# IB Maths Past Paper Overviews

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

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

**Paper 1 – Question 1**

Paper 1 commences with a number skills question involving some basic 3D geometry. This has become a recurring pattern in IB Maths Studies Past Papers, although this question is slightly more difficult, requiring a volume conversion in part (c).

Part (a) asks to find the volume of a cuboid, proving your answer to two significant figures. All 3 side lengths are provided, do this question is simply testing your ability to round an answer to significant figures. [2 marks]

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

Part (c) is where this question increases from Easy to Medium difficulty. The original cuboid dimensions (and volume in part (a)) is in mm, and this part asks to convert the volume into cm cubed. It’s recommended to watch the video solution on this if you’re unsure on exactly how to do this. [2 marks]

*2019 Mathematics Studies Paper 1 May TZ1 Question 1*

*Question Reference Code: 19M.1.studies.TZ1.1*

*M19/5/MATSD/SP1/ENG/TZ1/XX*

**Paper 1 – Question 2**

**Topic**: Descriptive Statistics

**Sub Topic**: Descriptive Statistics

**Difficulty**: Easy

**Marks**: 6

Question 2 is a basic descriptive statistics question, testing your knowledge of how to find statistics measures such as mean, median, range and standard deviation. Most of these measures can be found easily using your graphics display calculator.

Part (a) asks whether the data presented (speed) is a continuous or discrete variable. [1 mark]

Part (b) asks to find the median for the data set. [1 mark]

Part (c) asks to find the range of the data set. [1 mark]

Part (d) asks to find both the mean & standard deviation of the data set. [3 marks]

*2019 Mathematics Studies Paper 1 May TZ1 Question 2*

*Question Reference Code: 19M.1.studies.TZ1.2*

*M19/5/MATSD/SP1/ENG/TZ1/XX*

**Paper 1 – Question 3**

**Topic**: Logic, Sets & Probability

**Sub Topic:** Logic

**Difficulty**: Medium

**Marks**: 6

Question 3 is all about logic. It is quite common now in IB Maths Studies Past Papers for a basic logic question to be located in question 3-6 of Paper 1. Two simple propositions are presented at the start of the question.

Part (a) asks to write out the conjunction (“and”) of the two statements. [1 mark]

Part (b) asks to write out the inverse in symbolic form. [1 mark]

Part (c) asks to convert a compound statement, given in words, into symbolic form. The statement involves both negation & implication. [2 marks]

Part (d) then asks to complete two columns in a simple truth table, involving negation & implication. [2 marks]

*2019 Mathematics Studies Paper 1 May TZ1 Question 3*

*Question Reference Code: 19M.1.studies.TZ1.3*

*M19/5/MATSD/SP1/ENG/TZ1/XX*

**Paper 1 – Question 4**

**Topic**: Geometry & Trigonometry

**Sub Topic**: Coordinate Geometry

**Difficulty**: Medium

**Marks**: 6

Question 4 is a fairly straight forward coordinate geometry question. Two coordinates are presented at the start of the question, and it’s stated that a line passes through these coordinates.

Part (a) asks to find the gradient of this line. This can be found by using the gradient formula in your formula booklet. [2 marks]

Prior to part (b), a new line is introduced, that is parallel to the first line, and passes through a new coordinates. Part (b) asks to find the equation of this line, given in standard form. [2 marks]

Part (c) asks to find the coordinates of the x-intercept of this new line. Recall, the x-intercept can be found by substituting in y=0 into the equation of that line. [2 marks]

*2019 Mathematics Studies Paper 1 May TZ1 Question 4*

*Question Reference Code: 19M.1.studies.TZ1.4*

*M19/5/MATSD/SP1/ENG/TZ1/XX*

**Paper 1 – Question 5**

**Topic 1**: Descriptive Statistics

**Topic 2**: Logic, Sets & Probability

**Sub Topic 1**: Grouped Frequency Tables

**Sub Topic 2**: Basic Probability

**Difficulty**: Easy

**Marks**: 6

Question 5 is a combination of statistics & basic probability. A frequency data table is provided at the top of the question. Following this is an incomplete grouped frequency table (with a cumulative frequency column)

Part (a) asks to complete the incomplete grouped frequency table. This is fairly easy to do if you understand how cumulative frequency tables work (if you’re not sure, the video solution explains this in detail). [2 marks]

Part (b) is a straight-forward probability question that can be determined directly off your grouped frequency table. [2 marks]

Part (c) is another probability question, this one slightly harder than part (b) as it has a conditional probability component. [2 marks]

*2019 Mathematics Studies Paper 1 May TZ1 Question 5*

*Question Reference Code: 19M.1.studies.TZ1.5*

*M19/5/MATSD/SP1/ENG/TZ1/XX*

**Paper 1 – Question 6**

**Topic**: Geometry & Trigonometry

**Sub Topic**: 3D Geometry

**Difficulty**: Medium

**Marks**: 6

Question 6 is 3D geometry question, involving both a cylinder and a sphere. These types of questions are becoming quite common in IB Maths Studies past papers. At the start of the question, the radius and height of the cylinder is provided.

