# IB Maths Past Paper Overviews

## 2018 May Time Zone 1 Maths Studies – Paper 1

### Paper 1 – Question 1

Topic: Number & Algebra

Sub Topic 1: Scientific Notation, Rounding & Percentage Error

Sub Topic 2: Mean, Median & Mode

Difficulty: Easy

Marks: 6

Paper 1 starts with a fairly easy number skills question, looking at the topics of percentage error and converting numbers into Scientific Notation.

Part (a)starts of with a statistics type question, requiring finding the total attendance for a soccer season given the average number of attendees per game and the number of games in the season. [2 marks]

Part (b) is where the number skills start, which is very common for IB Maths Studies exams Paper 1, Question 1. In this part, the percentage error from Part (a) against an exact value needs to be found. [2 marks]

Part (c) requires converting your Part (b) answer into scientific notation. [2 marks]

2018 Mathematics Studies Paper 1 May TZ1 Question 1 – 18M.1.studies.TZ1.1

### Paper 1 – Question 2

Topic: Descriptive Statistics

Sub Topic 1: Mean, Median, Mode

Sub Topic 2: Standard Deviation & Interquartile Range

Difficulty: Medium

Marks: 6

Question 2 is an interesting question, surprisingly difficult for Paper 1, Question 2. It involves a thoroughly understanding of how to calculate the median of a set of unordered numbers, which then leads into Standard Deviation and Interquartile Range in later parts.

Part (a) asks to find an unknown number in a set of numbers, given the mean. This is a two step process; firstly to re-order the numbers in ascending order, followed by using an understanding of how the median is calculated to determine this. [2 marks]

Part (b) then asks to find the standard deviation and interquartile range for the set of numbers provided. These metrics can be found fairly easily using your graphics display calculator, it’s just important to know how to perform these functions. [4 marks]

2018 Mathematics Studies Paper 1 May TZ1 Question 2 – 18M.1.studies.TZ1.2

### Paper 1 – Question 3

Topic: Logic, Sets & Probability

Sub Topic: Logic

Difficulty: Medium

Marks: 6

Question 3 is a very common IB Maths Studies Past Paper question. It progresses through 3 parts of logic, in the following order:

Part (a) asks to write, in words, a compound proposition involving two statements provided, involving the logic terms negation & implication. [2 marks]

Part (b) asks to then complete three columns of a truth table, involving negation, conjunction and implication. A thorough understanding of how to complete truth tables is required here! [3 marks]

Part (c) concludes the question by asking if a compound proposition is a tautology, contradiction or neither. This simply requires looking at that particular compound propositions column in the truth table in Part (b) and assessing the values. Remember, tautology means all the values in that column are true, whereas contradiction is all false. [1 mark]

2018 Mathematics Studies Paper 1 May TZ1 Question 3 – 18M.1.studies.TZ1.3

### Paper 1 – Question 4

Topic: Statistical Application

Sub Topic: Two Variable Statistics

Difficulty: Easy

Marks: 6

Question 4 is a extremely common IB Maths Studies past paper question. It is very important to be able to master this question, there is no problem solving or tricky aspect to this one.

The question involves two variable statistics (often also called bivariate statistics).

Part (a) asks to determine the Pearson’s product-moment correlation coefficient, r, and the line of regression equation for a given data set. This requires an understanding of how to do this on your calculator, it’s fairly straight forward once understood. [4 marks]

Part (b) is a natural follow-on question from Part (a), asking to use the line of regression equation to make an estimate for a given independent variable value. This type of question is asked in perhaps every single IB Maths Studies Past Exam since 2014. [2 marks]

2018 Mathematics Studies Paper 1 May TZ1 Question 4 – 18M.1.studies.TZ1.4

### Paper 1 – Question 5

Topic: Geometry & Trigonometry

Sub Topic: Coordinate Geometry

Difficulty: Easy

Marks: 6

Question 5 is a fairly straight forward (and common) coordinate geometry question. These types of questions appear consistently in IB Maths Studies Past Papers.

