# 2018 November Maths HL – Paper 1

### Paper 1 – Question 1

Topic: Probability

Difficulty: Easy

Marks: 6

Question 1 (6 marks) in the 2018 November Maths HL Paper 1 Exam is a basic Probability Questions where events A and B are defined and information is given.

Part (a) asks to find P(A U B).

Part (b) asks to show that events A and B are not independent.

This is a standard Question 1 when comparing to other IB Math HL Past Papers.

## 2018 Mathematics HL Paper 1 November TZ0 Question 1 – 18N.1.hl.TZ0.1 – N18/5/MATHL/HP1/ENG/TZ0/XX

### Paper 1 – Question 2

Topic: Counting Principles

Difficulty: Easy

Marks: 5

Question 2 (5 marks) in the 2018 November Maths HL Paper 1 Exam is a Counting Principles Questions where a team of four is to be chosen from a group of four boys and four girls.

Part (a) asks to find the number of different possible teams that could be chosen.

Part (b) asks to find the number of different possible teams that could be chosen, given that the team must include at least one girl and at least one boy.

This is a standard Question 1-3 when comparing to other IB Math HL Past Papers.

## 2018 Mathematics HL Paper 1 November TZ0 Question 2 – 18N.1.hl.TZ0.2 – N18/5/MATHL/HP1/ENG/TZ0/XX

### Paper 1 – Question 3

Topic: Functions / Trig Calculus

Difficulty: Medium

Marks: 7

Question 3 (7 marks) in the 2018 November Maths HL Paper 1 Exam is a Functions / Trig Calculus Question. A function g(x) is given.

Part (a) asks to sketch the graph and indicate the maximum and minimum values of the function.

Part (b) asks to write down the least value of ‘a’ (lower limit of domain) such that the function has an inverse.

Part (c) asks to write down the domain of the inverse and to find an expression for the inverse.

This is a standard Question 2-5 when comparing to other IB Math HL Past Papers.

## 2018 Mathematics HL Paper 1 November TZ0 Question 3 – 18N.1.hl.TZ0.3 – N18/5/MATHL/HP1/ENG/TZ0/XX

### Paper 1 – Question 4

Topic: System of linear equations

Difficulty: Medium

Marks: 7

Question 4 (7 marks) in the 2018 November Maths HL Paper 1 Exam is a System of linear equations question. 3 equations are given with unknown variables.

Part (a) asks to find the value of ‘a’ for which the system of equations does not have a unique solution.

Part (b) asks to find the solution of the system of equations when a=2.

This is a standard Question 2-5 when comparing to other IB Math HL Past Papers.

## 2018 Mathematics HL Paper 1 November TZ0 Question 4 – 18N.1.hl.TZ0.4 – N18/5/MATHL/HP1/ENG/TZ0/XX

### Paper 1 – Question 5

Topic: Vectors

Difficulty: Medium

Marks: 6

Question 5 (6 marks) in the 2018 November Maths HL Paper 1 Exam is a Vector Questions. Vectors a and b are defined (containing the unknown variable ‘t’)

Part (a) asks to find an expression for the scalar product for a and b (in terms of t).

Part (b) asks to find the values of t for which the angle between a and b is obtuse.

This is a fairly easy section A question when comparing to other IB Math HL Past Papers.

## 2018 Mathematics HL Paper 1 November TZ0 Question 5 – 18N.1.hl.TZ0.5 – N18/5/MATHL/HP1/ENG/TZ0/XX

### Paper 1 – Question 6

Topic: Mathematical Induction

Difficulty: Medium / Hard

Marks: 6

Question 6 (6 marks) in the 2018 November Maths HL Paper 1 Exam is a Proof by Mathematical Induction Question.

This is quite a tricky proof question when comparing to other IB Math HL Past Papers (see video solution for more details and worked solution).

## 2018 Mathematics HL Paper 1 November TZ0 Question 6 – 18N.1.hl.TZ0.6 – N18/5/MATHL/HP1/ENG/TZ0/XX

### Paper 1 – Question 7

Topic: Calculus / Implicit Differentiationd

Difficulty: Medium / Hard

Marks: 6

Question 7 (6 marks) in the 2018 November Maths HL Paper 1 Exam is a Calculus Question. Two curves are defined C1 and C2.

Part (a) asks students to use implicit differentiation to find dy/dx for each curve.

Point P(a,b) is the point where C1 and C2 intersect.

Part (b) asks to show that the tangent to C1 at P is perpendicular to the tangent to C2 at P.

This is quite a challenging question when comparing to other IB Math HL Past Papers (see video solution for more details and worked solution).

## 2018 Mathematics HL Paper 1 November TZ0 Question 7 – 18N.1.hl.TZ0.7 – N18/5/MATHL/HP1/ENG/TZ0/XX

### Paper 1 – Question 8

Topic: Complex Numbers

Difficulty: Medium / Hard

Marks: 7

Question 8 (7 marks) in the 2018 November Maths HL Paper 1 Exam is a Complex Numbers Question. An equation with unknown variables a,b,c,d is defined.

