📝 Exam Questions — IB Mathematics AI

Calculate the expected frequency of a person aged 'Under 30' who prefers 'Tea'.

Draw a Venn diagram to represent this information.

A student is chosen at random from the group. Find the probability that the student uses neither Instagram nor TikTok.

Find the distance Leo runs in the 8th week of his training.

A new training program is introduced. A different group of 11 employees who completed the program had a median assembly time of 19 minutes and an interquartile range of 5 minutes. Interpret these results in the context of the training program.

Let p be the proposition “a person is under 1.4m tall” and q be the proposition “a person is accompanied by an adult”. Write down the rule in symbolic form.

In France, he sees a souvenir that costs 48 EUR. Calculate the cost of the souvenir in GBP.

One litre of paint covers 10 m². The paint is sold in 5-litre tins. Calculate the number of tins of paint that must be purchased.

Draw a tree diagram to represent this information. Show the probabilities on each branch.

Find the probability that both balls are green.

Find the probability that the two balls are of different colours.

For this data, find the median number of goals scored.

Calculate the mean number of goals scored.

The club's owner wants to present the most impressive scoring record to attract a new sponsor. State which measure of central tendency (mean, median, or mode) they should use. Justify your answer.

Find the value of the car after 5 years.

State one limitation of this linear model.

Write her original food budget as a percentage of her rent.

The calculated chi-squared value for this data is 1.48 (to 3 s.f.). The critical value at the 5% significance level is 3.84. State the conclusion of the test, with a reason.

Calculate the amount Anika pays in rent.

Anika's food budget is $400 per month. She decides to decrease this by 10%. Calculate her new monthly food budget.

Find the number of students who use only one of these social media platforms.

State the type of sequence that models the weekly distance Leo runs.

Write down the common difference of the sequence.

Find the total distance Leo runs in the first 8 weeks.

Estimate the time, in seconds, for light to travel from the Sun to the Earth.

Write your answer to part (a) in the form a × 10^k, where 1 ≤ a < 10 and k ∈ ℤ.

Convert your answer from part (a) to minutes and seconds.

Find the median time.

Find the interquartile range.

Draw a box-and-whisker plot for this data.

Write down the contrapositive of the statement in words.

A child is 1.3m tall and is with their 16-year-old sibling, who is not considered an adult by the park. State, with a reason, whether this child is allowed on the ride according to the rule.

The tourist exchanges 200 GBP. Calculate the amount in EUR he receives.

The tourist estimated the exchange rate as 1 GBP = 1.25 EUR. He wants to buy an item costing 60 EUR. Calculate the percentage error in his estimated cost in GBP.

Calculate the volume of the silo.

The curved surface of the silo needs to be painted. Calculate the area to be painted.

Write down the initial value of the car.

Calculate the number of years it takes for the car's value to decrease to zero.

State the null hypothesis for this test.

Write down the number of degrees of freedom for this test.

Find the total change in the population during the first 20 days of the study.

The population is considered endangered if it drops below 400 insects. By finding the population at t=20 and considering the minimum population, determine if the species becomes endangered during the first 30 days of the study.

Clara buys the car for $25,000. The value of the car is expected to depreciate by 15% each year. The value of the car after n years can be modelled by a geometric sequence. Find the value of the car 3 years after she buys it.

Her first strategy is to invest her current savings of $18,000 in an account that offers a nominal annual interest rate of 3.2%, compounded quarterly. Calculate the value of this investment after 5 years.

Her second strategy is to deposit $150 at the end of each month into a different savings account, which offers a nominal annual interest rate of 2.8%, compounded monthly. Calculate the total amount in this second account after 5 years.

After 5 years, Clara combines the money from both accounts. Determine whether she will have enough money to buy the car.

Interpret the meaning of the gradient, a, in the context of the question.

Use your regression equation to estimate the coral population density when the sea surface temperature is 27.0°C.

The biologist wants to predict the coral density in a region where the sea temperature is 30.5°C. Use your regression equation to find this estimate.

Comment on the reliability of your estimate in part (f).

Find the probability that a randomly selected smartphone of this model has a battery life of more than 16 hours.

Find the probability that a randomly selected smartphone has a battery life between 12.5 and 15 hours.

The manufacturer wants to advertise that 95% of their smartphones have a battery life of more than k hours. Find the value of k.

In a shipment of 500 smartphones, find the expected number of phones with a battery life of more than 16 hours.

A smartphone is considered 'sub-standard' if its battery life is less than 12 hours. A random sample of 20 smartphones is selected for a quality control check. (i) Find the probability that a randomly selected smartphone is sub-standard. (ii) Find the probability that in the sample of 20 smartphones, there are at least two sub-standard phones.

State the null and alternative hypotheses for this test.

Show that the expected frequency of a resident from District A who travels by Bicycle is 29.4.

Write down the number of degrees of freedom.

Perform the χ² test and write down the χ² statistic and the p-value.

State the conclusion for this test. Justify your answer.

The largest contribution to the χ² statistic comes from residents in District B who travel by Bicycle. For this cell, state the observed frequency, calculate the expected frequency, and comment on the difference.

Find the rate of change of the population at the start of the study.

Find the rate of change of the population after 10 days. Interpret your answer.

Find the time, t, at which the population of insects is at its maximum. Give your answer to the nearest day.

Find the number of years it will take for the car's value to be less than half of its purchase price.

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``` For this data, find the Pearson's product-moment correlation coefficient, r.

Describe the correlation between sea surface temperature and coral population density.

Find the equation of the regression line of y on x, in the form y = ax + b.