# IB Maths Past Paper Overviews

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**2017 November Maths HL – Paper 1**

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

**Paper 1 – Question 1**

**Paper 1 – Question 2**

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**

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**

**Paper 1 – Question 5**

**Paper 1 – Question 6**

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**

**Paper 1 – Question 8**

**Paper 1 – Question 9**

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**

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

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**

**Paper 2 – Question 2**

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**

**Paper 2 – Question 4**

**Paper 2 – Question 5**

**Paper 2 – Question 6**

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**

**Paper 2 – Question 8**

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 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**

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**

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**

Part (a) ask you to calculate the loan amount after 20 years. Just use the compound interest formula.

Part (b) explains that Phil also has a savings account where he deposits $P every year for 20 years receiving a different interest rate. The question asks to find an expression for how much Phil will have in his savings account after 20 years.

Part (c) asks to calculate ‘P’ such that Phil owns his home after 20 years.

Part (d) introduces David who makes a single deposit of $Q at a given interest rate and wishes to withdraw $5000 at the end of every year. There are two parts to this question. Part 1 asks you to find an expression for the minimum value of Q such that he stays afloat. Part 2 asks you to use this equation to find the value of Q if he wishes to take out the $5000 at the end of each year indefinitely. This is a sum to infinity question and a tricky one. Good Luck!

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September 23, 2020