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IB Maths AI SL 1.8 Technology for equations

IB Maths AI SL 1.8 Technology for equations
IB Mathematics: applications and interpretation guide, first assessment 2021

Students practise forming equations from worded constraints, then solving systems or finding unknowns using GDC graphing, solver, or algebraic substitution.

How this is tested

  • derive simultaneous equations from sales data and solve using GDC matrix or solver function
  • substitute the volume condition into the area formula to write area in one variable
  • use a cubic's visible roots with root relationships to determine a parameter

Question 3

[Maximum number: 8]

A bakery sells boxes of cupcakes at the following prices:
- a small box, containing 1 cupcake, costs $ 4.50
- a medium box, containing 6 cupcakes, costs $ 23.50
- a large box, containing 12 cupcakes, costs $ 44.75.

Figure for Question 3 — IB Maths AI SL

In a particular week, the bakery sold 88 boxes containing a total of 383 cupcakes. The bakery collected $ 1486 from cupcake sales for the week.

The number of boxes of cupcakes sold during the week can be represented by

x+y+z=88,

where x is the number of small boxes sold, y is the number of medium boxes sold, and z is the number of large boxes sold.

Question 3(a)

(a)

Write down an equation in terms of x, y, and z to represent

[ 6 ]

Question 3(a)(i)

(i)

the number of cupcakes sold during the week.

[ 3 ]

Question 3(a)(ii)

(ii)

the money collected from sales of cupcakes for the week.

[ 3 ]

Question 3(b)

(b)

Hence, use your graphic display calculator to determine the number of medium boxes that were sold during the week.

[ 2 ]