# IB Maths Past Paper Overviews

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**2018 November Maths Studies – Paper 1**

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

**Paper 1 – Question 1**

**Topic**: Number & Algebra

**Sub Topic**: Scientific Notation & Rounding

**Difficulty**: Easy

**Marks**: 6

Paper 1 starts with a fairly easy ‘Number Skills’ question, that all marks can be achieved with an understanding of rounding and scientific notation.

Part (a) asks to calculate the value of a provided formula, where one value needs to be substituted. This is a fairly common type of Paper 1, Question 1, and a calculator can be used, so shouldn’t provide too much difficulty.

Part (b) asks to round part (a) to the nearest integer (whole number).

Part (c) asks to provide the part (b) answer in scientific notation.

*2018 Mathematics Studies November Paper 1 Question 1 – 18N.1.studies.TZ0.1 – N18/5/MATSD/SP1/ENG/TZ0/XX*

**Paper 1 – Question 2**

**Topic**: Descriptive Statistics

**Sub Topics**: Histograms

**Sub Topics**: Mean, Median, Mode, Quartiles, IQR

**Difficulty**: Medium

**Marks**: 6

Question 2 is a descriptive statistics question, where a histogram is presented, displaying the data of length of 25 metal rods.

Part (a) asks to determine the modal length of the rods. To find this, simply look for the column with the highest frequency.

Part (b) asks to find the Median length of the rod. This is a little harder than part (a), and requires an understanding of how to find the median (medianth number: (n+1)/2).

Part (c) has two parts; firstly to find the lower quartile, then secondly, to determine the interquartile range (IQR) of the data. These questions require an understanding of how to find the upper and lower quartiles of a set of data, and that the IQR is the upper quartile subtract the lower quartile.

*2018 Mathematics Studies November Paper 1 Question 2 – 18N.1.studies.TZ0.2 – N18/5/MATSD/SP1/ENG/TZ0/XX*

**Paper 1 – Question 3**

**Topic**: Number & Algebra

**Sub Topic:** Currency Conversion

**Difficulty**: Medium

**Marks**: 6

Question 3 is a classic IB Maths Studies Currency Conversion question. These types of questions appear in pretty much every single IB Maths Studies Paper 1 exam (or if not, certainly in Paper 2).

Part (a) asks to do a straight forward currency conversion between USD and MXN. No tricks to this one.

Part (b) asks to calculate the amount of commission a currency exchange receives on a particular currency conversion. This requires an understanding of percentages; how much is 3% of a total value.

Part (c) asks to perform another currency conversion (back from MXN to USD), however this time, keeping in mind to subtract the commission the exchange earned in part (b).

*2018 Mathematics Studies November Paper 1 Question 3 – 18N.1.studies.TZ0.3 – N18/5/MATSD/SP1/ENG/TZ0/XX*

**Paper 1 – Question 4**

**Topic**: Statistical Application

**Sub Topic**: Two Variable Statistics

**Difficulty**: Medium

**Marks**: 6

Question 4 is a two-variable statistics question, displaying a table of two variables; gender and preferred career choice. Essentially, the question is asked to perform an analysis on if the variables are correlated (does career choice depend on gender). These type of questions are very common in IB Maths Studies exam papers, usually in Paper 2.

Part (a) asks to state the null hypothesis for the test. The null hypothesis is always that the two variables are independent of each other (i.e., one variable doesn’t influence the other).

Part (b) asks to calculate the ‘expected number’ of a data point (e.g., Male Engineers). The table provides the actual number from a survey, however this question asks the expected number, given the total number of people surveyed, and total number of Males and total number of Engineers. This requires an understanding of the calculation required here. Essentially, it’s the multiplication of the two totals (Males & Engineers), divided by the total number of people surveyed. This is a very common type of IB Maths Studies question, and it’s recommended to be familiar with how to do this calculation.

