# IB Maths Past Paper Overviews

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**2018 May Time Zone 2 Maths Studies – Paper 1**

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

**Paper 1 – Question 1**

**Topic**: Statistical Application

**Sub Topic**: Scatter Plots & Line of Best Fit

**Difficulty**: Easy

**Marks**: 6

Paper one starts nice and easy (although somewhat unusually in comparison to previous IB Maths Studies Past Papers) with a straight forward scatter plot & line of best fir conceptual question. A scatter plot with data points, plus the mean point, is provided in the question.

Part (a) asks to plot the mean point on the scatter plot.

Part (b) asks to draw a line of best fit onto the scatter plot. Note, this isn’t the line of regression equation, this is simply a line of best fit by eye. The important part to remember here is that half of the data points must be above, and half below the line.

Part (c) asks to use the line of best fit to estimate the output value of a new data point, for a given input value.

*2018 Mathematics Studies Paper 1 May TZ2 Question 1 – 18M.1.studies.TZ2.1 – M18/5/MATSD/SP1/ENG/TZ2/XX*

**Paper 1 – Question 2**

Question 2 steps up the difficulty on this paper, introducing a Logic question that tests many different parts of your Logic understanding. The question starts by providing three different logic propositions.

Part (a) asks to convert a Logic statement that is in symbolic form, into word form. This logic statement has quite a few parts to it, including implication, negation & disjunction.

Part (b) asks to complete two columns of a Truth Table.

Part (c) asks to determine if the right hand column of the Truth Table is a tautology, a contradiction, or neither. Recall here that you need to look at the values in the column or the Truth Table, to see if all the values are True (tautology), all are False (contradiction), or mixed (neither).

*2018 Mathematics Studies Paper 1 May TZ2 Question 2 – 18M.1.studies.TZ2.2 – M18/5/MATSD/SP1/ENG/TZ2/XX*

**Paper 1 – Question 3**

Question 3 is a tricky and somewhat unusual question. It doesn’t clearly fit into a particular topic, rather, it tests general thinking skills, with basics in algebra and scientific notation. These types of questions appear in IB Maths Studies Past Papers every couple of years.

Part (a) asks to complete a number conversion, then leave your answer in scientific notation.

Part (b) has two parts; firstly to convert a particular distance given in km, into cm (multiple by 10,000), and secondly, to do a bit of basic algebra to find a particular value.

*2018 Mathematics Studies Paper 1 May TZ2 Question 3 – 18M.1.studies.TZ2.3 – M18/5/MATSD/SP1/ENG/TZ2/XX*

**Paper 1 – Question 4**

Question 4 is a very easy question, assuming you can recall the 4 different types of number sets; Natural Numbers (N), Integers (Z), Rational Numbers (Q) and Real Numbers (R). If you can remember these numbers, this is 6 marks in one minute.

Part (a) asks to simple list an example number from each of these number sets.

Part (b) provides a statement about these number sets, and you are required to determine if this statement is correct or not.

*2018 Mathematics Studies Paper 1 May TZ2 Question 4 – 18M.1.studies.TZ2.4 – M18/5/MATSD/SP1/ENG/TZ2/XX*

**Paper 1 – Question 5**

**Topic**: Number & Algebra

**Sub Topic 1**: Compound Interest

**Sub Topic 2**: Currency Conversion

**Difficulty**: Medium

**Marks**: 6

Question 5 is an interesting mix of compound interest and currency conversion. Usually in IB Maths Studies Past Papers, particularly Paper 1, these sub topics are separated into individual questions. This question was given a Medium difficulty rating, due to the amount of content to recall across the two sub topics, although could have been rated Easy, as the questions are fairly straight forward.

Part (a) is a straight forward compound interest question, asking to calculate the future value, when all other inputs into the formula are provided. The only think to be careful of is that the interest rate is compounding quarterly, so the k value in the formula is 4 (4 quarters in a year).

Part (b) builds on from part (a), taking the interest earned during the compound interest, and then turns into a currency conversion question. Interestingly, the question provides you with the amount of the new currency, so you are required to determine the exchange rate. I recommend watching the video solution to this on how to set up currency conversion tables.

