IB Mathematics Applications & Interpretation Topic AHL 4.13—non-linear Regression Questionbank (HL)

IB Mathematics Applications & Interpretation Topic AHL 4.13—non-linear Regression Questionbank (HL) | RevisionDojo

Practice IB Mathematics Applications & Interpretation (AI) Topic AHL 4.13—non-linear Regression with authentic exam-style questions for both SL and HL students. This question bank focuses on the exact syllabus content for AHL 4.13—non-linear Regression and mirrors Paper 1, 2, 3 style where relevant.

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Paper

Level

Question 1

HLPaper 2

Elena is modeling the decay of a radioactive substance. The mass, $M$ (in grams), remaining after $t$ days is given by:

$t$	0	5	10	15
$M$	100	60.7	36.8	22.3

She proposes a model of the form $M = M_{0} e^{- k t}$ , where $M_{0}$ is in grams and $k$ is measured in $day^{- 1}$ .

Show that the model satisfies the differential equation $\frac{d M}{d t} = - k M$ .

[2]

Find the values of $M_{0}$ and $k$ using a logarithmic transformation and least squares regression.

[3]

Estimate the mass remaining after 20 days.

[2]

Calculate the sum of squared residuals for the model $M = 100 e^{- 0.100 t}$ at the given data points.

[2]

Question 2

HLPaper 1

A ski coach records the take-off angle, $x^{\circ}$ , and the jump length, $y$ metres, for six trials.

$x$	20	25	30	35	40	45
$y$	16	21	24	25	24	21

Using the data provided, find the quadratic regression equation of the curve of best fit.

[2]

Using the quadratic regression equation found in part 1, predict the jump length when the take-off angle is $3 3^{\circ}$ .

[2]

Question 3

HLPaper 2

A researcher is studying the relationship between the number of hours spent studying, $x$ , and the scores obtained in a test, $y$ . The data collected is as follows: $(2, 50), (3, 55), (5, 65), (7, 70), (8, 75), (10, 80)$ .

Using the data provided, find the quadratic regression equation of the curve of best fit.

[2]

Using the quadratic regression equation found in part 1, predict the test score for a student who studies for 6 hours.

[2]

Question 4

HLPaper 1

An online retailer investigates the relationship between the percentage discount offered on a product, $r$ , and the daily profit, $P$ , in dollars. The data are shown below.

$r$	2	4	6	8	10	12
$P$	86	116	134	140	134	116

Using the data provided, find the quadratic regression equation of the curve of best fit.

[2]

Using the quadratic regression equation found in part 1, predict the daily profit for a discount of $7%$ .

[2]

Question 5

HLPaper 2

An ecologist models the population density of a species, $D$ (in individuals per $km^{2}$ ), as a function of distance, $x$ (in km), from a pollution source. The data suggests a Gaussian distribution:

$x$	0	1	2	3
$D$	10	50	80	50

The ecologist proposes a model of the form $D = a e^{- b (x - c)^{2}}$ , where $a, b$ , and $c$ are constants.

Transform the model into a linear form for regression.

[2]

Use least squares regression to estimate $a, b$ , and $c$ .

[3]

Calculate the coefficient of determination, $R^{2}$ , for the linearized regression of $Y = ln D$ on $X = (x - c)^{2}$ .

[2]

Predict the population density at $x = 4 km$ .

[2]

Discuss one limitation of this model for predicting density at large distances.

[2]

IB Mathematics Applications & Interpretation AHL 4.13—non-linear Regression Questionbank

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IB Mathematics Applications & Interpretation AHL 4.13—non-linear Regression Questionbank

IB Mathematics Applications & Interpretation (AI) Topic AHL 4.13—non-linear Regression Questionbank

Unlock all 16 questions with a free account