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IB Mathematics AA SL - Mock Exams

Mock Exam Set 1 - Paper 2

Trial Examinations for IB Mathematics AA SL

Paper 2

9 Questions

90 mins

80 marks

Paper

Difficulty

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Medium
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--- Section A ---

Question 1

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easy

[Maximum mark: 6]

Greg has saved 20002000 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 8%\text{\(8\)\hspace{0.05em}\%}, compounded monthly, for two years.

  1. 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.

  1. Calculate the nominal annual interest rate the second bank offers. [3]

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Question 2

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easy

[Maximum mark: 4]

The following table shows the number of overtime hours worked by employees in a company.

AA928a

It is known that the mean number of overtime hours is 11.

  1. Find the value of xx. [2]

  2. Find the standard deviation of the data. [2]

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Question 3

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easy

[Maximum mark: 6]

A 33D printer builds a set of 4949 Eif\text{f}fel Tower Replicas in different sizes. The height of the largest tower in this set is 6464 cm. The heights of successive smaller towers are 9595 % of the preceding larger tower, as shown in the diagram below.

AA724a

  1. Find the height of the smallest tower in this set. [3]

  2. Find the total height if all 4949 towers were placed one on top of another. [3]

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Question 4

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[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 8080 metres of fence.

580f23d360211ad7dd2c45e79d30c7d9c7d24f56.svg

  1. Write down the equation for the total length of the fence, 8080 m, in terms of xx and yy. [1]

  2. Write down the total area of both parcels of land in terms of xx. [2]

  3. Find the maximum area, in m2^2, of one parcel of land. [3]

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Question 5

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[Maximum mark: 6]

AA and BB are independent events such that P(AB)=0.09\mathrm{P}(A \cap {B\,} ^\prime) = 0.09 and P(AB)=0.49\mathrm{P}({A\,}^\prime \cap B) = 0.49.

Let x=P(AB)x = \mathrm{P}(A\cap B).

    1. Express P(A)\mathrm{P}(A) in terms of xx.

    2. Express P(B)\mathrm{P}(B) in terms of xx. [2]

  1. Find the value of xx. [2]

  2. Find P(BA)\mathrm{P}(B\,|\,A). [2]

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Question 6

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[Maximum mark: 7]

The velocity, vms1v\hspace{0.15em}\text{m}\hspace{0.15em}\text{s}^{-1}, at time tt seconds, of a particle moving in a straight line is given by

v=(t21)sint2v=\dfrac{(t^2-1)\,\mathrm{sin}\hspace{0.15em}t}{2}\,,

for 0t20 \leq t \leq 2.

  1. Determine when the particle changes direction for the first time. [2]

  2. Find the times when the acceleration of the particle is 1.4ms21.4\hspace{0.15em}\text{m}\hspace{0.15em}\text{s}^{-2}. [3]

  3. Find the acceleration of the particle when its speed is at its greatest. [2]

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--- Section B ---

Question 7

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[Maximum mark: 12]

The following table shows the total revenue, yy, in Australian dollars (AUD), obtained\text{obtained} daily during the first week of January 20202020, by Peppy's Pizza restaurant\text{restaurant} and the number of guests, xx, served.

9736e8eb9c9cfe8a065bfa8f5344721e7887b704.svg

    1. Calculate the Pearson's product-moment correlation coefficient, rr, for this data.

    2. Comment on the result. [3]

  1. Write down the equation of the regression line yy on xx. [1]

  2. Use the line of the regression to estimate the revenue of serving 7070 guests. Give your answer correct to the nearest AUD. [2]

The daily maintenance cost for the restaurant is 300300 AUD. Additionally, the cost of serving one guest is 55 AUD.

  1. Determine if the restaurant expects to make a profit when serving 5050 guests on a particular\text{particular} day. [2]

    1. Find an expression for the profit of the restaurant when serving xx guests on a particular day.

    2. Find the least number of guests required to be served to result in a profit for the day. [4]

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Question 8

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[Maximum mark: 18]

A cannonball is fired from the top of a tower. The rate of change of the height, hh, of the cannonball above the ground is modelled by

h(t)=4t+20,t0,\begin{aligned} h'(t) = -4t + 20, \hspace{0.5em} t \geq 0,\end{aligned}

where hh is in metres and tt is the time, in seconds, since the moment the cannonball was fired.

  1. Determine the time tt at which the cannonball reached its maximum height. [2]

After one second, the cannonball is 26 metres above the ground.

    1. Find an expression for h(t)h(t), the height of the cannonball above the ground at time tt.

    2. Hence, determine the maximum height reached by the cannonball. [5]

  1. Write down the height of the tower. [1]

  2. Calculate the height of the cannonball 44 seconds after it was fired. [2]

The cannonball hits its target on the ground nn seconds after it was fired.

  1. Find the value of nn. [2]

  2. Determine the total time the cannonball was above the height of the tower.[3]

A second cannonball is fired from exactly halfway up the tower, with the same projectile motion as the first cannonball.

  1. Given that both cannonballs land at the same time, determine the length of time between the first cannonball and the second cannonball being fired. [3]

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Question 9

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hard

[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 AA, sAs_A cm, at time tt seconds can be modelled by the function sA(t)=7t+9s_A(t)=7t+9, where 0t100 \leq t \leq 10.

The physicist found that the displacement of particle BB, sBs_B cm, at time tt seconds can be modelled by the function sB(t)=cos(3t+5)+8t+4s_B(t)=\mathrm{cos}(3t+5)+8t+4.

  1. Use the physicist's models to find the initial displacement of

    1. Particle AA;

    2. Particle BB correct to three significant figures. [3]

  2. Find the values of tt when sA(t)=sB(t)s_A(t)=s_B(t). [3]

  3. For t>6t>6, prove that particle BB was always further away from the fixed origin than particle AA. [3]

  4. For 0t100 \leq t \leq 10, find the total amount of time that the velocity of particle AA was greater than the velocity of particle BB. [6]

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