*2018 Mathematics Studies Paper 1 May TZ2 Question 5 – 18M.1.studies.TZ2.5 – M18/5/MATSD/SP1/ENG/TZ2/XX*

**Paper 1 – Question 6**

**Topic**: Geometry & Trigonometry

**Sub Topic**: Coordinate Geometry

**Difficulty**: Medium

**Marks**: 6

Question 6 is a challenging coordinate geometry question, that could have potentially been rated as ‘Hard.’ A Cartesian Plane is presented, with two straight lines that interest at a point where the coordinate isn’t clear (between grid lines).

Part (a) asks to determine the gradient of one of the lines. This can be achieved fairly easily as the line passes through many grid intersection, therefore allowing use of the gradient formula.

Part (b) is where this question gets a bit harder. It asks to determine the exact coordinate of the intersection of the two lines. This requires letting the right hand side of the two equations be equal to each other, then solving for the x coordinate (either by hand or calculator). Then, this x value can be substituted back into either of the equations to find the y value.

Part (c) is a very common IB Maths Studies Past Paper question. It introduces a new line (not on the graph at the top) and informs you that it’s parallel to one of the lines and passes through a particular coordinate. You are required to determine the equation of this line. These types of questions appear all the time.

*2018 Mathematics Studies Paper 1 May TZ2 Question 6 – 18M.1.studies.TZ2.6 – M18/5/MATSD/SP1/ENG/TZ2/XX*

**Paper 1 – Question 7**

**Topic**: Logic, Sets & Probability

**Sub Topic**: Probability (Tree Diagrams)

**Difficulty**: Hard

**Marks**: 6

Question 7 is a subtly challenging probability question. It appears quite easy at first, however part (c), worth 3 of the 6 marks, is where it becomes quite challenging. A table with data involving two variables is presented at the top of the question.

Part (a) simple asks to read off the table for a particular data point. This is an easy one mark.

Part (b) is where the question turns into a probability question, although this part is still relatively easy. It asks to find the probability of selecting a particular scenario. This involves identifying the value on the table and dividing by the total.

Part (c) is the challenging part of the question, and involves multi-stage probability without replacement. A tree diagram is very useful here. I recommend watching the video solution (free for RV Members) if you’re unsure how to set these up.

*2018 Mathematics Studies Paper 1 May TZ2 Question 7 – 18M.1.studies.TZ2.7 – M18/5/MATSD/SP1/ENG/TZ2/XX*

**Paper 1 – Question 8**

**Topic**: Geometry & Trigonometry

**Sub Topic**: Triangle Trigonometry

**Difficulty**: Easy

**Marks**: 6

Question 8 is a very straight forward trigonometry question, that simply relies on direct application of formulas that can be found in the formula booklet. A triangle is presented at the top of the question.

Part (a) asks to determine the unknown side length, which can be found using the cosine rule.

Part (b) asks to determine the area of the triangle, which can be found using the area of a triangle formula.

There are no tricks to this question, one of the easier trigonometry questions seen on IB Mathematics Studies Past Papers.

*2018 Mathematics Studies Paper 1 May TZ2 Question 8 – 18M.1.studies.TZ2.8 – M18/5/MATSD/SP1/ENG/TZ2/XX*

**Paper 1 – Question 9**

**Topic**: Logic, Sets & Probability

**Sub Topic**: Venn Diagrams

**Difficulty**: Medium

**Marks**: 6

Question 9 is all about Venn Diagrams. While Venn Diagram questions usually lead to probability based questions, this questions is just about identifying regions and describing regions using set notation.

Part (a) requires describing three different diagrams using set notation. It’s important to recall notation like intersection (and), union (or) and complement (not).

Part (b) is the opposite of part (a), this time providing set notation and two empty Venn Diagrams, and you are required to shade the region described by the set notation.

*2018 Mathematics Studies Paper 1 May TZ2 Question 9 – 18M.1.studies.TZ2.9 – M18/5/MATSD/SP1/ENG/TZ2/XX*

**Paper 1 – Question 10**

**Topic**: Mathematical Models

**Sub Topic**: Exponential Models

**Difficulty**: Hard

**Marks**: 6

Question 10 is a difficult exponential model question, as it relies on strong conceptual understanding on how models work, as opposed to just substituting in values. An equation is provided at the start, with one of the values unknown (pro-numeral instead of number).

