# IB Maths Past Paper Overviews

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**2019 May Time Zone 2 Maths Studies – Paper 1**

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

**Paper 1 – Question 1**

Question 1 in Paper 1 starts in a very common format for IB Maths Studies Past Papers – an easy question testing your ability to round to significant figures and scientific notation. If you are confident with these skills, question 1 is a good opportunity to complete a 6 mark question in a just a couple of minutes.

Part (a) asks to calculate the circumference of a circle, with the diameter provided. [3 marks]

Part (b) asks to round your answer to part (a) to three significant figures. [1 mark]

Part (c) asks to convert your answer to part (b) into scientific notation. [2 marks]

*2019 Mathematics Studies Paper 1 May TZ2 Question 1*

*Question Reference Code: 19M.1.studies.TZ2.1*

*M19/5/MATSD/SP1/ENG/TZ2/XX*

**Paper 1 – Question 2**

**Topic**: Statistical Application

**Sub Topic**: Two Variable Statistics

**Difficulty**: Easy

**Marks**: 6

Question 2 is a fairly straight-forward two variable statistics question, testing your knowledge on scatter plots & line of regression equations.

A data table with 5 data points is provided at the start of the question. These data points are then plotted on a provided scatter plot.

Part (a) asks to determine the line of regression equation. This can be found using a graphics display calculator. [2 marks]

Prior to part (b), the coordinates of the mean values (of the x and y variables) are provided. Part (b) then asks to draw the line of regression equation onto the scatter diagram. This can be completed by using the y-intercept and the coordinates of the means. [2 marks]

Part (c) is a conceptual question, assessing your understanding of the difference between interpolation and extrapolation. [2 marks]

*2019 Mathematics Studies Paper 1 May TZ2 Question 2*

*Question Reference Code: 19M.1.studies.TZ2.2*

*M19/5/MATSD/SP1/ENG/TZ2/XX*

**Paper 1 – Question 3**

**Topic**: Number & Algebra

**Sub Topic**: Currency Conversion

**Difficulty**: Medium

**Marks**: 6

Question 3 is a very common IB Maths Studies Past Paper currency conversion question.

Part (a) asks to do a straight-forward currency conversion. [2 marks]

Part (b) asks to do another currency conversion, this time with a commission charged by the bank. [4 marks]

*2019 Mathematics Studies Paper 1 May TZ2 Question 3*

*Question Reference Code: 19M.1.studies.TZ2.3*

*M19/5/MATSD/SP1/ENG/TZ2/XX*

**Paper 1 – Question 4**

**Topic**: Logic, Sets & Probability

**Sub Topic**: Logic

**Difficulty**: Medium

**Marks**: 6

Question 4 is a moderately difficult question all about logic. 3 statements are provided at the start of the questions.

Part (a) asks to write down a compound proposition in words. The compound proposition involves implication and conjunction. [3 marks]

Part (b) asks to complete a truth table, again involving implication and conjunction. [2 marks]

Part (c) asks to justify whether the right hand column in the truth table completed in part (b) is a tautology, contradiction or neither. This is a very common logic question in IB Maths Studies Past Papers. [1 mark]

*2019 Mathematics Studies Paper 1 May TZ2 Question 4*

*Question Reference Code: 19M.1.studies.TZ2.4*

*M19/5/MATSD/SP1/ENG/TZ2/XX*

**Paper 1 – Question 5**

**Topic**: Logic, Sets & Probability

**Sub Topic**: Venn Diagrams

**Difficulty**: Medium

**Marks**: 6

Question 5 involves Venn Diagrams & probability. Information is provided at the start of the question involving the preferred flavour of smoothie at a school cafe.

Part (a) asks to complete a 3-set Venn Diagram for the information provided. It’s very important for this type of question to work from the inside of the Venn Diagram outwards. If you’re not sure of how to do this, it’s recommended to watch the video solution. [2 marks.