Part (a) asks to find the midpoint between two coordinates provided in the question. [2 marks]

Part (b) asks to find the gradient between two coordinates. [2 marks]

Part (c) then asks to find the equation of a line between two points, providing your answer in standard form (ax+by+d=0). [2 marks].

2018 Mathematics Studies Paper 1 May TZ1 Question 5 – 18M.1.studies.TZ1.5

### Paper 1 – Question 6

Topic:Descriptive Statistics

Sub Topics: Grouped Data Tables

Sub Topics: Box & Whisker Plots

Difficulty: Medium

Marks: 6

Question 6 is an interesting and new type of question. Most of the marks are to do with a grouped data table, and requires a fairly thorough understanding of how these tables work. Not many of these types of questions have appears in past IB Maths Studies papers, however it is a good one to practice.

Part (a) starts nice and easy, asking to read the median off a box & whisker plot. [1 mark]

Part (b) asks to fill in the missing values of a grouped data table, reading off the box & whisker plot. This requires an understanding of how box & whisker plots splits up data into quartiles. [2 mark]

Part (c) asks to calculate the mean from the grouped data table. This requires an understanding of how to find mid-interval values and then how to calculate the mean from there. [3 marks]

2018 Mathematics Studies Paper 1 May TZ1 Question 6 – 18M.1.studies.TZ1.6

### Paper 1 – Question 7

Topic: Number & Algebra

Sub Topic: Sequences & Series

Difficulty: Medium

Marks: 6

Question 7 is a very common sequences & series question, and requires mastering, as they very often appear in IB Maths Studies exams. This particular question focuses on arithmetic sequences.

Part (a) requires finding the common difference (d) and first term, given the third and eighth term. [4 marks]

Part (b) then asks to find the sum of the first 12 terms, which can be found fairly easily using the sum of terms formula, provided in your formula book. [2 marks]

2018 Mathematics Studies Paper 1 May TZ1 Question 7 – 18M.1.studies.TZ1.7

### Paper 1 – Question 8

Topic: Geometry & Trigonometry

Sub Topic: Triangle Trigonometry

Difficulty: Easy

Marks: 6

Question 8 is a fairly straight-forward triangle trigonometry question. Triangle trig questions, requiring an understanding of how to apply either the sine or cosine rules, appear in pretty much every Paper 1 IB Maths Studies Past Paper.

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

Part (b) then asks to determine the size of an unknown angle on the diagram, which can found fairly easily using the sine rule. [3 marks]

Part (c) then asks to find the size of the angle of depression marked in Part (a). This requires an understanding of complementary angles. [2 marks]

2018 Mathematics Studies Paper 1 May TZ1 Question 8 – 18M.1.studies.TZ1.8

### Paper 1 – Question 9

Topic: Mathematical Models

Sub Topic: Exponential Models

Difficulty: Medium

Marks: 6

Question 9 involves an exponential model, which is the most common mathematical model asked in IB Maths Studies Past Papers. A exponential model representing the population of fruit flies is provided at the start of the question:

Part (a) has two parts, firstly asking to find the initial population of fruit flies, and secondly to find the population after 6 days. These values can be found by substituting in values into time, t. [4 marks]

Part (b) then asks to find how long it takes (i.e., find t) for the population to reach a certain level. This is very common sequence of questions, asking to find the independent and then dependent variables. It’s important to master this skill, and how to solve it using your calculator. [2 marks]

2018 Mathematics Studies Paper 1 May TZ1 Question 9 – 18M.1.studies.TZ1.9

### Paper 1 – Question 10

Topic: Logic, Sets & Probability

Sub Topic: Venn Diagrams

Difficulty: Medium

Marks: 6

Question 10 is all about Venn Diagrams. Venn Diagrams appear quite often in IB Maths Studies Past Papers, with a mixed spread between Paper 1 and Paper 2.

This question involves a 3 set venn diagram, with a set of information provided in the question.