Part (a) asks to find this missing value, for a given piece of data (e.g., value of the equation after a certain period of time). This requires substituting this value in, rearranging and solving for the unknown (or using the solving function on the calculator).

Part (b) asks to describe what this unknown represents in the context of the question. This can be a difficult concept to wrap your head around, I recommend watching the video solution.

Part (c) asks to determine the time taken for the exponential model to equal a certain value. This is a very common type of mathematical model question in IB Maths Studies Past Papers.

*2018 Mathematics Studies Paper 1 May TZ2 Question 10 – 18M.1.studies.TZ2.10 – M18/5/MATSD/SP1/ENG/TZ2/XX*

**Paper 1 – Question 11**

Question 11 continues on with the difficult mathematical model questions, this time with a model with the independent variable on the denominator of a fraction. This creates a graph with both a horizontal and vertical asymptote. It’s highly recommended at the start of this question to plot the equation on your graphics calculator to get an idea what it looks like.

Part (a) asks to write the equation of the vertical asymptote.

Part (b) asks to write the equation of the horizontal asymptote.

Part (c) is a tricky question, asking to find the value for x where the function is equal to zero (or in other words, cuts through the x axis). This can actually be found quite easily on your calculator, using the zero function.

*2018 Mathematics Studies Paper 1 May TZ2 Question 11 – 18M.1.studies.TZ2.11 – M18/5/MATSD/SP1/ENG/TZ2/XX*

**Paper 1 – Question 12**

Question 12 is an interesting Histogram related question. Usually, Histograms (Descriptive Stats) appear early in IB Maths Studies Paper 1 exams, and are often easier type questions. This question has some challenges to it, however attainable if the concept of finding the mean is understood. A histogram is presented at the start of the question, with one of the columns missing.

Part (a) is a easy start, asking to write out the mid-interval for one of the Histogram intervals.

Part (b) is where the question gets challenging. The mean for the whole data set is provided, and you are therefore required to calculate the height of the missing column. A strong understanding of how to calculate the mean of a Histogram is required here.

Part (c) is very easy, assuming part (b) is obtained correctly. Part (c) simple asks to complete the Histogram, meaning to shade in the empty column.

*2018 Mathematics Studies Paper 1 May TZ2 Question 12 – 18M.1.studies.TZ2.12 – M18/5/MATSD/SP1/ENG/TZ2/XX*

**Paper 1 – Question 13**

**Topic**: Mathematical Models

**Sub Topic**: Quadratic Models

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

**Marks**: 6

Question 13 is one of those questions that is Easy/ Medium in difficulty if you know how to use your calculator, or quite Hard if you don’t. It is a quadratic model question (lots of Mathematical Model questions in this paper!), with a quadratic model provided in the question with all parts provided.

Part (a) simply requires substituting in a value for x. Easy start.

Part (b) is a conceptual question, which can be made easier if you plot the quadratic in your calculator and try to understand it. It’s a bit hard to explain via text, I recommend watching the video solution for this one.

Part (c) asks to locate the x coordinate of the minimum of the quadratic. This is quite straight forward on the calculator using the minimum function.

*2018 Mathematics Studies Paper 1 May TZ2 Question 13 – 18M.1.studies.TZ2.13 – M18/5/MATSD/SP1/ENG/TZ2/XX*

**Paper 1 – Question 14**

**Topic**: Introduction to Differential Calculus

**Sub Topics**: Differentiation

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

**Difficulty**: Hard

**Marks**: 6

Question 14 is one of the hard differential calculus questions seen on IB Maths Studies Past Papers in the last few years, especially in Paper 1 exams. A strong understanding of what the derivative actually means is required here. The question starts with a fairly simple equation provided.

Part (a) asks to find the derivative of the equation.

Part (b) asks to find the gradient of the tangent at a specific x coordinate.

Part (c) is where this question becomes challenging. You are required to find the x-coordinate of the equation where the normal (not tangent) has a specific gradient.

