# 2018 May Time Zone 1 Maths HL – Paper 1

### Paper 1 – Question 1

Topic: Functions

Difficulty: Easy

Marks: 5

Question 1 (5 marks) in the 2018 May Time Zone 1 (TZ1) Maths HL Paper 1 Exam is a functions question where a polynomial is given with 2 unknown constants, p & q. It is given that when the polynomial is divided by (x+1) the remainder is 7 and when the polynomial is divided by (x-2) the remainder is 1. The questions asks to find the values of the constants p & q.

This is a common IB Mathematics Higher Level Exam Question and appears in 30% – 40% of IB Math HL Past Papers (Paper 1).

2018 Mathematics HL Paper 1 May Time Zone 1 (TZ1) Question 1 – 18M.1.hl.TZ1.1 – M18/5/MATHL/HP1/ENG/TZ1/XX

### Paper 1 – Question 2

Topic: Trig & Calculus

Difficulty: Medium

Marks: 7

Question 2 (7 marks) in the 2018 May Time Zone 1 (TZ1) Maths HL Paper 1 Exam is a trigonometry question where the equation of y is given as sin^(theta). There is also a domain restriction for the function.

Part (a) asks students to find the derivative function.

Part (b) asks to hence find the values of theta for which the derivative function found in part (a) is equal to 2y.

This is an interesting IB Mathematics Higher Level Exam Question and similar questions only appear in 10% – 15% of IB Math HL Past Papers (mostly Paper 1).

2018 Mathematics HL Paper 1 May Time Zone 1 (TZ1) Question 2 – 18M.1.hl.TZ1.2 – M18/5/MATHL/HP1/ENG/TZ1/XX

### Paper 1 – Question 3

Topic: Probability

Difficulty: Medium

Marks: 5

Question 3 (5 marks) in the 2018 May Time Zone 1 (TZ1) Maths HL Paper 1 Exam is a Probability distribution question where a table is given with two unknown probabilities.

Part (a) asks students to find the values of the two unknowns with the information provided in the question.

Part (b) asks to find the expected value.

This is a very common IB Mathematics Higher Level Exam Question and appears in 40% – 45% of IB Math HL Past Papers (mostly Paper 1).

2018 Mathematics HL Paper 1 May Time Zone 1 (TZ1) Question 3 – 18M.1.hl.TZ1.3 – M18/5/MATHL/HP1/ENG/TZ1/XX

### Paper 1 – Question 4

Topic: Integration

Difficulty: Medium

Marks: 6

Question 4 (6 marks) in the 2018 May Time Zone 1 (TZ1) Maths HL Paper 1 Exam is an Integration question where the function f(x) is not given. The definite integral between known limits is given.

Part (a) asks students to use the information given in the question to find the definite integral of [f(x)+2] between given limits.

Part (b) asks students to use the information given in the question to find the definite integral of [f(x+2] between given limits.

This is quite a common IB Maths SL (Standard Level) question but slightly more difficult, hence now a HL question. Mathematics Higher Level Exam Question like this appear in 10% – 15% of IB Math HL Past Papers (mostly Paper 1).

2018 Mathematics HL Paper 1 May Time Zone 1 (TZ1) Question 4 – 18M.1.hl.TZ1.4 – M18/5/MATHL/HP1/ENG/TZ1/XX

### Paper 1 – Question 5

Topic: Logs

Difficulty: Medium

Marks: 6

Question 5 (6 marks) in the 2018 May Time Zone 1 (TZ1) Maths HL Paper 1 Exam is a logs questions where you are given an equation where you need to solve for x using multiple log laws.

This is an interesting twist on a common IB Mathematics Higher Level Exam Question. Logs/Exponents questions typically appear in 80% – 90% of IB Math HL Past Papers (Paper 1 or Paper 2) but a question like this is less common. Watch the video solution for detailed steps on the solution.

2018 Mathematics HL Paper 1 May Time Zone 1 (TZ1) Question 5 – 18M.1.hl.TZ1.5 – M18/5/MATHL/HP1/ENG/TZ1/XX

### Paper 1 – Question 6

Topic: Mathematical Induction

Difficulty: Medium / Hard

Marks: 7

Question 6 (7 marks) in the 2018 May Time Zone 1 (TZ1) Maths HL Paper 1 Exam is a proof by mathematical induction question.

The proof involves equating a series of fractions to a simplified expression (see video solution for more details).

This is a fairly common IB Mathematics Higher Level Exam Question and appear in 20% – 30% of IB Math HL Past Papers (mostly Paper 1).