Part (a) asks to complete the Venn Diagram for the given information. [3 marks]

Part (b) asks to find the value of an unknown value on the Venn Diagram, which can be found by adding up all the venn diagram values and then subtracting from the total number (provided in the question). [2 marks]

Part (c) is a set notation question, asking to find out find out the number for a given region on the Venn Diagram. [1 mark]

2018 Mathematics Studies Paper 1 May TZ1 Question 10 – 18M.1.studies.TZ1.10

### Paper 1 – Question 11

Topic: Number & Algebra

Sub Topic: Sequences & Series

Difficulty: Medium

Marks: 6

Interestingly, this Paper has two Sequences & Series questions in the one paper. Usually they appear split between Papers 1 and 2.

This question involves a decreasing geometric sequence and is fairly easy, so long as you can determine the common ratio, requiring an understanding of percentages.

Part (a) asks to find the last term on the sequence (the 51st term). This can be found fairly easily using the Term Value formula in the formula booklet. [3 marks]

Part (b) then asks to find the sum of all 51 terms, which can be found using the sum of terms formula. [3 marks]

2018 Mathematics Studies Paper 1 May TZ1 Question 11 – 18M.1.studies.TZ1.11

### Paper 1 – Question 12

Topic: Mathematical Models

Difficulty: Hard

Marks: 6

Question 12 involves a fairly challenging quadratic model question. A quadratic equation is provided with unknown coefficients of the x squared and x terms (a and b). The equation of the line of symmetry is also provided.

Part (a) asks to write an equation using the axis of symmetry, in terms of a and b. [1 mark]

Prior to Part (b), a coordinate that the quadratic passes through is provided. Part (b) then asks to find another equation in terms of a and b, using this coordinate. [1 mark]

Part (c) then asks to find the values of a and b using the two equations found in Parts (a) and (b). This is a simultaneous equations question now, which can be solved using your graphics display calculator, or by hand using the elimination or substitution method. [2 marks]

Part (d) finalises the question, asking to find one of the x intercepts of the quadratic. [2 marks]

2018 Mathematics Studies Paper 1 May TZ1 Question 12 – 18M.1.studies.TZ1.12

### Paper 1 – Question 13

Topic: Statistical Application

Sub Topic: Normal Distribution

Difficulty: Medium

Marks: 6

Question 13 is all about the Normal Distribution, which is a fairly common IB Maths Studies Past Paper theme.

Part (a) involves two different types of questions requiring use of the NormalCDF command on your calculator. [4 marks]

Part (b) then follows on from Part (a), asking to find the expected value for a probability found in Part (b). [2 marks]

2018 Mathematics Studies Paper 1 May TZ1 Question 13 – 18M.1.studies.TZ1.15

### Paper 1 – Question 14

Topic: Geometry & Trigonometry

Sub Topic: Geometry

Difficulty: Medium

Marks: 6

Question 14 is a difficult geometry question, which usually appears towards the end of either Paper 1 or Paper 2. The shape involved in the question is a cone that has it’s top part cut off.

Part (a) requires finding one of the dimensions on the diagram, which can be found using Pythagoras theorem. [2 marks]

Part (b) asks to find the curved surface area of the part of the cone that has been removed. This requires use of the cone curved surface area formula. [2 marks]

Part (c) asks to find the curved surface area of the remaining section of the cone. This is the challenging part of the question – realising that you need to find the total curved surface area, and then subtract away the top part you found in Part (b). [2 marks]

2018 Mathematics Studies Paper 1 May TZ1 Question 14 – 18M.1.studies.TZ1.14

### Paper 1 – Question 15

Topic: Mathematical Models

Difficulty: Hard

Marks: 6

Question 15 concludes Paper 1 with a difficult mathematical models question involving two different equations; a quartic (power of 4) and cubic (power of 3). The equations are provided, as well as sections of their graphs on a diagram.

Part (a) asks to find the range of the quartic. Recall, range is all the y-values for which the equation exists. [2 marks]

Part (b) asks to find the coordinates the points where the two equations intersect. This could be found in a few different ways, however the calculator is recommended. [2 marks]

Part c asks to determine the possible x values for which the quartic is greater than the cubic (ie., it’s graph is higher). [2 marks.

