the slope of the ramp if it needs to rise 1 meter over a horizontal distance of 15 meters.
Determine whether this ramp meets the maximum slope requirement.
If the total rise needed is 1.5 meters, calculate the minimum horizontal distance required to meet the slope standard.
If the available space for the ramp is only 12 meters in length, determine the rise that this ramp will achieve.
Two cities, A(2, 3) and B(-4, 7), are connected by a straight road.
Find the equation of the road passing through these points in slope-intercept form
Write the equation of the road in standard form
Write the equation of the road in point-slope form, using the midpoint of A and B as a point on the line
A solar energy company is planning to install solar panels on the roof of a community center. The roofline can be modeled by the equation . To maximize sunlight exposure, the solar panels must be installed along a line that is perpendicular to the roofline.
Find the equation of the line along which the solar panels should be installed, passing through the point and perpendicular to the roofline.
Write the equation of the solar panel line in normal form.