IB Mathematics AA HL - Mock Exams
Mock Exam Set 1 - Paper 2
Trial Examinations for IB Mathematics AA HL
Paper 2
12 Questions
120 mins
110 marks
Paper
Question Type
All
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--- Section A ---
Question 1
[Maximum mark: 4]
The following table shows the number of overtime hours worked by employees in a company.
It is known that the mean number of overtime hours is .
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Find the value of . [2]
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Find the standard deviation of the data. [2]
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Question 2
[Maximum mark: 6]
Greg has saved British pounds (GBP) over the last six months. He decided to deposit his savings in a bank which offers a nominal annual interest rate of , compounded monthly, for two years.
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Calculate the total amount of interest Greg would earn over the two years. Give your answer correct to two decimal places. [3]
Greg would earn the same amount of interest, compounded semi-annually, for two years if he deposits his savings in a second bank.
- Calculate the nominal annual interest rate the second bank
offers. [3]
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Question 3
[Maximum mark: 6]
A farmer is going to fence two equal adjacent parcels of land. These parcels share one side (which also requires fencing) as shown in the following diagram. The farmer has only metres of fence.
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Write down the equation for the total length of the fence, m, in terms of and . [1]
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Write down the total area of both parcels of land in terms of . [2]
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Find the maximum area, in m, of one parcel of land. [3]
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Question 4
[Maximum mark: 6]
and are independent events such that and .
Let .
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Express in terms of .
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Express in terms of . [2]
-
-
Find the value of . [2]
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Find . [2]
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Question 5
[Maximum mark: 6]
A D printer builds a set of Eifel Tower Replicas in different sizes. The height of the largest tower in this set is cm. The heights of successive smaller towers are % of the preceding larger tower, as shown in the diagram below.
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Find the height of the smallest tower in this set. [3]
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Find the total height if all towers were placed one on top of another. [3]
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Question 6
[Maximum mark: 6]
Consider the function , .
- Show that is an odd function. [2]
Now, consider the function given by , .
- By considering the graph of , solve for . [4]
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Question 7
[Maximum mark: 6]
The following diagram shows the curve , where .
The curve from point C to point P is rotated about the -axis to form a lamp shade. The rectangle ABCD, of height cm, is rotated about the -axis to form a solid ceiling fixture.
The lamp shade is assumed to have a negligible thickness.
Given that the interior volume of the lamp shade is to be , determine the height of the ceiling fixture, length AD in the diagram.
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Question 8
[Maximum mark: 7]
A professor and five of his students attend a talk given in a lecture series. They have a row of 8 seats to themselves.
Find the number of ways the professor and his students can sit if
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the professor and his students sit together. [3]
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the students decide to sit at least one seat apart from their professor. [4]
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Question 9
[Maximum mark: 9]
Consider two vectors and such that and .
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Find the possible range of values for . [2]
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Given that for some , find when is a minimum. [2]
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Find the vector such that , and is perpendicular to . [5]
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--- Section B ---
Question 10
[Maximum mark: 19]
Consider the differential equation
for and . It is given that when .
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Use Euler's method, with a step length of , to find an approximate value for when . [4]
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Use the substitution to show that . [3]
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By solving the differential equation, show that . [10]
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Find the actual value of when .
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Using the graph of , suggest a reason why the approximation given by Euler's method in part (a) is not a good estimate to the actual value of at . [2]
-
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Question 11
[Maximum mark: 15]
A physicist is studying the motion of two separate particles moving in a straight line. She measures the displacement of each particle from a fixed origin over the course of 10 seconds.
The physicist found that the displacement of particle , cm, at time seconds can be modelled by the function , where .
The physicist found that the displacement of particle , cm, at time seconds can be modelled by the function .
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Use the physicist's models to find the initial displacement of
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Particle ;
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Particle correct to three significant figures. [3]
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Find the values of when . [3]
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For , prove that particle was always further away from the fixed origin than particle . [3]
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For , find the total amount of time that the velocity of particle was greater than the velocity of particle . [6]
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Question 12
[Maximum mark: 20]
Consider the function , where .
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Sketch the curve , indicating the coordinates of the endpoints. [2]
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Show that .
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State the domain and range of . [5]
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The curve is rotated through about the -axis to form a solid of revolution that is used to model a vase.
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Show that the volume cm, of liquid in the vase when it is filled to a height of centimetres is given by .
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Hence, determine the volume of the vase. [5]
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At , the vase is filled to its maximum volume with water. Water is then removed from the vase at a constant rate of .
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Find the time it takes to completely empty the vase. [2]
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Find the rate of change of the height of the water when half of the water has been emptied from the vase. [6]
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