Part (b) asks to calculate the number of people who did not like any of the smoothie flavours. This requires adding up all the people in the Venn Diagram and comparing with the total providing at the start of the question. [2 marks]

Part (c) is a probability question, that can be read off the Venn Diagram. [2 marks]

*2019 Mathematics Studies Paper 1 May TZ2 Question 5*

*Question Reference Code: 19M.1.studies.TZ2.5*

*M19/5/MATSD/SP1/ENG/TZ2/XX*

**Paper 1 – Question 6**

**Topic**: Descriptive Statistics

**Sub Topic**: Box & Whisker Plots

**Difficulty**: Medium

**Marks**: 6

Question 6 is all about box & whisker Plots, a component of Descriptive Statistics. A box and whisker plot is presented at the start of the question, with all the important information provided (min, max, Q1, Q3, Median).

Part (a) asks to state what one of the numbers shown on the Box & Whisker plot represents. [1 mark]

Part (b) has two parts. The first is to determine the interquartile range for the data. The second is to approximate the amount of data between Q3 and the maximum. This requires multiplying the total number of data points by 0.25 (25%). [3 marks]

Prior to part (c), two more Box & Whisker Plots are provided. Part (c) is a conceptual question, comparing the data between the two plots. It’s recommended to watch the video solution to this part. [2 marks]

*2019 Mathematics Studies Paper 1 May TZ2 Question 6*

*Question Reference Code: 19M.1.studies.TZ2.6*

*M19/5/MATSD/SP1/ENG/TZ2/XX*

**Paper 1 – Question 7**

**Topic**: Mathematical Models

**Sub Topic**: Linear Models

**Difficulty**: Medium

**Marks**: 6

Question 7 is a moderately difficult linear models question. Information about a rectangular garden is provided at the start of the question, with a relationship between the length and width.

Part (a) asks to write down an expression for the width of the garden, in terms of the length. [1 mark]

Prior to part (b), the perimeter of the rectangle is provided. Part (b) asks to create another linear model, this time an expression for the perimeter of the rectangle. [1 mark]

Part (c) now asks to solve for the length of the rectangle, using the linear model created in part (b). [2 marks]

Part (d) transitions away from mathematical models, assessing your ability to calculate the percentage error of an estimate. [2 marks]

*2019 Mathematics Studies Paper 1 May TZ2 Question 7*

*Question Reference Code: 19M.1.studies.TZ2.7*

*M19/5/MATSD/SP1/ENG/TZ2/XX*

**Paper 1 – Question 8**

**Topic**: Geometry & Trigonometry

**Sub Topic**: Coordinate Geometry

**Difficulty**: Medium

**Marks**: 6

Question 8 is a moderately challenging coordinate geometry question. It’s challenging as it requires strong algebraic skills to determine equations of lines.

A scatterplot with a straight lines is provided at the start of the question. The x and y intercept is provided.

Part (a) has two parts. The first is to find the gradient of the line. The second is to determine the equation of the line.

Prior to part (b), information about a new line that is perpendicular to the first line is provided. In addition, the coordinates of a point this new line passes through is also provided.

Part (c) also has two parts. The first is to find the gradient of this new line. The second is to find the equation of this new line.

*2019 Mathematics Studies Paper 1 May TZ2 Question 8*

*Question Reference Code: 19M.1.studies.TZ2.8*

*M19/5/MATSD/SP1/ENG/TZ2/XX*

**Paper 1 – Question 9**

**Topic**: Geometry & Trigonometry

**Sub Topic**: Trigonometry

**Difficulty**: Easy

**Marks**: 6

Question 9 is a fairly easy trigonometry question, as it only involves the use of trig ratios (sin, cos & tan). A diagram is presented at the start of the question, showing a fire truck with its ladder leaning at an incline against a wall.

Part (a) asks to find the angle of elevation the ladder makes. [3 marks]

Part (b) asks to find the maximum height the ladder can make with the wall, for a given maximum angle of elevation. The only trick here is to understand that the ladder starts at the top of the truck, not the ground, so the height of the truck needs to be added on at the end. [3 marks]

*2019 Mathematics Studies Paper 1 May TZ2 Question 9*

*Question Reference Code: 19M.1.studies.TZ2.9*

*M19/5/MATSD/SP1/ENG/TZ2/XX*

**Paper 1 – Question 10**

**Topic**: Mathematical Models

**Sub Topic**: Quadratic Models

**Difficulty**: Hard

**Marks**: 6

Question 10 is a challenging quadratic models question. It involves a form of quadratic equation rarely seen in IB Maths Studies Past Papers – in factor form. The equation of the quadratic is provided, with 3 unknown coefficients/ constants. A sketch of the quadratic is also provided, with all the intercepts labelled.