*2018 Mathematics Studies Paper 1 May TZ2 Question 14 – 18M.1.studies.TZ2.14 – M18/5/MATSD/SP1/ENG/TZ2/XX*

**Paper 1 – Question 15**

Question 15 is a challenging geometry question to finish Paper 1. However, with strong calculator skills, this question is quite attainable. A shape is presented in the question, which involves a cylinder and a cone sitting on top of it. The height of both the cylinder and cone is provided, however the radius of both are not (listed as the pro-numeral r instead).

Part (a) asks to find an expression for the slant height of the cone, in terms of r.

Part (b) asks to calculate r, for a given total surface area of the shape. Whilst this seems quite challenging at first (particularly if you’re going to solve it algebraically), if you can set up the equation correctly, an easier option will be to solve using your calculator.

*2018 Mathematics Studies Paper 1 May TZ2 Question 15 – 18M.1.studies.TZ2.15 – M18/5/MATSD/SP1/ENG/TZ2/XX*

**2018 May Time Zone 2 Maths Studies – Paper 2**

**Paper 2 – Question 1**

**Topic**: Let, Sets & Probability

**Sub Topics**: Tree Diagrams

**Sub Topics**: Venn Diagrams

**Difficulty**: Medium

**Marks**: 16

Paper two starts with a moderately difficult probability question, involving both tree and Venn diagrams. This is a somewhat unusual start to a IB Maths Studies Paper 2, which usually starts with a statistics type question, and easier than this one.

Part (a) involves determining some of the missing values on a tree diagram.

Part (b) introduces probability based, tree diagram questions (3).

Part (c) is where the question transitions into Venn Diagrams. This question requires filling in some of the missing values on the Venn Diagram by interpreting the information given in the question.

Part (d) again asks to complete a specific missing value from the Venn Diagram.

Part (e) requires interpretation of a tricky set notation phrase, and therefore write down the Venn Diagram value in this region.

*2018 Mathematics Studies Paper 2 May TZ2 Question 1 – 18M.2.studies.TZ2.1 – M18/5/MATSD/SP2/ENG/TZ2/XX*

**Paper 2 – Question 2**

**Topic**: Descriptive Statistics

**Sub Topics**: Cumulative Frequency Graphs

**Sub Topics**: Box & Whisker Plots

**Difficulty**: Medium

**Marks**: 15

Question 2 involves both a cumulative frequency chart and box & whisker plot; both falling under the topic of ‘Descriptive Statistics.’ A cumulative frequency chart is presented at the start of the question.

Part (a) asks to interpret the cumulative frequency chart for a particular value.

Part (b) asks to find the median and lower and upper quartiles, by reading off the cumulative frequency chart.

Part (c) follows on from part (b), asking to calculate the Interquartile Range (IQR), which is straight forward if the quartiles in part (b) are correctly found.

Part (d) asks to determine the frequency that is greater than the upper quartile.

Part (e) asks to determine the number of data points that have a frequency less than a certain value.

Part (f) is another question requiring interpretation of the cumulative frequency chart.

Part (g) is where the box & whisker plot comes in. You are required to draw on graph paper a box & whisker plot that represents the data on the cumulative frequency chart, using the information you found in previous parts (quartiles, median etc.)

*2018 Mathematics Studies Paper 2 May TZ2 Question 2 – 18M.2.studies.TZ2.2 – M18/5/MATSD/SP2/ENG/TZ2/XX*

**Paper 2 – Question 3**

**Topic**: Statistical Application

**Sub Topic**: Normal Distribution

**Sub Topic**: Two Variable Statistics

**Difficulty**: Medium

**Marks**: 14

Question 14 is is made up of 9 marks on normal distribution and 5 marks on two variable stats. All questions are fairly straight forward (no unusual problem solving). The question starts out with normal distribution.

Parts (a) to (c) are all about the normal distribution, and a strong understanding of the normal distribution curve and the two calculator functions (NormalCDF & InverseNormal) should allow you to obtain all of the marks here.

Part (d) and (e) is where this question turns into two variable statistics. You are required to state the null hypothesis (always that the variables are independent), the p-value, and therefore, a conclusion for the test. These are very common questions asked in IB Maths Studies Past Papers. It is highly recommended to watch the video solutions on these parts if you’re not confident in this topic, as you can be certain they will appear on your upcoming papers.