Part (c) asks to find the p-value of the test. This can be found quite easily using a graphics calculator. Keep in mind, the ‘p-value’ is the probability value that the null hypothesis is true (and therefore the variables are independent). This type of question is usually just before a question asking to determine if the null hypothesis should be rejected.

Part (d) asks to determine if the null hypothesis should be rejected or not. To do this, you’ll need to compare the p-value from part (c) with the significance level (1% for this question. 0.01 as a decimal).

*2018 Mathematics Studies November Paper 1 Question 4 – 18N.1.studies.TZ0.4 – N18/5/MATSD/SP1/ENG/TZ0/XX*

**Paper 1 – Question 5**

Question 5 is a fairly straight forward Sequences & Series question. You’ll need to know or the required formulas (or have the formula booklet handy, as they are on there. Three different sequences are presented, each with 5 terms. It is not stated in the question which of the sequences are arithmetic or geometric (or neither), so you’ll need to know how to recognize which is which. If you’re not sure on this, I recommend watching the video solution (free for RV Members), which explains the difference.

Part (a) asks to determine which of the sequences are arithmetic and geometric.

Part (b) asks to find the 11th term of the geometric sequence. The formula can be used here.

Part (c) asks to find the sum of the first 20 terms of the arithmetic sequence. Again, there if a formula for this.

*2018 Mathematics Studies November Paper 1 Question 5 – 18N.1.studies.TZ0.5 – N18/5/MATSD/SP1/ENG/TZ0/XX*

**Paper 1 – Question 6**

**Topic**: Logic, Sets & Probability

**Sub Topic**: Logic (Truth Tables)

**Difficulty**: Medium

**Marks**: 6

Question 6 is a moderately difficult and long logic question. A truth table is provided, with four empty columns to fill in.

Part (a) asks to complete the truth table. This requires an understanding of the truth table rules for negation, disjunction, conjunction and implication (all of which are provided in the formula booklet). This is one of the longer truth table completion questions asks in recent IB Maths Studies papers, so some practice on how to complete them quickly is recommended.

Part (b) asks to determine if the very right column of the truth table is a contradiction, tautology or neither. The key here is to look at the values in that column of the truth table, whether they are all true (tautology), all false (contradiction) or mixed (neither).

*2018 Mathematics Studies November Paper 1 Question 6 – 18N.1.studies.TZ0.6 – N18/5/MATSD/SP1/ENG/TZ0/XX*

**Paper 1 – Question 7**

**Topic**: Number & Algebra

**Sub Topics**: Sequences & Series

**Sub Topics**: Compound Interest

**Difficulty**: Hard

**Marks**: 6

Question 7 is an interesting question with a tricky part (a) question (thus the ‘hard’ difficulty rating). At first glance is looks to be all about compound interest, as there are dollar signs and percentage symbols throughout, however after solving part (a), I realised that perhaps using a geometric sequences & series method may be more appropriate.

Part (a) is the tricky part of this question. A dollar value is provided, and the question says that this amount decreases by 8% every year (thus, geometric). The question asks to determine how many years it will take for the amount in the account to go below another value, however the wording in the question asks to state the year just before this (i.e., “how many years is it before the amount goes below amount x”). I recommend watching the video solution for this one.

Part (b) is a more straight forward compound interest question asking to find a future value, with all the information provided. Just be careful with applying the formula correctly, as the interest rate is compounding quarterly.

*2018 Mathematics Studies November Paper 1 Question 7 – 18N.1.studies.TZ0.7 – N18/5/MATSD/SP1/ENG/TZ0/XX*

**Paper 1 – Question 8**

**Topic**: Logic, Sets & Probability

**Sub Topic**: Probability – Tree Diagrams

**Difficulty**: Medium

**Marks**: 6

Question 8 is a common type of tree diagram question, with no tricks to it.

Part (a) asks to complete the missing probabilities on a tree diagram. Just be sure to understand that this is a “without replacement” type of question. I recommend watching the video solution if you’re not sure on what this means.

