# IB Maths Past Paper Overviews

## 2017 November Maths SL – Paper 1

### Paper 1 – Question 1

Topic: Probability

Difficulty: Easy

Marks: 6

Question 1 (6 marks) is a basic probability question with a tree diagram. The question has a bag containing Green & White balls and two balls are selected without replacement.

Part (a) asks to complete the tree diagram given.

Part (b) asks to find the probability that exactly one of the selected balls taken from the bag is green.

### Paper 1 – Question 2

Topic: Sequences & Series

Difficulty: Easy

Marks: 6

Question 2 (6 marks) is an arithmetic sequence question. The first and second terms are given in the question.

Part (a) asks you to find the common difference of the sequence.

Part (b) asks you to find the tenth term in the sequence.

Part (c) asks to find the sum of the first ten terms of the sequence.

### Paper 1 – Question 3

Topic: Functions

Difficulty: Medium

Marks: 6

Question 3 (6 marks) is a functions question where a graph is given within a specific domain. Points on the graph are also provided.

Part (a) asks you to find the range of the function. You can read this off the given diagram.

Part (b) asks you to find a point on the curve as well as a point on the inverse function.

Part (c) asks you to sketch the inverse function on the same gird.

### Paper 1 – Question 4

Topic: Trigonometry

Difficulty: Medium

Marks: 7

Question 4 (7 marks) is a trig question where a triangle is shown with two side lengths given. The angle between the two side lengths is also given.

Part (a) asks you to find the length of the third side length. This can be done using the cosine rule with the given information.

Part (b) is a new diagram where an open semicircle has been attached to the triangle from part (a). The question asks you to find the perimeter of this shape.

### Paper 1 – Question 5

Topic: Functions

Difficulty: Medium

Marks: 6

Question 5 (6 marks) is a functions question where f(x) is given to be an exponential function and g(x) is given to be a linear function.

Part (a) asks you to find the composite function (g o f)(x).

Part (b) gives you information about the limit of (g o f)(x) as x approaches positive infinity.  You are then asked to find the constant in the g(x) equation which wasn’t originally given.

### Paper 1 – Question 6

Difficulty: Hard

Marks: 7

Question 6 (7 marks) is a quadratics mixed with optimization (calculus) question. An upside-down quadratic is given, and a shaded rectangle is created on the left side of the y-axis underneath the curve. The question asks you to find the x-coordinate of the bottom left hand corner of the shaded rectangle that would make the area of the rectangle a maximum. This is quite a challenging question for IB Maths SL.

### Paper 1 – Question 7

Topic: Logs & Discriminant Test

Difficulty: Hard

Marks: 7

Question 7 (7 marks) is a nice tricky logs and quadratics question. This type of question is the flavour of the month at the moment amongst the IB Examiners. It is given that when a logarithmic function is made equal to a constant, there is one solution. We then need to work backwards and find out what the base of the logarithmic function is. This is a very nice question and similar questions have been asked in recent years.

### Paper 1 – Question 8

Difficulty: Medium

Marks: 16

Question 8 (16 marks) is a quadratics & calculus question. A quadratic function is given with a diagram.

Part (a) asks you to find the derivative of the function at a given point.

Part (b) asks you to find the equation of the normal at that same point from part (a).

Part (c) asks you to find the second time that normal intersects with the original function.

Part (d) asks you to find the area between the function and it’s normal.

This is a good question to practice! IB have asked very similar questions to this in the past and will do in the future as it is a good test of your basic calculus knowledge.

### Paper 1 – Question 9

Topic: Vectors

Difficulty: Hard

Marks: 15

Question 9 (15 marks) is a good, solid vectors question. It is given that a line passes through two points. The coordinates of the points are given.

Part (a) asks you to find the vector connecting these two points and the vector equation of the line. This is straightforward – easy 3 marks.

Part (b) tells you that the line also passes through another point. One of the coordinates of this point is unknown. The question asks you to find the unknown variable.

Part (c) is quite challenging – 7 marks on offer. Another point is introduced, and information is given that a vector is perpendicular to our original line. We need to work backwards and find the coordinates of the point. The scalar product is needed to solve this question. This question is a good test of your vector knowledge.

### Paper 1 – Question 10

Topic: Sequences & Series

Difficulty: Hard

Marks: 14

Question 10 (14 marks) is a sequences & series question referring to diagrams given in the question.

Part (a) which is 5 marks, is a sum to infinity question where the length of a line is being divided into different length segments. This question is pretty standard, nothing crazy.

Part (b) which is 9 marks, has a new diagram showing different sized squares. This is also a sum to infinity question…. but more challenging than part (a). Good Luck!

