# IB Maths Past Paper Overviews

## 2017 November Maths HL – Paper 1

### Paper 1 – Question 1

Topic: Logs

Difficulty: Easy

Marks: 5

Question 1 is a simple logs question where it asks you to solve for x. This is a fairly common question when looking through IB Maths HL past papers. Just apply your log laws correctly and you should be on your way to 5 out of 5.

### Paper 1 – Question 2

Topic: Vectors

Difficulty: Easy

Marks: 6

Question 2 is a vectors question where two points are given, and a plane equation is also given.

Part (a) asks you to find the vector equation of the line that passes through the two given points.

Part (b) asks you to find the coordinates of the point of intersection of the vector equation and the plane.

### Paper 1 – Question 3

Topic: Functions

Difficulty: Medium

Marks: 6

Question 3 is a common IB Maths HL question where a cubic function is given with the coefficient of the ‘x’ term unknown, ‘k’.

Part (a) tells you that (x-4) is a factor of the function, and to find the unknown variable in the function, ‘k’.

Part (b) asks you to hence or otherwise, factorize the function as a product of linear factors. This is straight forward considering we know (x-4) is a factor.

### Paper 1 – Question 4

Topic: Binomial Expansion

Difficulty: Easy

Marks: 4

Question 4 is an easy Binomial Expansion question where the question asks you to find the coefficient of a term. There is no trick to this question. Hopefully 4/4.

### Paper 1 – Question 5

Topic: Kinematics

Difficulty: Medium

Marks: 5

Question 5 is a kinematics question where the velocity function of a particle is given. The question asks you to find the exact distance traveled in the first half second. When integrating the velocity function, integration by parts is required.

### Paper 1 – Question 6

Topic: Functions

Difficulty: Medium

Marks: 9

Question 6 is quite a generous 9-mark question involving a simple rational function.

Part (a) asks you to sketch the rational function on the grid provided, clearly showing any asymptotes and intercepts with axes.

Part (b) is a common question amongst HL past papers where it asks you to solve the inequality of when the function (with absolute value signs around it) is less than 2. Watch the video solution if you are not comfortable with modulus functions and inequalities.

### Paper 1 – Question 7

Topic: Calculus

Difficulty: Hard

Marks: 8

Question 7 is an interesting implicit differentiation question. A curve is given (name: ‘folium of Descartes’) and the question asks you to find the exact coordinate of the point on the curve where the tangent is parallel to the y-axis. There are multiple ways to solve this. Watch the video solution to this question for the most straight forward method.

### Paper 1 – Question 8

Topic: Complex Numbers

Difficulty: Medium

Marks: 7

Question 8 is a very common HL past paper question. It asks you to find the roots of the given complex number equation. Use De Moivre’s theorem. If you are strong with complex numbers, this should be 7/7.

### Paper 1 – Question 9

Topic: Vectors

Difficulty: Hard

Marks: 18

Question 9 is the first of three challenging Section B questions in this exam. A diagram is given and vectors connecting points are defined as well as ratios of side lengths.

Part (a) asks you to express certain side lengths in terms of the vectors a and b.

Part (b) is similar to (a) where it asks you to express certain side lengths in terms of a, b as well as other ratios and variables that were given in the question. This is where this questions start to get tricky.

Part (c) asks you to find one of the unknown variables defined in the question.

Part (d) is similar to parts (a) and (b) asking you to express a side length in terms of a and b only. This is more challenging.

Part (e) compares two areas in the diagram and asks you to find the value of ‘k’ which is the ratio of the two areas. This is very challenging.

### Paper 1 – Question 10

Topic: Counting Principles and Probability

Difficulty: Medium

Marks: 11

Question 10 is a smaller Section B question with only 2 parts to the question. Chloe and Selena play a game with four cards each, ABCD.

Part (a) explains that if the cards line up together and match, Selena wins the game and if none of them match, Chloe wins the game. The question asks you to show that the probability of Chloe winning the game is 3/8. Counting principles are required to show this. Watch the video solution to this question if this topic is not a strength of yours as it is a little bit confusing.

Part (b) then turns into a binomial distribution question asking for the mean and variance given that the two girls play the game 50 times. Even if you don’t get Part (a), this should be an easy 5/5 marks as its one of the easier HL questions when going through IB past papers.

### Paper 1 – Question 11

Topic: Circular Functions, Mathematical Induction, Calculus

Difficulty: Hard

Marks: 21

Question 11 is a beast! A continuous trigonometric is defined.

Part (a) asks you to determine whether the function is odd or even.

Part (b) is an 8-mark mathematical induction question where trig identities are needed throughout. This is a pretty standard question when comparing to other IB Maths HL past paper questions that involve mathematical induction. Watch the video solution if you want step by step working.

Part (c) asks you to find the derivative of the function using the answer from part (b).

Part (d) asks you to find the equation of the tangent to the curve at a given x point. This is 8 marks and requires a lot of trig and calculus knowledge. A nice tough question to finish off the paper.

