# IB Maths Past Paper Overviews

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**2017 November Maths SL – Paper 1**

**Paper 2 (Click here to scroll down)**

**Paper 1 – Question 1**

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**

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**

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**

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**

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**

**Paper 1 – Question 7**

**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**

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**

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**

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**

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**

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**

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**

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**

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**

**Paper 2 – Question 7**

**Paper 2 – Question 8**

**Topic**: Statistics, Bivariate Statistics & Probability

**Difficulty**: Medium

**Marks**: 14

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**

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**

Part (a) asks you to sub in an ‘x’ value into the function and find the ‘y’. This is fairly straight forward.

Part (b) introduces a strange concept where any point can be found on the function by subbing in values for ‘k’….. if you understand it, 6 marks are gettable, but some students won’t know where to start. If you are not strong in the above topics, watch the video solution a few times to fully underrated what the question is asking.

Part (c) asks you to find the distance between points on the curve…. Once again, pretty tricky and confusing. This is a hard question.

Part (d) introduces a diagram of a saw and how the tooth-edge of the saw relates to the original function. The question works off part (c) and asks you to find the number of teeth there will be on the saw edge given that the saw edge is 300mm in total length. There are multiple ways to solve this however the method explained in the video solution is the most simple and will get you full marks (6 available). This question could be a disaster for students hoping to achieve a 4 or 5 as it is hard to scrape marks. Watch the videos twice and you should get 17/17 in your mocks.

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December 4, 2020