## 2017 November Maths SL – Paper 2

### Paper 2 – Question 1

Topic 1: Trigonometry

Difficulty: Easy

Marks: 6

Question 1 (6 marks) is a trig question where a triangle is given. Two angles are provided as well as one side length.

Part (a) asks you to find the length of another side length. This is straight forward sin rule question.

Part (b) asks you to find the area of the triangle. There is a little trap here because you have to find the third angle in the triangle in order to use the area formula.

### Paper 2 – Question 2

Topic: Functions & Calculus

Difficulty: Medium

Marks: 7

Question 2 (7 marks) gives you a bit of a strange function.

Part (a) asks you to find the x-intercept. This can be done on your calculator.

Part (b) asks you to find the max. This can be done on your calculator.

Part (c) asks you to sketch the function on the grid provided. Be careful of the domain!

### Paper 2 – Question 3

Topic: Vectors

Difficulty: Medium

Marks: 6

Question 3 (6 marks) is a short vector question. A 3-dimensional vector is given.

Part (a) asks you to find the magnitude of the vector. This is an easy 2 marks.

Part (b) gives you another vector and asks you to find the angle between the two vectors. If you can understand the relationship between the two vectors its pretty straight forward from there.

### Paper 2 – Question 4

Topic: Probability Distribution

Difficulty: Medium

Marks: 6

Question 4 (6 marks) gives you a probability distribution table with unknown probabilities. This type of question is asked frequently around Q4-6 in IB Maths SL exams.

Part (a) asks you to find the value of ‘k’ which is the unknown variable in the table. This is pretty tricky as ‘k’ appears multiple times in the table.

Part (b) asks you to find the probability of the discrete random variable when it is equal to a specific number. Once you worked out ‘k’ in part (a), this is pretty easy.

Part (c) is a conditional probability question. Bit tricky.

### Paper 2 – Question 5

Topic: Functions & Calculus

Difficulty: Medium

Marks: 5

Question 5 (5 marks) gives you a logarithmic function which is symmetrical about the y-axis.

Part (a) asks you to find the x-coordinate of a point on the function where the y-coordinate is given.

Part (b) shows you a diagram of a shaded region and asks you to find the volume of the solid formed when the shaded region is rotate 360deg about the x-axis.

### Paper 2 – Question 6

Topic: Binomial Expansion

Difficulty: Hard

Marks: 6

Question 6 (6 marks) is a very common binomial expansion question with a little twist. The coefficient of a term is given, and you have to work backwards and find the unknown variable ‘a’ in the brackets. There are terms before the bracket however making this question quite difficult. Definitely practice this question a few times as IB are asking this type of question more and more in recent years.

### Paper 2 – Question 7

Topic: Normal Distribution

Difficulty: Hard

Marks: 7

Question 7 (7 marks) is one of the most difficult Section A questions asked in recent years. The question gives you information about male heights (normally distributed data) and asks you to find an unknown variable ‘h’. You will be scratching your head when you first see this question. Watch the video solution a few times to grasp the key steps as this could be the difference between getting a 6 or a 7 in your mocks.

### Paper 2 – Question 8

Topic: Statistics, Bivariate Statistics & Probability

Difficulty: Medium

Marks: 14

Question 8 (14 marks) is a long statistics question which tests nearly every stats skill you need to know. The question starts out with a bivariate statics table.

Part (a) asks you to find the regression line equation. Straight forward.

Part (b) asks you to use the regression line equation and estimate a ‘y’ value given an ‘x’ (interpolation).

Part (c) displays the same data in a cumulative frequency table and also an accompanying frequency table. The question asks you to find unknow values in the frequency table. You can read the answers off the cumulative frequency table.

Part (d) is similar to part (c) asking you to read values off the cumulative frequency table and find unknown variables.

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: Kinematics

Difficulty: Hard

Marks: 14

Question 9 (14 marks) is a classic kinematics question for IB Maths SL. A particle is given along with its acceleration formula and a given domain.

Part (a) asks you to find the values for t when the acceleration is zero. Use you calculator.

Part (b) asks you to find all the possible times when the velocity of the particle is decreasing. This is a tricky question and a deep understanding of calculus and graphing is needed.

Part (c) gives you information about the initial velocity of the particle and then asks you to find an expression for the velocity. Integrate, remember to put +c and then use the initial conditions to find ‘c’.

Part (d) asks you to find the total distance travelled when the velocity is increasing. This is a challenging question!! Watch the video solution to understand. Not many students will get this correct (4 marks on offer).

### Paper 2 – Question 10

Topic: Circular Functions & Calculus

Difficulty: Hard

Marks: 17