Part (a) asks to find the volume of the cylinder. This can be found by applying the volume of a cylinder formula, provided in your formula booklet. [3 marks]

Part (b) is where this question goes from Easy to Medium difficulty. The sphere is introduced and the question states that its volume is the same as the cylinder from part (a). It’s your task to determine the diameter of the sphere. This requires using the volume of a sphere formula, than solving for the unknown radius, and converting this to a diameter. [3 marks]

*2019 Mathematics Studies Paper 1 May TZ1 Question 6*

*Question Reference Code: 19M.1.studies.TZ1.6*

*M19/5/MATSD/SP1/ENG/TZ1/XX*

**Paper 1 – Question 7**

**Topic**: Logic, Sets & Probability

**Sub Topics**: Number Sets

**Sub Topics**: Venn Diagrams

**Difficulty**: Hard

**Marks**: 6

Question 7 is a surprisingly difficult question, testing your understanding of number tests, and then set notation that hasn’t been seen in IB Maths Studies Past Papers for a number of years. Four different types of numbers are presented at the start of the question.

Part (a) asks to place the found numbers on a number set venn diagram. [4 marks]

Part (b) then asks to determine whether four statements are correct or incorrect. The statements involve set notation: proper subset, intersection, union & complement. [2 marks]

*2019 Mathematics Studies Paper 1 May TZ1 Question 7*

*Question Reference Code: 19M.1.studies.TZ1.7*

*M19/5/MATSD/SP1/ENG/TZ1/XX*

**Paper 1 – Question 8**

**Topic**: Geometry & Trigonometry

**Sub Topic**: Triangle Trigonometry

**Difficulty**: Easy

**Marks**: 6

Question 8 is a fairly straight-forward right angled triangle trigonometry question. A diagram is presented at the start of the question.

Part (a) asks to draw a specific angle of depression on the diagram. [1 mark]

Part (b) asks to determine an unknown length on the diagram. This can be found using one of the trig ratios (SOHCAHTOA). [2 marks]

Part (c) asks to find another unknown side length on the diagram. Although this is worth 3 marks, it can simply found using Pythagoras theorem. [3 marks]

*2019 Mathematics Studies Paper 1 May TZ1 Question 8*

*Question Reference Code: 19M.1.studies.TZ1.8*

*M19/5/MATSD/SP1/ENG/TZ1/XX*

**Paper 1 – Question 9**

**Topic**: Mathematical Models

**Sub Topic**: Linear Models

**Difficulty**: Medium

**Marks**: 6

Question 9 is a linear mathematical model question, which is becoming less common in IB Maths Studies Past Papers over time. The most common mathematical model questions recently have been either exponential or quadratic.

A linear model is presented at the start of the question, which represents the amount of money spent for a given number of movie tickets.

Part (a) asks to determine the maximum number of movie tickets that could be purchased for a given amount spent. This is essentially asking you to substitute in a value for the x variable. [3 marks]

Prior to part (b), a different movie ticket purchase arrangement is presented, which results in a different linear model to part (a).

Part (b) asks to use the information to create a new linear model that represents the amount of money spent for a given number of tickets purchased. [1 mark]

Part (c) is a good question. It asks to determine the number of tickets purchased whereby the two purchasing models will result in the same mount spent. [2 marks]

*2019 Mathematics Studies Paper 1 May TZ1 Question 9*

*Question Reference Code: 19M.1.studies.TZ1.9*

*M19/5/MATSD/SP1/ENG/TZ1/XX*

**Paper 1 – Question 10**

**Topic**: Geometry & Trigonometry

**Sub Topic**: Trigonometry

**Difficulty**: Easy

**Marks**: 6

Question 10 is the second trigonometry question for the paper, although this one is now non-right-angled. A triangle is presented at the start of the question, with all 3 side lengths provided.