Part (b) asks to calculate the probability of a certain outcome. This requires finding the probability of two scenarios in which this outcome occurs, and then adding these probabilities together.

*2018 Mathematics Studies November Paper 1 Question 8 – 18N.1.studies.TZ0.8 – N18/5/MATSD/SP1/ENG/TZ0/XX*

**Paper 1 – Question 9**

**Topic**: Geometry & Trigonometry

**Sub Topic**: Geometry of Shapes

**Difficulty**: Medium

**Marks**: 6

Question 9 is a geometry question, where a shape is provided at the start of the question. The shape is a combination of two shapes; a cuboid as the base, with a hemisphere sitting on top of this.

Part (a) has two parts to it. Firstly, it asks to determine the height of the cuboid, which requires an understanding that the height is the same as the radius of the hemisphere (this is stated in the question). Secondly, it asks to determine the total volume of the shape. This require calculating the volume of the two individual shapes and then adding them together. The formulas for both cuboid and sphere is provided in the formula booklet.

Part (b) asks to calculate the total mass of the shape, with a per cm^3 of the material provided. This requires multiplying the total volume of the shape (part (a)) with the per cm^3 mass.

*2018 Mathematics Studies November Paper 1 Question 9 – 18N.1.studies.TZ0.9 – N18/5/MATSD/SP1/ENG/TZ0/XX*

**Paper 1 – Question 10**

Question is an interesting logic question, where two short logic statements are provided.

Part (a) asks to convert a written statement into symbolic form. This requires an understanding of the implication and negation logic terms.

Part (b) is essentially the opposite of part (a). A symbolic logic argument is presented, and you are required to convert this into written form.

Part (c) asks to write out in words the ‘inverse’ of part (b). An understanding of the inverse of a logic statement is required here.

*2018 Mathematics Studies November Paper 1 Question 10 – 18N.1.studies.TZ0.10 – N18/5/MATSD/SP1/ENG/TZ0/XX*

**Paper 1 – Question 11**

**Topic**: Introduction to Differential Calculus

**Sub Topics**: Differentiation

**Sub Topics**: Gradients & Equations of Tangents

**Difficulty**: Medium

**Marks**: 6

Question 11 introduces Differential Calculus to this exam paper. The question starts with a fairly straight forward equation, without any fractions or anything else tricky.

Part (a) asks to differentiate the equation.

Part (b) asks to find the gradient of the tangent at a particular point on the curve.

Part (c) builds on from part (b), asking to determine the equation of the tangent at this particular point.

*2018 Mathematics Studies November Paper 1 Question 11 – 18N.1.studies.TZ0.11 – N18/5/MATSD/SP1/ENG/TZ0/XX*

**Paper 1 – Question 12**

**Topic 1**: Geometry & Trigonometry

**Sub Topic**: Coordinate Geometry

**Difficulty**: Hard

**Marks**: 6

Question 12 initially appears to be a triangle trigonometry question, as a triangle is presented at the start of the question. However, upon closer look, the question is actually a coordinate geometry question, asking to find gradients and equations of straight lines. It is given a ‘Hard’ difficulty rating, as parts (b) and (c) require a very strong understanding of coordinate geometry; gradients of lines, the relationships between gradients of perpendicular lines, and finding equations of straight lines and leaving it in a certain form.

Part (a) is a fairly simple start, asking to find the gradient of one of the triangle sides.

Part (b) is a step up in difficulty, asking to determine if one of the angles inside the triangle is a right angle or not. This requires an understanding that perpendicular lines meet at right angles, and therefore the question is essentially asking if the two side lengths are perpendicular. In order to determine this, an understanding of the relationship of the gradients of perpendicular lines is required.

Part (c) asks to find the equation of a straight line, and leave in standard form.

This question is one of the harder Coordinate Geometry questions found in a IB Maths Studies Paper 1 exam.