Two of the roots of the equation are given and the sum of all the roots is also given. The question asks students to show 6a+d+12=0.

This is quite a challenging question when comparing to other IB Math HL Past Papers (see video solution for more details and worked solution).

## 2018 Mathematics HL Paper 1 November TZ0 Question 8 – 18N.1.hl.TZ0.8 – N18/5/MATHL/HP1/ENG/TZ0/XX

### Paper 1 – Question 9

Topic: Vectors

Difficulty: Hard

Marks: 15

Question 9 (15 marks) in the 2018 November Maths HL Paper 1 Exam is a Vector Question. A triangle OAB is defined and co-ordinates O, A and B are given (containing the unknown variable b).

Part (a) asks to find a Cartesian equation of the plane containing this triangle (in terms of b).

M is introduced as the midpoint of the line segment [OB].

Part (b) asks to find (in terms of b) the equation of the line ‘L’ which passes through M and is perpendicular to the plane found in part (a).

Part (c) asks to show that ‘L’ does not intersect the y-axis for any negative value of b.

This is a standard question when comparing to other IB Math HL Past Papers (see video solution for more details and worked solution).

## 2018 Mathematics HL Paper 1 November TZ0 Question 9 – 18N.1.hl.TZ0.9 – N18/5/MATHL/HP1/ENG/TZ0/XX

### Paper 1 – Question 10

Topic: Calculus

Difficulty: Hard

Marks: 19

Question 10 (19 marks) in the 2018 November Maths HL Paper 1 Exam is a Calculus Question.

Part (a) asks students to integrate the given equation using integration by parts.

Part (b) follows on from (a) with a ‘hence, show that’….. (see video solution for more details).

A function f(x) is defined and a sketch of the curve is provided. The function is the same as the equation in part (b).

Part (c) asks to find the x-coordinates points A and C on the diagram.

Part (d) asks to find the area enclosed by the curve and the x-axis between B and D (as shaded on the diagram.

This is a standard question when comparing to other IB Math HL Past Papers (see video solution for more details and worked solution).

## 2018 Mathematics HL Paper 1 November TZ0 Question 10 – 18N.1.hl.TZ0.10 – N18/5/MATHL/HP1/ENG/TZ0/XX

### Paper 1 – Question 11

Topic: Complex Numbers

Difficulty: Hard

Marks: 16

Question 11 (16 marks) in the 2018 November Maths HL Paper 1 Exam is a Complex Numbers Question.

Part (a) asks to find the roots of z^24=1 expressing answers in polar form.

Part (b) tells us that ‘S’ represents the sum of the roots found in part (a). (i) asks to show that Re’S’=Im’S’. (ii) and (iii) follow on from (i) asking students to find an expression for S.

This is a challenging question when comparing to other IB Math HL Past Papers (see video solution for more details and worked solution).

# 2018 November Maths HL – Paper 2

### Paper 2 – Question 1

Topic: Sequences & Series

Difficulty: Easy

Marks: 5

Question 1 (5 marks) in the 2018 November Maths HL Paper 2 Exam is a Sequences & Series Question. A geometric sequence is defined with the first and fourth terms given.

Part (a) asks to find the common ratio.

Part (b) asks to find the sum infinity.

This is a standard Question 1 when comparing to other IB Math HL Past Papers.

## 2018 Mathematics HL Paper 2 November TZ0 Question 1 – 18N.2.hl.TZ0.1 – N18/5/MATHL/HP2/ENG/TZ0/XX

### Paper 2 – Question 2

Topic: Calculus

Difficulty: Easy / Medium

Marks: 7

Question 2 (7 marks) in the 2018 November Maths HL Paper 2 Exam is a Calculus Question. Information about a function is provided and the 2nd derivative is given. The questions asks to find the function f(x).

This is a standard Question 2-4 when comparing to other IB Math HL Past Papers.

## 2018 Mathematics HL Paper 2 November TZ0 Question 2 – 18N.2.hl.TZ0.2 – N18/5/MATHL/HP2/ENG/TZ0/XX

### Paper 2 – Question 3

Topic: Probability (Normal Distribution)

Difficulty: Easy / Medium

Marks: 8

Question 3 (8 marks) in the 2018 November Maths HL Paper 2 Exam is a Probability Question. The question refers to battery life and information is given but the mean and standard deviation is unknown.

Part (a) asks to find the value of the mean and the standard deviation.

Part (b) asks to find the probability that a randomly selected battery will have a life of at least 15 hours.

This is a standard Question 2-4 when comparing to other IB Math HL Past Papers.

## 2018 Mathematics HL Paper 2 November TZ0 Question 3 – 18N.2.hl.TZ0.3 – N18/5/MATHL/HP2/ENG/TZ0/XX

### Paper 2 – Question 4

Topic: Binomial Theorem

Difficulty: Easy

Marks: 5

Question 4 (5 marks) in the 2018 November Maths HL Paper 2 Exam is a Binomial Theorem Question.

The question asks students to find the value of the constant term in a given binomial expansion.

This is a standard HL Math Question when comparing to other IB Math HL Past Papers.