Part (a) asks to determine the axis of symmetry of the quadratic. [2 marks]

Parts (b) and (c) asks to determine the 3 unknowns in the equation of the quadratic. This requires some sound algebraic skills and understanding of the null factor law. It’s recommended to watch the video solution to the parts, particularly part (b). Part (b) [4 marks]. Part (c) [2 marks].

*2019 Mathematics Studies Paper 1 May TZ2 Question 10*

*Question Reference Code: 19M.1.studies.TZ2.10*

*M19/5/MATSD/SP1/ENG/TZ2/XX*

**Paper 1 – Question 11**

**Topic**: Logic, Sets & Probability

**Sub Topic**: Number Sets & Set Notation

**Difficulty**: Easy

**Marks**: 6

Question 11 assesses your knowledge of set notation. If you understand these symbols, this question is quite easy and is an opportunity to get 6 quick marks. Three number sets are presented at the start of the question.

Part (a) asks to determine the elements (numbers) that belong to two of the sets (asked with an intersection symbol (“and”)). [3 marks]

Part (b) has 2 parts: The first is to determine the elements that belong to one set “and not” another set. The second part is to simply write down how many elements there are in the first part. [3 marks]

2019 Mathematics Studies Paper 1 May TZ2 Question 11

Question Reference Code: 19M.1.studies.TZ2.11

M19/5/MATSD/SP1/ENG/TZ2/XX

**Paper 1 – Question 12**

**Topic**: Descriptive Statistics

**Sub Topics**: Grouped Frequency Tables

**Sub Topics**: Cumulative Frequency Graphs

**Difficulty**: Medium

**Marks**: 6

It’s unusual for a descriptive statistics question to appear this late in an IB Maths Studies Past Paper. Usually these questions are in the first 5 questions of paper 1 or first 2 questions of paper 2. This question is moderately difficult, and involves both a grouped frequency table and cumulative frequency graph.

A grouped frequency table is provided at the start of the question, with two values missing. Part (a) asks to find these two missing values. This requires your understanding of how grouped data tables involving a cumulative frequency column work. [2 marks]

Prior to part (b), an incomplete cumulative frequency graph is provided. Part (b) asks to complete this graph. [2 marks]

Part (c) assess your ability to read off values from a cumulative frequency graph. [2 marks]

*2019 Mathematics Studies Paper 1 May TZ2 Question 12*

*Question Reference Code: 19M.1.studies.TZ2.12*

*M19/5/MATSD/SP1/ENG/TZ2/XX*

**Paper 1 – Question 13**

**Topic**: Mathematical Models

**Sub Topic**: Exponential Models

**Difficulty**: Hard

**Marks**: 6

Question 13 is an extremely common exponential model question. This type of question appears in nearly every single IB Maths Studies Past Paper (paper 1). An exponential model is provided at the start of the question that describes the decreasing population of turtles over time. The exponential model has an unknown coefficient.

In part (a), you are required to use the starting population to determine the unknown coefficient. [2 marks]

Part (b) asks you to determine how long it will take for the population of turtles to reach a certain amount. [2 marks]

Part (c) asks to determine the long term steady state population of turtles (i.e., the population that, once reached, no longer decreases). Highly recommend watching the video solution to this part or an understanding of how to think about it. [2 marks]

*2019 Mathematics Studies Paper 1 May TZ2 Question 13*

*Question Reference Code: 19M.1.studies.TZ2.13*

*M19/5/MATSD/SP1/ENG/TZ2/XX*

**Paper 1 – Question 14**

**Topic**: Statistical Application

**Sub Topic**: Normal Distribution

**Difficulty**: Medium

**Marks**: 6

Question 14 is all about the Normal Distribution. If you are confident with Normal Distribution and the two commands on the calculator (NormalCDF & InverseNormal), then this might be an opportunity to pick up 6 marks at the end of the paper when questions usually get difficult.

A scenario is presented involving the mean & standard deviation of the price of a kilogram of tomatoes. Both the mean & SD are provided.