*2018 Mathematics Studies November Paper 1 Question 12 – 18N.1.studies.TZ0.12 – N18/5/MATSD/SP1/ENG/TZ0/XX*

**Paper 1 – Question 13**

**Topic**: Mathematical Models

**Sub Topic**: Quadratic Models

**Difficulty**: Easy (assuming confident calculator skills)

**Marks**: 6

Question 13 is the first quadratics question in this exam paper. The difficulty rating could either be ‘Easy’ if you are confident with your graphics calculator, or ‘Hard’ if you are trying to solve the questions by hand. The question involves a quadratic curve that represents the flight of a ball, thrown from a wall, landing on the ground below the wall and a distance away.

Part (a) asks to find the height of the wall.

Part (b) asks to find the maximum height that the ball reached.

Part (c) asks to find the distance from the bottom of the wall, to the location that the ball lands on the ground.

All three of these questions can be found very easily and quickly by entering the initially equation of the quadratic (provided in the question) into the graphing section of your calculator, then using the analysis functions to find the points of interest.

*2018 Mathematics Studies November Paper 1 Question 13 – 18N.1.studies.TZ0.13 – N18/5/MATSD/SP1/ENG/TZ0/XX*

**Paper 1 – Question 14**

**Topic**: Statistical Application

**Sub Topic**: Normal Distribution

**Difficulty**: Hard

**Marks**: 6

Question 14 is a Normal Distribution question, with a little bit of Conditional Probability at the end. It is a relatively hard question, one of the hard Normal Distribution questions seen on IB Maths Studies Exam Papers. The question involves a data set, with a mean and standard deviation provided.

Part (a) asks to find the value at which only 10% of the data is greater than that value. This requires an understanding of how to use the InverseNormal function on the calculator.

Part (b) is the opposite of part (a), asking what percentage of the data is greater than a certain value. This requires an understanding of how to use the NormalCdf function on the calculator

Part (c) is a difficult question, and is why the question overall is rated as ‘Hard.’ It involves conditional probability, asking to find the probability of a certain value, given another condition. A strong understanding of how to use the conditional probability formula (provided in your formula booklet) is required here.

*2018 Mathematics Studies November Paper 1 Question 14 – 18N.1.studies.TZ0.14 – N18/5/MATSD/SP1/ENG/TZ0/XX*

**Paper 1 – Question 15**

**Topic**: Mathematical Models

**Sub Topic**: Exponential Models

**Difficulty**: Hard

**Marks**: 6

Question 15 is a fairly difficult exponential models question. An equation is provided at the start of the question, with not all of the terms provided (e.g., the numbers replaced with letters, to find in the questions). A sketch of the equation is also provided.

Part (a) asks to find one of the unknown terms in the equation, when the time is initially zero.

Part (b) asks to find another of the unknown terms in the equation, this time for a given coordinate. This requires substituting this coordinate it and solving for the unknown (either by hand or using the calculator)

Part (c) is a conceptual question, asking for the value in which the curve stops rising and flat lines (the asymptote).

These types of mathematical model questions that require finding terms in the equations are fairly common in IB Mathematics Studies Exams, usually at the ends of either Paper 1 or Paper 2.

*2018 Mathematics Studies November Paper 1 Question 15 – 18N.1.studies.TZ0.15 – N18/5/MATSD/SP1/ENG/TZ0/XX*

**2018 November Maths Studies – Paper 2**

**Paper 2 – Question 1**

**Topic**: Statistical Application

**Sub Topic**: Correlation & Line of Regression

**Difficulty**: Easy (assuming confident calculator skills)

**Marks**: 14

Paper 2 starts with a fairly straight forward question involving the correlation and line of regression equation between two variables. This is a very common Question 1 or 2 in IB Maths Studies Paper 2 exams.

Part (a) asks to use the calculator to find the mean of the two variables, and also the Pearson’s product-moment correlation coefficient (r).

Part (b) asks to find the line of regression equation for the data (this can be found fairly easy on the calculator), and then show that the coordinates of the means (from part (a)) lie on this line of regression equation.

