IB Maths AI HL 1.8 Technology for equations and models Question Bank

Practise IB Maths AI HL 1.8 by using technology to solve and evaluate equations in multi-step applied models.

Exam points

Use technology to solve simultaneous or nonlinear equations and report the required precision.
Interpret multiple numerical roots and reject solutions that violate the model constraints.
Check a technology-generated result using substitution, graph behaviour or an independent estimate.

[Maximum number: 3]

A sports player on a horizontal athletic field hits a ball. The height of the ball above the field, in metres, after it is hit can be modelled using a quadratic function of the form $f(x)=a x^{2}+b x+c$ , where x represents the horizontal distance, in metres, that the ball has travelled from the player.
A specialized camera tracks the initial path of the ball after it is hit by the player. The camera records that the ball travels through the three points (3,2.36),(10,5) and (17,7.16), as shown in Diagram 1.

Diagram 1

Use your answer to part (a) and two similar equations to find the equation of the quadratic model for the height of the ball.

finding other equations to solve simultaneously
$5=a(10)^{2}+b(10)+c$ AND 7.16 $=a(17)^{2}+b(17)+c$
OR 5=100 a+10 b+c AND 7.16 =289 a+17 b+c
any one coefficient in equation correct
$f(x)=-0.00490 x^{2}+0.441 x+1.08$ $\left(f(x)=-0.00489795 \ldots x^{2}+0.440816 \ldots x+1.08163 \ldots\right)$ $\left(f(x)=-\frac{6}{1225} x^{2}+\frac{108}{245} x+\frac{53}{49}\right)$
Note: Award at most (M1)(A1)A0 if answer is not expressed as an equation.

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SL 1.8—Technology for equations question 1