Part (a) involves shading a region on a normal distribution curve. [2 marks]

Part (b) asks to find the probability that a randomly selected kilogram of tomatoes is between two values. This requires using the NormalCDF command on your calculator. [2 marks]

Part (c) is the opposite of part (b), this time asking to find the price of a kilogram of tomatoes for a given probability. This requires using the InverseNormal command. [2 marks]

*2019 Mathematics Studies Paper 1 May TZ2 Question 14*

*Question Reference Code: 19M.1.studies.TZ2.14*

*M19/5/MATSD/SP1/ENG/TZ2/XX*

**Paper 1 – Question 15**

**Topic**: Differential Calculus

**Sub Topic**: Optimisation

**Difficulty**: Hard

**Marks**: 6

Paper 1 concludes with a differential calculus optimisation question. A cubic mathematical model is provided that represents the profit a potter makes for a given number of vases sold each month.

Part (a) asks to determine the profit if no vases are sold (i.e., substituting in x = 0 into the model). [1 mark]

Part (b) is where the differential calculus is introduced, asking the differentiate the cubic model with respect to x. [2 marks]

Part (c) is the challenging part of this question and is where optimisation is involved. The question asks to use the derivative found in part (b) to determine the number of vases that maximises the profit. The conceptual understanding of this question is very important, and it’s recommended to watch the video solution for this. [3 marks]

*2019 Mathematics Studies Paper 1 May TZ2 Question 15*

*Question Reference Code: 19M.1.studies.TZ2.15*

*M19/5/MATSD/SP1/ENG/TZ2/XX*

**2019 May Time Zone 2 Maths Studies – Paper 2**

**Paper 2 – Question 1**

**Topics**: Statistical Application

**Topics**: Logic, Sets & Probability

**Sub Topics**: Two Variable Statistics

**Sub Topics**: Probability

**Difficulty**: Medium

**Marks**: 15

Question 1 starts Paper two with a long question involving two variable statistics (hypothesis testing more specifically) and then finishing with a few probability questions. At the start of the question, a data table is provided, looking at the gender of students (male/ female) and preferred language choice.

Part (a) asks to write out the null hypothesis. [1 mark]

Part (b) asks to determine the number of degrees of freedom for the test. [1 mark]

Part (c) has two parts: the first is to determine the expected number of a certain cell in the table. The second is to use your graphics display calculator to find the Chi-Squared statistic. [3 marks]

Prior to part (d), the significance level and critical value is given.

Part (d) asks to determine the conclusion for the test of independence (i.e., should the null hypothesis be rejected or not). This requires a comparison between the Chi-Squared value found in part (c) and the critical value. [2 marks]

Part (e) is where probability is introduced. There are three questions to complete, with the second and third increasing in complexity as they involve multi-stage events without replacement. [8 marks]

*2019 Mathematics Studies Paper 2 May TZ2 Question 1*

*Question Reference Code: 19M.2.studies.TZ2.1*

*M19/5/MATSD/SP2/ENG/TZ2/XX*

**Paper 2 – Question 2**

**Topic**: Geometry & Trigonometry

**Sub Topics**: Trigonometry

**Difficulty**: Medium

**Marks**: 13

Question 2 is all about non-right-angled trigonometry. There are 4 parts to the question (parts (a) to (d)), and the parts require the use of the sine rule, cosine rule and area of a triangle formula find specific values on a diagram.

This type of long trig question is becoming increasingly common in IB Maths Studies Past Papers, especially paper 2.

*2019 Mathematics Studies Paper 2 May TZ2 Question 2*

*Question Reference Code: 19M.2.studies.TZ2.2*

*M19/5/MATSD/SP2/ENG/TZ2/XX*

**Paper 2 – Question 3**

**Topic**: Geometry & Trigonometry

**Sub Topic**: Geometry

**Difficulty**: Medium

**Marks**: 15

Question 3 is a 3D geometry question, involving both a cone and cylinder. At the start of the question, the dimensions of the cone (radius and height) are provided.

Part (a) asks to calculate the volume of the cone. This can be found by direct application of the volume of a cone formula. [2 marks]

Part (b) asks to determine the slant height of the cone. (hint: Pythagoras theorem). [2 marks]

Part (c) asks to calculate the total surface area (both curved surface & base circle) of the cone. [3 marks]

Prior to part (d) the cylinder is introduced. The question states that the radius of the cylinder, and the area is the same as the cone in the previous parts.