Part (a) asks to find the size of one of the angles. This can be found by direct application of the cosine rule. [3 marks]

Part (b) asks to find the area of the triangle. By using your answer in part (a), this can be found by directly applying the area of a triangle formula. [3 marks]

*2019 Mathematics Studies Paper 1 May TZ1 Question 10*

*Question Reference Code: 19M.1.studies.TZ1.10*

*M19/5/MATSD/SP1/ENG/TZ1/XX*

**Paper 1 – Question 11**

**Topic**: Statistical Application

**Sub Topic**: Normal Distribution

**Difficulty**: Medium

**Marks**: 6

Question 11 is all about the Normal Distribution. At the start of the question, 4 different normal distribution curves are presented.

Part (a) asks to identify which of the 4 normal distribution curves match up with a pair of means & standard deviations provided. [2 marks]

Part (b) & (c) are very common IB Maths Studies past paper normal distribution questions. They require you to use either the NormalCDF or InverseNormal commands on your calculator to answer questions. Part (b) [2 marks]. Part (c) [2 marks]

*2019 Mathematics Studies Paper 1 May TZ1 Question 11*

*Question Reference Code: 19M.1.studies.TZ1.11*

*M19/5/MATSD/SP1/ENG/TZ1/XX*

**Paper 1 – Question 12**

**Topic**: Logic, Sets & Probability

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

**Difficulty**: Medium

**Marks**: 6

Question 12 involves probability, and more specifically, tree diagrams. A completed tree diagram is presented at the start of the question.

All three question parts (a, b & c) asks to determine probabilities that are based on the tree diagram provided. It requires your knowledge in how to calculate probabilities for multi-stage events (with replacements). If you’re not sure how to do this, or the difference between with or without replacement, it is recommended to watch the video tutorials. Part (a) [2 marks]. Part (b) [3 marks]. Part (c) [1 mark]

*2019 Mathematics Studies Paper 1 May TZ1 Question 12*

*Question Reference Code: 19M.1.studies.TZ1.12*

*M19/5/MATSD/SP1/ENG/TZ1/XX*

**Paper 1 – Question 13**

**Topic**: Mathematical Models

**Sub Topic**: Quadratic Models

**Difficulty**: Hard

**Marks**: 6

Question 13 is a Quadratic Model question that requires strong algebraic skills. A sketch of the quadratic function is provided at the start of the question, showing the y-intercept and both x-intercepts.

Part (a) asks to determine the equation of the quadratic function. There are quite a few steps to this, so it’s recommended to watch the video solution if you’re not sure how to approach it. [4 marks]

Part (b) asks to write down the axis of symmetry of the quadratic. This is fairly easy if you know what this term means and the symmetrical nature of quadratic functions. [2 marks]

*2019 Mathematics Studies Paper 1 May TZ1 Question 13*

*Question Reference Code: 19M.1.studies.TZ1.13*

*M19/5/MATSD/SP1/ENG/TZ1/XX*

**Paper 1 – Question 14**

**Topic**: Number & Algebra

**Sub Topic**: Compound Interest

**Difficulty**: Medium

**Marks**: 6

Question 14 is a moderately difficult compound interest question. What is interesting is that it includes a depreciation component, which is quite rare in IB Maths Studies past papers.

An investment scenario is presented at the start of the question, whereby the initial amount (PV) is unknown, and the end amount (FV) is known. Both the number of years and compounding periods are also known.

Part (a) asks to find the initial amount (PV). This can be found using the compound interest formula and then using numerical solve on your calculator to determine PV. [3 marks]

Part (b) now introduces the depreciation component. The end amount (FV) in part (a) is used to purchase a computer that depreciates for 4 years to a known end value. The question asks to determine the annual depreciation rate. [3 marks]

*2019 Mathematics Studies Paper 1 May TZ1 Question 14*

*Question Reference Code: 19M.1.studies.TZ1.14*

*M19/5/MATSD/SP1/ENG/TZ1/XX*

**Paper 1 – Question 15**

**Topic**: Differential Calculus

**Sub Topic**: Optimisation

**Difficulty**: Hard

**Marks**: 6

Question 15 is a differential calculus, optimisation question, which is a bit unusual to be in Paper 1. Usually this subtopic is either question 5 or 6 in Paper 2 in IB Maths Studies Past Papers.

A cylinder is presented at the start of the question, with a dimension constraint that mentions the sum of the radius and height is 12 cm.