2018 Mathematics HL Paper 1 May Time Zone 1 (TZ1) Question 6 – 18M.1.hl.TZ1.6 – M18/5/MATHL/HP1/ENG/TZ1/XX

### Paper 1 – Question 7

Topic: Calculus

Difficulty: Hard

Marks: 9

Question 7 (9 marks) in the 2018 May Time Zone 1 (TZ1) Maths HL Paper 1 Exam is a calculus question with both differentiation and integration components. The function y is given as arccos(x/2).

Part (a) asks you to find dy/dx.

Part (b) asks to find the definite integral of y with given limits. Integration by parts is needed.

This is a challenging IB Mathematics Higher Level Exam Question and similar questions appear in 60% – 70% of IB Math HL Past Papers (Paper 1 or Paper 2).

2018 Mathematics HL Paper 1 May Time Zone 1 (TZ1) Question 7 – 18M.1.hl.TZ1.7 – M18/5/MATHL/HP1/ENG/TZ1/XX

### Paper 1 – Question 8

Topic: Trigonometry

Difficulty: Medium / Hard

Marks: 5

Question 8 (5 marks) in the 2018 May Time Zone 1 (TZ1) Maths HL Paper 1 Exam is a Trigonometry question.

The equation a=sin(b) is defined and the question asks students to find (in terms of b) the solutions of: sin2x=-a for a given domain. Understanding of the unit circle is required.

This is tricky IB Mathematics Higher Level Exam Question and typically appear in 20% – 30% of IB Math HL Past Papers (mostly Paper 1).

2018 Mathematics HL Paper 1 May Time Zone 1 (TZ1) Question 8 – 18M.1.hl.TZ1.8 – M18/5/MATHL/HP1/ENG/TZ1/XX

### Paper 1 – Question 9

Topic: Calculus

Difficulty: Hard

Marks: 17

Question 9 (17 marks) in the 2018 May Time Zone 1 (TZ1) Maths HL Paper 1 Exam is calculus question where a function is given.

Part (a) asks to find the coordinates of the local maximum.

Part (b) asks to show that there is exactly 1 point of inflection.

Part (c) asks you to sketch the function showing the 2 points found in parts a and b.

This is a fairly challenging IB Math HL Exam Question and similar to questions seen in IB Past Papers.

2018 Mathematics HL Paper 1 May Time Zone 1 (TZ1) Question 9 – 18M.1.hl.TZ1.9 – M18/5/MATHL/HP1/ENG/TZ1/XX

### Paper 1 – Question 10

Topic: Vectors

Difficulty: Hard

Marks: 19

Question 10 (19 marks) in the 2018 May Time Zone 1 (TZ1) Maths HL Paper 1 Exam is a challenging vectors question. 4 coordinates are given and are vertices of a square based pyramid.

Part (a) asks to find the Cartesian equation of the plane that passes through points A,B,D.

Part (b) asks to find the angle between two faces of the shape.

Part (c) asks to find the Cartesian equation of the plane that passes through O and is normal to the line BD.

Part (d) asks you to show that the point P is a mid point to AD.

Part (e) asks you to find the area of the triangle OPQ.

This is a very challenging IB Mathematics Higher Level Exam Question and similar questions appears in 20% – 30% of IB Math HL Past Papers (Paper 1 or Paper 2).

2018 Mathematics HL Paper 1 May Time Zone 1 (TZ1) Question 10 – 18M.1.hl.TZ1.10 – M18/5/MATHL/HP1/ENG/TZ1/XX

### Paper 1 – Question 11

Topic: Complex Numbers

Difficulty: Hard

Marks: 14

Question 11 (14 marks) in the 2018 May Time Zone (TZ1) Maths HL Paper 1 Exam is Complex Numbers question. A complex number w is given.

Part (a) asks to express w^2 and w^3 in modulus-argument form.

Part (b) asks to show that the vertices of w^0, w^1, w^2, w^3 on an Argand diagram form a quadrilateral with a given area.

Part (c) is a problem solving extension from parts a and b (see video solution for more details).

This is a challenging IB Mathematics Higher Level Exam Question. Part (c) is worth 6 marks and you need a strong understanding of parts a and b in order to answer part c. This type of question typically only appear in 10% – 20% of IB Math HL Past Papers (Paper 1 or Paper 2).

