IB Mathematics AA HL - Mock Exams
Mock Exam Set 1 - Paper 1
Trial Examinations for IB Mathematics AA HL
Paper 1
12 Questions
120 mins
110 marks
Paper
Difficulty
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--- Section A ---
Question 1
[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 2
[Maximum mark: 6]
Prove by contradiction that the equation has no integer roots.
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Question 3
[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 4
[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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Question 5
[Maximum mark: 5]
Using the substitution , find the value of
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Question 6
[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 7
[Maximum mark: 7]
Points A and B represent the complex numbers and as shown on the Argand diagram below.
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Find the angle AOB. [3]
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Find the argument of . [1]
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Given that the real powers of , for , all lie on a unit circle centred at the origin, find the exact value of . [3]
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Question 8
[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 9
[Maximum mark: 8]
Consider the function for .
-
Show that the -intercept of is [3]
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Find the least positive value of for which . [5]
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--- Section B ---
Question 10
[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 11
[Maximum mark: 15]
Consider the planes , , given by the following equations:
- Show that the three planes do not intersect. [4]
It is given that the point Q lies on both and .
Let be the line of intersection of and .
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Find a vector expression for . [4]
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Show that is parallel to plane . [2]
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Hence or otherwise, find the distance between and Express your answer in the form , where , . [5]
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Question 12
[Maximum mark: 20]
Consider the function defined by for , , .
- Sketch the graph of , showing the values of any axes intercepts, the coordinates of any local maxima and minima, and the graphs of any asymptotes. [6]
Next, consider the function defined by for , .
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Show that . [6]
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State the domain of . [1]
Now, consider the function defined by .
- Given that , find the value of . Give your answer in the form where , . [7]
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