2018 Mathematics Studies Paper 1 May TZ1 Question 15 – 18M.1.studies.TZ1.15

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

### Paper 2 – Question 1

Topic: Geometry & Trigonometry

Sub Topics: Triangle Trigonometry

Sub Topics: Geometry

Difficulty: Medium

Marks: 18

Paper 2 starts with a with a fairly long Geometry & Trigonometry question, mainly focused on triangle trigonometry; sine & cosine rules, area of triangle, trig ratios, Pythagoras theorem, etc. Although it looks like a geometry question, there is actually minimal geometry involved. It is a heavily weighted question worth 18 marks, 20% of the total paper marks.

Part (a) asks to determine the area of a triangle, which is fairly straight forward with two adjacent sides and angle provided. This is a direct application of the area of a triangle rule provided in your formula booklet.

Part (b) is where the geometry comes into this question, asking to find the total volume of the shape in the diagram. This is a combination of two shapes; a rectangular prism and triangular prism.

Parts (c) and (d) are triangle trig questions, using both the sine rule and cosine rule. Fairly straight forward if these two formulas are understood.

Part (e) is an interesting question, asking to determine whether a particular point on a line is the midpoint of the line. One side of the line requires to be found and then compare against the total length to determine if it is the midpoint (note, it isn’t.)

Part (f) is a fairly long question, asking to find the total length of all the lines in the shape. This requires finding an unknown side length using the cosine rule, then adding this to all the other side lengths that were either provided or found in previous questions.

2018 Mathematics Studies Paper 2 May TZ1 Question 1 – 18M.2.studies.TZ1.1

### Paper 2 – Question 2

Topic: Descriptive Statistics

Sub Topics: Two Variable Statistics

Sub Topics: Probability

Difficulty: Hard

Marks: 16

Question 2 is a fairly difficult long question, starting with two variable statistics and then transitioning into probability. There are 8 parts to this question! Worth a total of 15 marks. As usual with two variable statistics questions in IB Maths Studies Past Papers, a situation is presented at the top of the question involving two variables: in this case, the distance traveled by planes and their subsequent arrival time (on time, slightly delayed or heavily delayed). The crux of the question is to determine whether the distance the plane travels influences arrival status.

Part (a) asks to state the alternative hypothesis. This is an unusual question for IB Maths Studies exams, usually the null hypothesis is asked.

Part (b) asks to determine the expected frequency of one of the cells in the table. Recall, to do this we multiply the row and column totals, and divide by the grand total.

Part (c) asks to calculate the number of degrees of freedom.

Part (d) asks to find the chi-squared statistic and associated p-value of the test. These two metrics are fairly easy to find on the calculator.

Prior to Part (e), the critical value of the test is provided, and the question then asks whether the null hypothesis would be rejected or not. To do this we compare the chi-squared values with the critical value. If the chi-squared value is greater than the critical value (which is the case in this question), the null hypothesis is rejected.

Part (f) is where this question turns into a probability. This part is a fairly straight forward, single event, probability question. Recall the probability formula; (number of successful outcomes)/(total number of outcomes)

Part (g) is a conditional probability question, however the conditional probability formula isn’t required as it can be determined from the table.

Part (h) is a difficult multi-stage probability question. It’s important to recall that the probabilities are multiplied, and to determine if the question is an example of with, or without, replacement.

2018 Mathematics Studies Paper 2 May TZ1 Question 2 – 18M.2.studies.TZ1.2

### Paper 2 – Question 3

Topic: Number & Algebra

Sub Topics: Compound Interest

Sub Topic: Currency Conversion

Difficulty: Medium

Marks: 11

Question 3 in Paper 2 is a fairly short question, involving compound interest and currency conversion. It’s presented as a pure compound interest question with two two investment options, however the second investment option is an other currency, and thus, requires conversion to compare with option 1. This question is worth 11 marks, 12% of the paper.