## 2018 Mathematics HL Paper 2 November TZ0 Question 4 – 18N.2.hl.TZ0.4 – N18/5/MATHL/HP2/ENG/TZ0/XX

### Paper 2 – Question 5

Topic: Calculus

Difficulty: Easy / Medium

Marks: 5

Question 5 (5 marks) in the 2018 November Maths HL Paper 2 Exam is a Calculus Question.

A function f(x) is given and the question asks students derive the function using first principles.

This is a standard HL Math Question when comparing to other IB Math HL Past Papers.

## 2018 Mathematics HL Paper 2 November TZ0 Question 5 – 18N.2.hl.TZ0.5 – N18/5/MATHL/HP2/ENG/TZ0/XX

### Paper 2 – Question 6

Topic: Functions & Equations

Difficulty: Medium

Marks: 6

Question 6 (6 marks) in the 2018 November Maths HL Paper 2 Exam is a Functions & Equations Question. A polynomial is given, P(x).

Part (a) asks to find the relationship between the unknown variables a,b,c given that (x-5) is a factor of P(x).

Part (b) asks to write down the value of P'(5) given that (x-5)^2 is a factor of P(x).

Part (c) asks to find the values of b and c given that (x-5)^2 is a factor of P(x) and a=2.

This is a challengning HL Math Question when comparing to other IB Math HL Past Papers.

## 2018 Mathematics HL Paper 2 November TZ0 Question 6 – 18N.2.hl.TZ0.6 – N18/5/MATHL/HP2/ENG/TZ0/XX

### Paper 2 – Question 7

Topic: Trigonometry

Difficulty: Medium / Hard

Marks: 6

Question 7 (6 marks) in the 2018 November Maths HL Paper 2 Exam is a Trigonometry Question. A diagram of two overlapping circles is given with information about the dimensions of the circles. The overlapping region of the two circles is shaded and the question asks students to find the area of this shaded region.

This is a challenging HL Math Question when comparing to other IB Math HL Past Papers.

## 2018 Mathematics HL Paper 2 November TZ0 Question 7 – 18N.2.hl.TZ0.7 – N18/5/MATHL/HP2/ENG/TZ0/XX

### Paper 2 – Question 8

Topic: Rational Functions

Difficulty: Hard

Marks: 8

Question 8 (8 marks) in the 2018 November Maths HL Paper 2 Exam is a Rational Functions Question. A function f(x) is given (with unknown variables). A diagram is given of the sketch of (f(x))^2.

Part (a) asks to sketch the two possible graphs of f(x).

Part (b) asks to use the information provided to find the values of the unknown variables a,b,c.

This is a challenging HL Math Question when comparing to other IB Math HL Past Papers.

## 2018 Mathematics HL Paper 2 November TZ0 Question 8 – 18N.2.hl.TZ0.8 – N18/5/MATHL/HP2/ENG/TZ0/XX

### Paper 2 – Question 9

Topic: Calculus

Difficulty: Medium / Hard

Marks: 19

Question 9 (19 marks) in the 2018 November Maths HL Paper 2 Exam is a Calculus Question. A function f(x) is defined.

Part (a) asks to find f'(x).

Part (b) asks to find the co-ordinates of the point of inflection.

Part (c) asks to sketch the function and its inverse within a specific domain.

Part (d) asks to solve when the function is greater than the inverse.

This is a standard HL Math Question when comparing to other IB Math HL Past Papers.

## 2018 Mathematics HL Paper 2 November TZ0 Question 9 – 18N.2.hl.TZ0.9 – N18/5/MATHL/HP2/ENG/TZ0/XX

### Paper 2 – Question 10

Topic: Statistics & Probability

Difficulty: Hard

Marks: 18

Question 10 (18 marks) in the 2018 November Maths HL Paper 2 Exam is a Statistics & Probability Question.

Part (a) is a Poisson distribution question asking to find a specific probability and to calculate the standard deviation of the data.

Part (b) introduces a table of grouped data. (i) asks to estimate the mean of the data. (ii) asks to estimate the standard deviation of the data.

Part (c) asks to give evidence that the Poisson distribution model (from part a) is not a good fit.

A different set of information is introduced with a different Poisson distribution model.

Part (d) is a probability questions related to the new data.

Part (e) follows on from Part (d) and is a conditional probability question.

This is a challenging HL Math Question when comparing to other IB Math HL Past Papers.

## 2018 Mathematics HL Paper 2 November TZ0 Question 10 – 18N.2.hl.TZ0.10 – N18/5/MATHL/HP2/ENG/TZ0/XX

### Paper 2 – Question 11

Topic: Trigonometry

Difficulty: Hard

Marks: 13

Question 11 (13 marks) in the 2018 November Maths HL Paper 2 Exam is a Trigonometry Question. A diagram is provided showing a rectangle with triangle segments inside. Various dimensions are given.

Part (a) asks to find an expression for the angle at point P.

Part (b) asks to show a given equation (see video solutions for more details).

Part (c) asks to sketch the equation given in part (b) and to determine the range of values of the side length ‘p’ (refer to diagram in video solution).

This is a very challenging HL Math Question when comparing to other IB Math HL Past Papers.