Part (a) asks to write down an expression for the curved surface area of the cylinder, in terms of r only. [2 marks]

Part (b) asks to differentiate the equation from part (a), with respect to the radius. [2 marks]

Part (c) is where optimisation is introduced. The question asks to find the value for the radius that maximises the curved surface area of the cylinder. [2 marks]

*2019 Mathematics Studies Paper 1 May TZ1 Question 15*

*Question Reference Code: 19M.1.studies.TZ1.15*

*M19/5/MATSD/SP1/ENG/TZ1/XX*

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

**Paper 2 – Question 1**

**Topic**: Statistical Application

**Sub Topic**: Two Variable Statistics

**Difficulty**: Medium

**Marks**: 16

Question 1 is a very common IB Maths Studies Paper 2 question. It is all about two-variable statistics; scatter diagrams, correlation & equations of lines of regression.

A data table is presented at the start of the question, involving body temperature and the resulting heart rate.

Part (a) asks to draw a scatter diagram for the data set. [4 marks]

Part (b) asks to find the means of both the body temperature (x variable) and heart rate (y variable). [2 marks]

Part (c) asks to plot the coordinates of the means found in part (b) onto the scatter diagram. [2 marks]

Part (d) asks to both find and describe the correlation coefficient of the data. [4 marks]

Part (e) asks to find the equation of the line of regression. [2 marks]

Part (f) asks to draw this line of regression onto the scatter diagram. [2 marks]

*2019 Mathematics Studies Paper 2 May TZ1 Question 1*

*Question Reference Code: 19M.2.studies.TZ1.1*

*M19/5/MATSD/SP2/ENG/TZ1/XX*

**Paper 2 – Question 2**

**Topic**: Geometry & Trigonometry

**Sub Topics**: Trigonometry

**Sub Topics**: Geometry

**Difficulty**: Hard

**Marks**: 16

Question 2 in paper 2 is quite a difficult Geometry & Trigonometry question. One of the harder geometry & trigonometry questions seen in IB Maths Studies past papers.

A diagram of the exterior of a house is presented at the start of the question.

Part (a) asks to find one of the lengths of the roof, which can be found by some problem solving & using the sine rule. [5 marks]

Part (b) asks to find the total area of the room of the house, which consists of two rectangles.[3 marks]

Before part (c), new information is introduced, whereby the house owner is looking to install rectangular solar panels onto the roof of the house.

Part (c) asks to find the maximum number of panels that could be installed. This requires some working through and problem solving. Watch the video solution if you’re not sure how to approach this. [3 marks]

Part (d) asks to find the total surface area of the installed solar panels, and to then determine the percentage error of the house owners estimate of this error. [3 marks]

Part (e) asks to investigate whether more solar panels could have been installed onto the roof if the panels were orientated in a different way. This question part is quite similar to part (c), and requires some thinking and problem solving again. [2 marks]

*2019 Mathematics Studies Paper 2 May TZ1 Question 2*

*Question Reference Code: 19M.2.studies.TZ1.2*

*M19/5/MATSD/SP2/ENG/TZ1/XX*

**Paper 2 – Question 3**

**Topics**: Descriptive Statistics

**Topics**: Statistical Application

**Sub Topics**: Descriptive Statistics

**Sub Topic**: Two-variable Statistics

**Difficulty**: Medium

**Marks**: 15

Question 3 is a long statistics question, with a mixture of descriptive statistics (mean, median, mode, etc.) and two-variable statistical application.

A data table is presented at the start of the question, showing the number of people that own a certain number of pets.

Part (a) starts by asking how many people own pets. This has a small trick to it, as you need to sum up the total people row in the table, but exclude the people that own zero pets. [1 mark]

Part (b) asks to write down the modal number of pets (which pet ownership number is the most common). [1 mark]

Part (c) asks to find 3 statistics measures; the median, lower quartile and upper quartile. All three of these can be found using the statistics section of your graphics calculator. [3 marks]

Prior to part (d) another data table is presented, this time showing the preferred pet type for age category (teenager or non-teenager). This type of data table is very common in IB Maths Studies Past Papers, for statistical application questions.

Part (d) asks to write down the ratio of teens to non-teens in simplest form. [1 mark]

Part (e) asks to state the null and alternative hypothesis for a statistical test of independence. [2 marks]

Part (f) asks to write out the number of degrees of freedom for the test. [1 mark]

Part (g) asks to calculate the expected number of teens that prefer cats. [2 marks]

Part (h) asks to find the p-value for the test. This can be found fairly quickly using your graphics calculator (the video solution shows this process). [2 marks]

Part (i) asks to state the conclusion for the test of independence. This requires comparing the p-value found in part (h) with the significance level outlined for the test (in this case, 10%). [2 marks]

*2019 Mathematics Studies Paper 2 May TZ1 Question 3*

*Question Reference Code: 19M.2.studies.TZ1.3*

*M19/5/MATSD/SP2/ENG/TZ1/XX*

**Paper 2 – Question 4**

**Topics**: Mathematical Models

**Topics**: Mathematical Models

**Difficulty**: Medium

**Marks**: 15

Question 4 in paper 2 progresses through a range of mathematical model questions; substituting values into the function, linear models, exponential models, cubic models, etc.