Part (c) is a classic line of regression question, whereby a new piece of data is introduced, and the question asks to estimate the other variable using the equation. It is very important that you understand how to do this, at it appears in pretty much every single IB Maths Studies exam. Part (c) also asks to justify if the estimation is reliable or not (interpolation or extrapolation).

Part (d) changes course from statistics, asking to find the percentage error from the estimation found in part (c), from the actual data point, which is provided. This requires an understanding of how to apply the percentage error formula, found in the formula booklet.

*2018 Mathematics Studies November Paper 2 Question 1 – 18N.2.studies.TZ0.1 – N18/5/MATSD/SP2/ENG/TZ0/XX*

**Paper 2 – Question 2**

**Topic**: Logic, Sets & Probability

**Sub Topic**: Venn Diagrams

**Difficulty**: Medium

**Marks**: 14

Question 2 in Paper 2 is all about Venn Diagrams (quite common in IB Maths Studies Paper 2 exams). A three set Venn Diagram is presented in the question, with some accompanying information.

Part (a) asks to analyse and interpret the Venn Diagram to identify how many elements (data points) are in three different regions.

Part (b) is similar to part (a), however this time the question is in set notation, as opposed to written out in words.

Part (c) now asks some probability questions, whereby you need to divide the number of elements by the total.

*2018 Mathematics Studies November Paper 2 Question 2 – 18N.2.studies.TZ0.2 – N18/5/MATSD/SP2/ENG/TZ0/XX*

**Paper 2 – Question 3**

**Topic**: Descriptive Statistics

**Sub Topics**: Cumulative Frequency Charts

**Sub Topics**: Grouped Frequency Tables

**Difficulty**: Medium

**Marks**: 16

Question 3 is a fairly challenging, although achievable, statistics question involving cumulative frequency charts and grouped frequency tables. The question opens with a large cumulative frequency chart displayed.

Part (a) asks to find both the median and interquartile range (IQR) of the the data, reading from the cumulative frequency chart.

Part (b) is a conceptual question, asking to read off a particular value from the cumulative frequency chart.

Part (c) is where the grouped frequency table is introduced. This particular part is fairly easy, asking to identify the modal class (the class that has the highest frequency) and it’s mid-interval (the middle of the class).

Part (d) asks to find the mean and standard deviation of the grouped frequency table. This can be found fairly easily using your calculator. Just be sure you know how to enter the data in the spreadsheet section, using the mid-intervals and frequency.

Part (e) is a good challenging conceptual question, requiring an understanding of what standard deviation is. It asks to find the frequency (from the cumulative frequency table at the start) who are above ‘one standard deviation below the mean.’ This is a good question, testing many parts of the IB Mathematics Studies course.

*2018 Mathematics Studies November Paper 2 Question 3 – 18N.2.studies.TZ0.3 – N18/5/MATSD/SP2/ENG/TZ0/XX*

**Paper 2 – Question 4**

**Topic 1**: Mathematical Models

**Topic 2**: Introduction to Differential Calculus

**Sub Topic**: Gradients & Equations of Tangents

**Difficulty**: Medium (assuming confident calculator skills)

**Marks**: 13

Question 4 is an interesting question, and its difficulty relies heavily on your calculator skills. If you are confident plotting equations and using the analysis functions, this question could potentially be rated as ‘Easy.’ The question is a blend of mathematical models and differential calculus the whole way through.

Part (a) asks to plot the equation provided for a given domain and range. The equation is a cubic, so drawing this by hand is quite difficult. As the video solution suggests, I recommend simply sketching the equation in your calculator, changing the window settings to match the domain and range, and then just copying down on your exam paper what you see on the screen.

Part (b) starts by asking to find some of the important points on the equation; the x-intercept & the turning point (both can be found quickly and easily using the calculator. The third part of part (b) asks to find the equation of the tangent at a particular point on the curve. There is quite a bit too this, I recommend watching the video solution for the steps (free for RV Members).