*2018 Mathematics Studies Paper 2 May TZ2 Question 3 – 18M.2.studies.TZ2.3 – M18/5/MATSD/SP2/ENG/TZ2/XX*

**Paper 2 – Question 4**

**Topic**: Number & Algebra

**Sub Topic**: Sequences & Series

**Difficulty**: Medium

**Marks**: 16

Question 4 in Paper 2 is all about Sequences & Series, which is a bit rare in IB Maths Studies Paper 2 exams, which usually blend a mixture of topics & sub topics. If you are confident in applying the arithmetic & geometric formulas, you can quite easily get most of the marks here.

Parts (a) and (b) are about arithmetic sequences, asking you to find a specific term value, and also the sum of terms (formulas for both of these in the formula booklet).

Parts (c) and (d) turn to geometric sequences, and similar to parts (a) and (b), you are required to find a specific term value and sum of terms (formulas also available for both these).

If you interpret the question correctly and apply the formulas directly, you are on track for all the marks so far (12).

Part (e) is where this question gets harder, and is why the question overall has a difficulty rating of Medium and not Easy. You are required to find the point at which the sum of terms for the geometric sequence will exceed the sum of terms for arithmetic sequence (due to compounding growth). I recommend watching the video solution for this one for a conceptual understanding and tips on how to solve this using your calculator.

*2018 Mathematics Studies Paper 2 May TZ2 Question 4 – 18M.2.studies.TZ2.4 – M18/5/MATSD/SP2/ENG/TZ2/XX*

**Paper 2 – Question 5**

**Topic**: Geometry & Trigonometry

**Sub Topic**: Triangle Trigonometry

**Difficulty**: Hard

**Marks**: 14

Question 5 in Paper 2 is one of the harder trigonometry questions seen in IB Maths Studies past papers. Interestingly enough, only the Sine rule is required to be used, and it is used only once. All the other questions only require use of basic trig ratios (sin, cos & tan). What is difficult is the interpretation of the question and the problem solving aspect to it.

Describing what is required in individual parts is a bit pointless and misleading, as it’s the understanding of the diagram that is the critical part. I recommend studying this question with the paper in front of you, and viewing the video solutions for the sections that are difficult to understand and interpret.

*2018 Mathematics Studies Paper 2 May TZ2 Question 5 – 18M.2.studies.TZ2.5 – M18/5/MATSD/SP2/ENG/TZ2/XX*

**Paper 2 – Question 6**

**Topic 1**: Mathematical Models

**Sub Topic**: Cubic Models

**Topic 2**: Introduction to Differential Calculus

**Sub Topics**: Differentation

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

**Difficulty**: Hard

**Marks**: 15

As usual, Paper 2 finishes with quite a challenging question. This time, the question focuses on mathematical models, and ends with some differential calculus components. A cubic model is presented at the start of the question.

Part (a) asks to sketch the cubic model for a given domain and range. This is worth 4 marks, and is actually quite easy if you are confident using your calculator to graph the function. I recommend graphing the function and setting your calculators window settings to match the domain and range, then simply copying down what you see on the screen.

Part (b) asks to interpret the curve and decide which of three statements is incorrect.

Part (c) asks to find the value for y when x is equal to 1. This can be found by substituting in 1 for x into the cubic equation.

Part (d) asks to find the derivative of the cubic. There is nothing tricky here, as the cubic doesn’t involve fractions or anything else unusual.

Part (e) asks to locate the coordinate of the stationary points. Since it follows on from the derivative, it’s recommended to solve this using your understanding of differential calculus, what stationary points mean, and how to find them.

Part (f) is a challenging way to finish the paper, asking to find the possible values where the original cubic function has 3 solutions (in other words, has 3 x values for one y value). I recommend watching the video solution to this part on what this means conceptually and how to solve it.

*2018 Mathematics Studies Paper 2 May TZ2 Question 6 – 18M.2.studies.TZ2.6 – M18/5/MATSD/SP2/ENG/TZ2/XX*

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