Two functions are presented at the start of the question, one that represents the path of a river (cubic) and the other the path of a highway (exponential).

Part (a) asks to find the value of the exponential function for a given x value. This requires substituting this x value into the function. [2 marks]

Part (b) is the most challenging part of this question. It essentially asks you to find a linear function that describes a straight path from the origin to a certain point on the river (the cubic model). There are quite a few steps to this, so it’s recommended that you watch the video solution if you’re unsure. [5 marks]

Part (c) asks to determine the two coordinates where the river crosses the highway. These can be found fairly quickly using analysis tools on your graphics display calculator. [4 marks]

Part (d) asks to determine the distance from the origin to the point where the highway crosses the y axis. This is essentially asking you to find the y-intercept of the exponential function. [2 marks]

Part (e) is an interesting question, and tests your knowledge of domain & range. It asks whether the river (the cubic model) will over cross over a road that travels directly north from the origin. So essentially, the question is asking if the cubic model will cross the y axis. [2 marks]

*2019 Mathematics Studies Paper 2 May TZ1 Question 4*

*Question Reference Code: 19M.2.studies.TZ1.4*

*M19/5/MATSD/SP2/ENG/TZ1/XX*

**Paper 2 – Question 5**

**Topic**: Number & Algebra

**Sub Topics**: Currency Conversion

**Sub Topics**: Sequences & Series

**Difficulty**: Medium

**Marks**: 14

Question 5 is a combination of currency conversion & sequences & series. The question involves the purchase of a bicycle, that was purchased in USD, by a person in Canada.

Part (a) asks to determine how much the bicycle cost in Canadian dollars, including a transaction fee. This is a common currency conversion question found in IB Maths Studies Past Papers. [3 marks]

Prior to part (b), information is provided outlining the depreciation of the value of the bicycle over time. The question states that the depreciation follows a geometric pattern, and here is where the sequences & series is introduced.

Part (b) asks to find the value of the bicycle after 5 years. [3 marks]

Part (c) asks to calculate when the bicycle will be worth less than 50 dollars. [2 marks]

Prior to part (d), more information is provided. The information outlines the amount of insurance that the bicycle owner pays each year to insure his bicycle. The amount reduces over time, following an arithmetic sequence.

Part (d) asks to find the total amount of insurance paid over 5 years. [3 marks]

Part (e) is a good conceptual question, asking if the bicycle owner should insure his bike in the 12th year. This requires calculating both the bike value (geometric sequence) and insurance payment (arithmetic sequence) in that year, making a comparison and drawing a conclusion. [3 marks]

*2019 Mathematics Studies Paper 2 May TZ1 Question 4*

*Question Reference Code: 19M.2.studies.TZ1.4*

*M19/5/MATSD/SP2/ENG/TZ1/XX*

**Paper 2 – Question 6**

**Topics**: Mathematical Models

**Topics**: Differential Calculus

**Sub Topics**: Cubic Models

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

**Difficulty**: Hard

**Marks**: 14

Like usual, Question 6 in Paper 2 is a challenging conclusion to the paper. A cubic function is provided, with an unknown coefficient of the x term. There is also information on the coordinates of the local maximum.

Part (a) asks to find the unknown coefficient of the x term. This requires using the information on the local maximum & utilising differential calculus. This is a challenging question and it’s recommended to watch the video solution. [5 marks]

Part (b) asks to find the coordinates of the local minimum. This is fairly straight-forward after part (a) as the full cubic function is known. This coordinate can be found using a graphics calculator. [2 marks]

Part (c) asks to write down the interval where the cubic model is sloping downwards (i.e., gradient is negative). [2 marks]

Part (d) asks to determine the equation of the normal at a given location on the cubic function. This is a challenging question and has quite a few steps involved. [5 marks]

*2019 Mathematics Studies Paper 2 May TZ1 Question 6*

*Question Reference Code: 19M.2.studies.TZ1.6*

*M19/5/MATSD/SP2/ENG/TZ1/XX*