2018 Mathematics HL Paper 1 May Time Zone (TZ1) Question 11 – 18M.1.hl.TZ1.11 – M18/5/MATHL/HP1/ENG/TZ1/XX

# 2018 May Time Zone 1 Maths HL – Paper 2

### Paper 2 – Question 1

Topic 1: Sequences & Series

Difficulty: Easy

Marks: 7

Question 1 (7 marks) in the 2018 May Time Zone 2 (TZ1) Maths HL Paper 2 Exam is a simple sequences and series question where the third and tenth terms of an arithmetic sequence is given.

Part (a) asks to find the first term and the common difference.

Part (b) asks to calculate the number of positive terms in the sequence.

This is very common IB Mathematics Higher Level Exam Question and typically appear in Section A of IB Math HL Past Papers (Paper 1 or Paper 2).

2018 Mathematics HL Paper 2 May Time Zone 1 (TZ1) Question 1 – 18M.2.hl.TZ1.1 – M18/5/MATHL/HP2/ENG/TZ1/XX

### Paper 2 – Question 2

Topic: Functions

Difficulty: Easy

Marks: 6

Question 2 (6 marks) in the 2018 May Time Zone 1 (TZ1) Maths HL Paper 2 Exam gives you a quadratic with roots alpha, beta. The question also gives you a different quadratic with roots (alpha+1) and (beta+1). The question then asks you to find the values of p and q which are constants in the first quadratic.

This is a fairly easy IB Mathematics Higher Level Exam Question. Similar questions to this typically appear in Section A of IB Math HL Past Papers (mostly Paper 1).

2018 Mathematics HL Paper 2 May Time Zone 1 (TZ1) Question 2 – 18M.2.hl.TZ1.2 – M18/5/MATHL/HP2/ENG/TZ1/XX

### Paper 2 – Question 3

Topic: Trigonometry

Difficulty: Medium

Marks: 5

Question 3 (5 marks) in the 2018 May Time Zone 1 (TZ1) Maths HL Paper 2 Exam is a trigonometry question where a function is defined.

The question asks you to express the original function in terms of only sinx and cosx. Trig identities are needed in this question.

This is tricky IB Mathematics Higher Level Exam Question. Similar questions to this typically appear in Section A of IB Math HL Past Papers (mostly Paper 1).

2018 Mathematics HL Paper 2 May Time Zone 1 (TZ1) Question 3 – 18M.2.hl.TZ1.3 – M18/5/MATHL/HP2/ENG/TZ1/XX

### Paper 2 – Question 4

Topic: Normal/Binomial Distribution

Difficulty: Medium

Marks: 5

Question 4 (5 marks) in the 2018 May Time Zone 1 (TZ1) Maths HL Paper 2 Exam is a Normal & Binomial Distribution question involving the age of wolves.

Part (a) is a normal distribution question asking for a specific probability. This is straight forward on the GDC.

Part (b) tells you that 8 wolves are selected at random and you need to find the probability a certain amount of the wolves are at least 5 years old. This is a Binomial distribution question using GDC.

This is a fairly common IB Mathematics Higher Level Exam Question. Similar questions to this typically appear in Section A of IB Math HL Past Papers (mostly Paper 2).

2018 Mathematics HL Paper 2 May TZ1 Question 4 – 18M.2.hl.TZ1.4 – M18/5/MATHL/HP2/ENG/TZ1/XX

### Paper 2 – Question 5

Topic: Integration

Difficulty: Medium

Marks: 7

Question 5 (7 marks) in the 2018 May Time Zone 1 (TZ1) Maths HL Paper 2 Exam is functions and Integration question.

Part (a) asks you to rearrange a given quadratic into a different form.

Part (b) asks to hence find the integral of the original function. You must get part a correct to proceed to part b.

This is fairly common IB Mathematics Higher Level Exam Question. When looking at IB Math HL Past Papers, this type of question has been successfully answered by HL candidates.

2018 Mathematics HL Paper 2 May TZ1 Question 5 – 18M.2.hl.TZ1.5 – M18/5/MATHL/HP2/ENG/TZ1/XX

### Paper 2 – Question 6

Topic: Poisson Distribution

Difficulty: Medium

Marks: 5

Question 6 (5 marks) in the 2018 May Time Zone 1 (TZ1) Maths HL Paper 2 Exam is a Poisson Distribution question.

The mean number of squirrels in an enclosure is given and the question asks a conditional probability question with a proportionally larger area.

This is a common IB Mathematics Higher Level Exam Question. When looking at IB Math HL Past Papers, students need to practice these types of questions as they appear in most exam.

