IB Mathematics AA SL - Mock Exams
Mock Exam Set 1 - Paper 1
Trial Examinations for IB Mathematics AA SL
Paper 1
9 Questions
90 mins
80 marks
Paper
Difficulty
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--- Section A ---
Question 1
[Maximum mark: 6]
The diagram below shows the graph of a quadratic function .
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Write down the value of . [1]
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Find the value of and write down . [3]
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Calculate the coordinates of the vertex of the graph of . [2]
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Question 2
[Maximum mark: 5]
The random variable is normally distributed with a mean of . The following diagram shows the normal curve for .
Let be the shaded region under the curve between and . The area of is .
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Write down . [1]
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Find . [2]
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Find . [2]
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Question 3
[Maximum mark: 8]
The equation of a line is .
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Find the gradient of . [2]
A second line, , is perpendicular to .
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State the gradient of . [1]
The point P lies on .
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Find the equation of , giving your answer in the form , where . [2]
The point Q is the intersection of and .
- Find the coordinates of Q. [3]
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Question 4
[Maximum mark: 6]
Consider the curve where and .
The tangent to the curve at is perpendicular to the line .
Find the value of .
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Question 5
[Maximum mark: 7]
Consider the functions and , where and .
- Describe a sequence of two transformations that transforms the graph of to the graph of . [3]
The -intercept of the graph is at the point
- Find the range of . [4]
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Question 6
[Maximum mark: 7]
A real estate company keeps a register of the monthly cost of rent, , of their apartments and their corresponding area, , in m.
The areas of the apartments registered are summarised in the following box and whisker diagram.
- Find the smallest area that would not be considered an outlier. [3]
The regression line on is .
Meanwhile, the regression line on is .
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One of the apartments has a monthly rent of . Estimate the area of the rental. [2]
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Find the mean rental cost of all the real estate company's apartments. [2]
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--- Section B ---
Question 7
[Maximum mark: 12]
A particle moves along the -axis with a velocity, , at time seconds given by the function
For . The particle is initially at the origin.
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Find the value of when the particle reaches its maximum velocity. [3]
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Sketch a graph of against showing any points of intersection with the axes. [5]
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Find the displacement of the particle from the origin after 2 seconds. [4]
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Question 8
[Maximum mark: 18]
The first three terms of an infinite sequence, in order, are
First consider the case in which the series is geometric.
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Find the possible values of .
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Hence or otherwise, show that the series is convergent. [3]
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Given that and , find the value of . [3]
Now suppose that the series is arithmetic.
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Show that .
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Write down the common difference in the form , where . [4]
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Given that the sum of the first terms of the sequence is , find the value of . [8]
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Question 9
[Maximum mark: 11]
Carmen plays a game at a stall at a local fair. The stall owner lays cards face down on a table. Three of the cards say "Win" on the hidden side, the others say "Try Again". Carmen draws cards from the table, one after the other, without replacement. The game ends when Carmen draws a card that says "Win".
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Find the probability, in terms of , that the game will end on her nd draw. [2]
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Given that , find the probability that the game will end on her th draw. [2]
Carmen plays the game when . She pays to play and can earn money back depending on the number of draws it takes to obtain a card that says "Win". She earns no money back if she obtains a card that says "Win" on her th draw. Let be the amount of money that she earns back playing the game. This information is shown in the following table.
- Find the value of so that this is a fair game. [7]
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