Part (d) asks to find the height of the cylinder. This can be found by utilising the area. [4 marks]

Part (e) asks you to determine which of the cylinder or cone has a larger volume. Since you already calculated the volume of the cone in part (a), you just need to calculate the volume of the cylinder and draw a comparison. [4 marks]

*2019 Mathematics Studies Paper 2 May TZ2 Question 3*

*Question Reference Code: 19M.2.studies.TZ2.3*

*M19/5/MATSD/SP2/ENG/TZ2/XX*

**Paper 2 – Question 4**

**Topic**: Number & Algebra

**Sub Topic**: Sequences & Series

**Difficulty**: Medium

**Marks**: 16

Question 4 is all about sequences and series. This type of papers two question has become quite common in IB Maths Studies Past Papers, whereby the question starts with an arithmetic sequence, and then a geometric is introduced later.

The question starts out with an arithmetic sequence scenario, looking at the quantity of antibiotic a patient should consume per day.

Part (a) asks you to determine two equations that describe the amount of antibiotic consumed on day 7 and 11. [2 marks]

Pat (b) requires you to solve the two simultaneous equations from part (a), to determine the first term and the common difference. [2 marks]

Part (c) asks you to calculate the total amount of antibiotic consumed in the first 5 days. This requires the use of the sum of n terms in an arithmetic sequence formula. [3 marks]

Prior to part (d), more information is provided about a new patient who consumes the antibiotic on a schedule that follows a geometric sequence (decreasing).

Part (d) is a long question part, with 3 sub-questions. The first is to determine the amount of antibiotic consumed on the 5th day. The second part asks to determine how many days until that amount of antibiotic consumed is less than a certain value. The third part then follows on, asking to calculate the total amount of antibiotic consumed in this timeframe. [9 marks]

*2019 Mathematics Studies Paper 2 May TZ2 Question 4*

*Question Reference Code: 19M.2.studies.TZ2.4*

*M19/5/MATSD/SP2/ENG/TZ2/XX*

**Paper 2 – Question 5**

**Topics**: Mathematical Models

**Topics**: Differential Calculus

**Sub Topics**: Cubic Models

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

**Difficulty**: Hard

**Marks**: 20

Question 5 is a long and challenging question involving a cubic model with differential calculus involved. A cubic function is presented at the start of the question.

Part (a) asks to find the value of the function when x equals 2. [2 marks]

Part (b) asks to find the y-intercept of the function. [1 mark]

Part (c) requires you to sketch the function for a given domain and range. It’s recommended to utilise your graphics display calculator for this. [4 marks]

Part (d) asks you to differentiate the original cubic function. [3 marks]

Part (e) asks you to find the gradient of the function at a specific point. This can be achieved by using the derivative found in the previous part. [2 marks]

Part (f) builds on from part (e), asking you to find the gradient of the tangent at a specific point. [2 marks]

Part (g) asks you to use the derivative found in part (d) to find the coordinates of the local maximum and minimum.

Part (h) asks you to determine the range of the function between this local max and min.

*2019 Mathematics Studies Paper 2 May TZ2 Question 5*

*Question Reference Code: 19M.2.studies.TZ2.5*

*M19/5/MATSD/SP2/ENG/TZ2/XX*

**Paper 2 – Question 6**

**Topics**: Number & Algebra

**Topics**: Mathematical Models

**Sub Topics**: Compound Interest

**Sub Topics**: Linear Models

**Difficulty**: Hard

**Marks**: 11

Question 6 ends Paper 2 with a question involving compound interest (which is just an exponential model) and a linear model. So this question is really about two mathematical models, how they compare and when they are equal to each other.

Part (a) starts with a straight-forward compound interest question, asking to calculate the future value of an investment. All other values are provided, so this is a direct application of the compound interest formula. [3 marks]

Part (b) introduces a linear model, and you are required to find the future value for a given year (x value). [3 years]

Part (c) is where this question gets challenging. You are required to calculate the number of years until the exponential model (the compound interest scenario in part (a)) exceeds the linear model (in part (b)). This problem can be approached in a few different ways. It’s recommended to watch the video solution to this part to understand how to think about it conceptually.

*2019 Mathematics Studies Paper 2 May TZ2 Question 6*

*Question Reference Code: 19M.2.studies.TZ2.6*

*M19/5/MATSD/SP2/ENG/TZ2/XX*