2018 Mathematics HL Paper 2 May TZ1 Question 6 – 18M.2.hl.TZ1.6 – M18/5/MATHL/HP2/ENG/TZ1/XX

### Paper 2 – Question 7

Topic: Algebra

Difficulty: Medium / Hard

Marks: 8

Question 7 (8 marks) in the 2018 May Time Zone 1 (TZ1) Maths HL Paper 2 Exam is worded problem involving the number of fish in a lake. The number of fish decreases by 7% each year but 250 new fish are added at the end of each year. The initial amount of fish is given.

Part (a) asks to show that there will be 2645 fish in the lake in 2020.

Part (b) asks to calculate the number of fish in the lake in 2042.

This is a difficult IB Mathematics Higher Level Exam Question and similar questions appears in 10% – 15% of IB Math HL Past Papers (mostly Paper 2).

2018 Mathematics HL Paper 2 May TZ1 Question 7 – 18M.2.hl.TZ1.7 – M18/5/MATHL/HP2/ENG/TZ1/XX

### Paper 2 – Question 8

Topic: Probability

Difficulty: Medium / Hard

Marks: 7

Question 8 (7 marks) in the 2018 May Time Zone 1 (TZ1) Maths HL Paper 2 Exam is challenging Probability question looking at the number of pets students own (class of 25). Information is given in the question and the task is to find the number of students in the class who don’t own a pet. Your formula booklet is needed for this question!

This is an interesting and challenging IB Mathematics Higher Level Exam Question. When comparing to other IB Math HL Past Papers, this question has a different feel and will challenge a lot of students.

2018 Mathematics HL Paper 2 May TZ1 Question 8 – 18M.2.hl.TZ1.8 – M18/5/MATHL/HP2/ENG/TZ1/XX

### Paper 2 – Question 9

Topic: Calculus

Difficulty: Hard

Marks: 22

Question 9 (22 marks) in the 2018 May Time Zone 1 (TZ1) Maths HL Paper 2 Exam is a Calculus question where an implicit equation is defined with a diagram.

Part (a) asks to show that there are exactly 2 points on the curve where the gradient is zero.

Part (b) asks to find the equation of the normal to the curve at a point P(2,1).

Part (c) asks to find the 2nd point where the normal at P cuts the curve (point Q).

Part (d) asks to find the volume of the solid formed when the shaded region in the diagram is rotated 2pi about the y-axis.

This is an interesting and fairly common IB Mathematics Higher Level Exam Question. When comparing to other IB Math HL Past Papers, this question is similar in difficulty to most Section B Calculus questions.

2018 Mathematics HL Paper 2 May TZ1 Question 9 – 18M.2.hl.TZ1.9 – M18/5/MATHL/HP2/ENG/TZ1/XX

### Paper 2 – Question 10

Topic: Probability Density Function

Difficulty: Hard

Marks: 13

Question 10 (13 marks) in the 2018 May Time Zone 1 (TZ1) Maths HL Paper 2 Exam is Probability Density Function question. The function is given.

Part (a) asks to show that the constant ‘a’ in the function is = 2/3.

Part (b) asks to find the probability that X<1.

Part (c) is a challenging conditional probability question (see video for more details).

This is a very challenging IB Mathematics Higher Level Exam Question. When comparing to other IB Math HL Past Papers, this question is similar / slightly more difficult to most Section B functions questions.

2018 Mathematics HL Paper 2 May TZ1 Question 10 – 18M.2.hl.TZ1.10 – M18/5/MATHL/HP2/ENG/TZ1/XX

### Paper 2 – Question 11

Topic: Vectors

Difficulty: Hard

Marks: 15

Question 11 (15 marks) in the 2018 May Time Zone 1 (TZ1) Maths HL Paper 2 Exam is Vectors question involving two Submarines and their position in time respectively

Part (a) asks to show that the two submarines will collide at a point P.

Part (b) describes how Submarine B adjusts its velocity to avoid the collision. It then asks to show that the submarine is still travelling the same direction (direction vector is just scaled down).

Part (c) asks to find the time and the distance when the two submarines are closest together.

This is a challenging IB Mathematics Higher Level Exam Question, especially part (c). When comparing to other IB Math HL Past Papers, this question is similar / slightly more difficult to most Section B questions.

2018 Mathematics HL Paper 2 May TZ1 Question 11 – 18M.2.hl.TZ1.11 – M18/5/MATHL/HP2/ENG/TZ1/XX

The 2018 May Time Zone 1 Paper 1 and Paper 2 IB Exams are great exams to practice for IB Exam revision. This Time Zone has a nice spread of easy/difficult questions that challenge IB Math HL Candidates. It is recommended that students attempt these IB exams in full with the help of the Revision Village video worked solutions.