## 2017 November Maths HL – Paper 2

### Paper 2 – Question 1

Topic 1: Linear Functions

Difficulty: Easy

Marks: 4

Question 1 gives you information about boxes containing three different types of fruit and the overall price of the box. We have three equations, with three unknown variables. As this is a calculator question, we can put these equations straight into our calculator and using the ‘linsolve’ function to solve. Watch the video solution if you do not know where this button is.

### Paper 2 – Question 2

Topic: Probability

Difficulty: Easy

Marks: 6

Question 2 is an easy probability question where the union, intersection and conditional probabilities of events A and B are given.

Part (a) asks you to find the probability of event B.

Part (b) asks you to find the probability of event A.

Part (c) asks you to show that events A’ and B are independent.

### Paper 2 – Question 3

Topic: Trigonometry

Difficulty: Easy

Marks: 4

Question 3 is an interesting trig question where are unusual shaped diagram is provided and the question asks you to find the total area of the shape. The area of a sector formula is needed and also the ability to convert given angles that are in degrees into radians in order to use the area equations.

### Paper 2 – Question 4

Topic: Normal Distribution

Difficulty: Medium

Marks: 6

Question 4 is a very common IB Maths HL past paper question involving normally distributed data. Two probabilities are given, and the question asks you to find the mean and standard deviation of the data.

### Paper 2 – Question 5

Topic: Trigonometry

Difficulty: Easy

Marks: 6

Question 5 is a simple trigonometry question where a diagram of triangles is provided. The question asks you to find the distance between two yachts out at sea and as long as you know what an angle of depression is, SOHCAHTOA and the cosine rule, this should be a 6/6 question.

### Paper 2 – Question 6

Topic: Poission Distribution, Binomial Distribution

Difficulty: Easy

Marks: 6

Question 6 is a Poisson distribution question where the mean is given.

Part (a) asks you to find the probability of at least one…… hopefully we know what to do here. If these questions say at least one, we need to make that ‘1-P(X=0)’. Pretty standard HL past paper question.

Part (b) asks you to find the expected number per week over the course of a year. Here you need to convert you Poisson distribution mean to weekly (x7) and then do the binomial distribution calculation for expected value.

### Paper 2 – Question 7

Difficulty: Medium

Marks: 5

Question 7 gives you a quadratic equation where the constant is unknown, ‘p’. It tells you that one of the roots is three times the other root and to solve for ‘p’. They key to this question is to use the sum and product of roots and simultaneous equations. Watch the video solution if this is not an area of strength for you.

### Paper 2 – Question 8

Topic: Integration

Difficulty: Hard

Marks: 7

Question 8 is a difficult integration by substitution question involving multiple trig identities. This type of question is common across IB Maths HL past papers and is the type of question that will separate the 6’s from the 7’s. Watch the video solution for the step by step working.

Part (e) is another head scratcher. It gives you a paragraph explaining changes made to the data and ask you to find a probability. Not many students will score arks in this question (3 marks on offer). There aren’t many questions like this, so this will be another separator of the 6/7 students. Hint: it’s a binomial distribution question in disguise!

### Paper 2 – Question 9

Topic: Counting Principles

Difficulty: Medium

Marks: 6

Question 9 is an interesting question where a 3×4 grid of desks is shown in a diagram.

Part (a) asks you to calculate the number of ways the 12 students can sit on the desks….. ‘12!’ of course! But only worth 1-mark 🙁

Part (b) asks you to find the number of ways the 12 students can be arranged if Helen and Nicki must sit directly behind each other. Drawing a diagram helps.

Part (c) asks you to find the total number of ways the 12 students can be arranged if Helen and Nicki must not sit next to each other.

When comparing this type of question to other IB HL Past paper questions, there has been easier but there has been much harder.

### Paper 2 – Question 10

Topic: Functions, Trig, Calculus

Difficulty: Medium

Marks: 17

Question 10 is the first Section B question and isn’t too bad. A function is given.

Part (a) asks you to show that x-coordinate of the minimum satisfies the equation tanx=2x. We just need to derive the original function (quotient rule) and make it equal to zero and this is achieved. The question also asks you to determine the values for x for which the function is decreasing.

Part (b) asks you to sketch the curve.

Part (c) asks you to find the coordinates of the point where the normal to the curve is parallel to a given equation.

Part (d) gives you limits and an enclosed region to be rotated 360deg about the x-axis to find the volume of revolution.

### Paper 2 – Question 11

Topic: Trig Function, Calculus

Difficulty: Hard

Marks: 18

Question 11 gives you a trigonometric function within a specified domain.

Part (a) asks you to find the derivative. Straight forward. It then asks you to sketch the derivative. It finally asks you to find and label the coordinates of the point of inflection. This requires some understanding of calculus curves.

Part (b) defines u=tanx. It then asks you to express sinx and sin2x in terms of u and then finally to hence solve a cubic function given which ties in ‘u’ with the original trigonometric function. This is challenging with lots of trig identities needed along the way (7 marks on offer).

Part (c) asks you to solve for when the original function is made equal to zero. This isn’t too bad but the question as a whole is quite difficult.

### Paper 2 – Question 12

Topic: Sequences & Series

Difficulty: Hard

Marks: 15