Part (c) asks to sketch another equation on your axes from part (a), this time a linear equation. Again, this is fairly simple to do on the calculator, then simply copy down onto the exam paper.

Part (d) asks to ‘solve’ the two equations (part (a) and part (c)). ‘Solve’ in this context, means to find where the two equations are equal to each other (or meet on the graph). This can be completed by hand, or also using the calculator.

*2018 Mathematics Studies November Paper 2 Question 4 – 18N.2.studies.TZ0.4 – N18/5/MATSD/SP2/ENG/TZ0/XX*

**Paper 2 – Question 5**

**Topic**: Geometry & Trigonometry

**Sub Topic**: Triangle Trigonometry

**Difficulty**: Medium

**Marks**: 15

Question 5 in Paper 2 is all about triangle trigonometry, using all of the sine rule, cosine rule, area of a triangle, and standard trig ratios (sohcahtoa). These types of questions are starting to become quite common in IB Maths Studies Paper 2 exams. The question starts with a triangle presented.

Part (a) asks to find a missing angle in the triangle. This can be achieved in a fairly straight manner using the Sine rule.

Part (b) asks to find the area of the triangle. This does require one step prior to applying the area of a triangle formula, as the angle required to be used (in relation to the two adjacent side lengths) is missing.

Part (c) asks to find the length of one of the missing side lengths. This can be completed using the cosine rule, with no tricks or prior work.

Part (d) is where this questions moves from ‘Easy’ to ‘Medium’ on the difficult rating, and is worth 5 marks. It involved a few new points on the triangle and to calculate a new angle between these points. This requires a conceptual understanding, a use of the Sine rule, and then use of a the tan trig ratio. Overall, a good challenging question.

*2018 Mathematics Studies November Paper 2 Question 5 – 18N.2.studies.TZ0.5 – N18/5/MATSD/SP5/ENG/TZ0/XX*

**Paper 2 – Question 6**

**Topic 1**: Geometry & Trigonometry

**Sub Topic**: Geometry of Shapes

**Topic 2**: Introduction to Differential Calculus

**Sub Topic**: Optimization/ Concept of the Turning Point

**Difficulty**: Hard

**Marks**: 18

Question 6 is a very challenging and long Paper 2 question, which perhaps makes up for the rest of the exam paper which was on the easier side to normal. The question is about a cuboid shape and then moves to how the dimensions can be altered to minimize the total surface area required to make the shape. These types of geometry/ optimization questions are very commonly found in IB Maths Studies Paper 2, usually question 5 or 6.

Part (a) starts nice and easy, asking to calculate the total surface area of the cuboid (dimensions are given).

Part (b) is also an easy question, asking to calculate the volume of the cuboid. The formula for the volume of a cuboid is given in the formula booklet.

Part (c) is where this question starts to get difficult and more algebraic. A new cuboid is introduced, this time with pronumerals (x and y) as the dimensions, rather than numbers. Part (c) asks to determine an expression for the volume of the new cuboid, in terms of x and y.

Part (d) follows on from part (c), this time asking to find an expression for the total surface area of the new cuboid, in terms of x and y.

Part (e) is where the fun starts. It asks to use the two expressions from parts (c) and (d) and find an expression for the area, in terms of x only. This requires manipulation of the volume expression (part (c)) such that y is the subject, then substituting this into the area expression.

Part (f) following on from part (e), asking to differentiate this are expression, with respect to x. This is a bit tricky, as the expression has a fraction in it, with the x on the denominator.

Part (g) is the crux of the question, asking to find the value for x that minimizes the total surface area of the new cuboid. This is the whole point of the question, and is where the concept of optimization comes in. I recommend watching the video solution to this part for a conceptual understanding.

Part (h) is a relatively easy finish to this question, asking to find the total cost to produce the cuboid, given a cost per square cm of material.

*2018 Mathematics Studies November Paper 2 Question 5 – 18N.2.studies.TZ0.5 – N18/5/MATSD/SP2/ENG/TZ0/XX*

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