Practice IB Mathematics Applications & Interpretation (AI) Topic SL 1.8—use of Technology to Solve Systems of Linear Equations and Polynomial Equations with authentic exam-style questions for both SL and HL students. This question bank focuses on the exact syllabus content for SL 1.8—use of Technology to Solve Systems of Linear Equations and Polynomial Equations and mirrors Paper 1, 2, 3 style where relevant.
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A survey models the vertical profiles of two cables by and , for . Here is horizontal position in metres and is height in metres relative to a reference level. The cables meet at three points.
(a) all three -coordinates of intersection.
(b) the coordinates of the three points.
A technician calibrates three signed offsets , and , measured in millimetres. The calibration readings satisfy
(a) Solve the system.
A flare's height is modelled by , where is in metres and is in seconds. In the first two parts, use technology where appropriate.
(a) Find the time when the flare hits the ground, giving your answer correct to three significant figures.
(b) A signal reading is modelled by . Write down an equation whose solutions are the -values for which the signal reading is , and solve it.
(c) The cost of a subscription is modelled by , where is in dollars and is in years. Find the value of when the cost reaches .
The amount of substrate in a chemical reactor, , in kilograms, is modelled by where is the time, in hours, since the start of the reaction.
The chemist records the times at which .
(a) Write down the initial amount of substrate in the reactor.
(b) Find the three values of at which .
A bakery sells three types of bread: sourdough, multigrain, and rye. The table below shows the number of loaves sold of each type to three customers on a particular day, and the total amount each customer paid.
| Customer | Sourdough | Multigrain | Rye | Total () |
|---|---|---|---|---|
| Alex | 3 | 2 | 1 | 38.00 |
| Brenda | 2 | 4 | 3 | 61.00 |
| Cyrus | 1 | 1 | 4 | 44.80 |
Let , , and be the prices, in dollars, of one loaf of sourdough, multigrain, and rye respectively.
(a) Write down a system of three linear equations in , , and to represent this information.
(b) Use technology to solve your system and find the price of each type of bread.
(b) An additional reading is , where is a calibration coefficient. .
(c) The first calibration reading changes to mm, while the other two readings are unchanged. The technician requires . and the new offsets.
(d) Hence the first whole year for which the cost exceeds .
(c) Hence the total number of distinct times during the -hour period at which .
(c) Daria buys sourdough loaves, multigrain loaves, and rye loaves.
the total amount Daria pays.