Part (a) is a fairly difficult compound interest question to start. Usually in IB Maths Studies Papers, the first question asks to determine either the future or present value of the investment, however this part asks to find the interest rate, which can be hard to solve algebraically. Watch the video worked solution to see how to find r using your graphics calculator.

Part (b) is a straight forward currency conversion question.

Part (c) is an easier compound interest question than part (a), this time asking for the future value of the investment. This is a direct application of the compound interest formula.

Part (d) is a challenging problem solving question, requiring a step of currency conversion and then comparison between the two investment options.

2018 Mathematics Studies Paper 2 May TZ1 Question 3 – 18M.2.studies.TZ1.3

### Paper 2 – Question 4

Topics: Mathematical Models

Topics: Differential Calculus

Difficulty: Hard

Marks: 14

Question 4 is a challenging question involving both mathematical model concepts and differential calculus. It is worth 14 marks, equating to 15% of the Paper marks. An equation is presented at the start, involving an unknown coefficient of the x squared term, and also a fraction with x on the denominator.

Part (a) asks to find the value of the unknown coefficient of the x squared term, after providing a coordinate the graph passes through. This requires substitution of the coordinate and solving for the unknown.

Part (b) asks to find the derivative of the function. This is one of the more difficult difficult differentiation questions in IB Maths Studies, due to the fraction with the x term on the denominator.

Part (c) asks to show that the minimum point of the graph of the equation is at a certain y value. This requires letting the derivative equal to zero, rearranging and solving for x, then substituting this x value back into the original equation. A difficult question!

Part (d) asks to find x intercepts of the original equation. This can be determined fairly easily by plotting the equation in your graphing section of your calculator and then using analysis tools to find the intercepts.

Part (e) asks to sketch the graph of the equation for a given domain and range. My advice here is to simply plot the equation in the graphing section of your calculator, set your window/zoom settings to match the domain and range, use analysis tools to identify the key points (intercepts, turning points), and then simply draw what is shown on your screen onto your exam paper.

2018 Mathematics Studies Paper 2 May TZ1 Question 4 – 18M.2.studies.TZ1.4

### Paper 2 – Question 5

Topic: Logic, Sets & Probability

Sub Topics: Probability

Difficulty: Medium

Marks: 15

Question 5 a long, 15 mark question all about probability. A sound understanding of tree diagrams is very important to achieving most of the marks on this one. A diagram is presented at the top of the question, involving a three stage event (multi-stage events in probability).

Part (a) starts with a straight forward, single-stage, probability question

Part (b) increases in difficulty with a multi-stage probability question, without replacement. Drawing a tree diagram is strongly advised on this one to ensure accuracy.

Part (c) asks to complete a incomplete tree diagram, which is fairly straight forward, remembering that the total probabilities coming out of each join is equal to one.

Part (d) involves two probability questions, reading off the completed tree diagram from part (d).

Part (e) introduces a total number of participants, and is an expected number question. These are very common in IB Maths Studies Past Papers. This requires multiplying the number of participants with the probability that the question is referring to.

2018 Mathematics Studies Paper 2 May TZ1 Question 5 – 18M.2.studies.TZ1.5

### Paper 2 – Question 6

Topic 1: Mathematical Models

Topic 2: Geometry & Trigonometry

Difficulty: Hard

Marks: 16

As usual, the final question in Paper 2 is a challenging one, for this paper focused on mathematical models and geometry.  A shape is presented at the start of the question, involving a cylinder and hemisphere (positioned on top of the cylinder). The total height of the shape and radius of the cylinder (which is also the radius of the hemisphere) are provided.

Part (a) asks to determine the height of the cylinder. Fairly straight forward if you can recognize that the height will be the total height subtract the radius of the hemisphere.

Part (b) asks to find the total volume of the shape, which involves finding the volume of the cylinder and hemisphere, then adding these together. The formula for the volume of a cylinder is provided in in the formula booklet. The formula for the volume of a sphere is also provided, and a hemisphere will just be half this this.

Prior to part (c), a new diagram is presented. This diagram is in the same shape is the previous, however this time the dimensions for total height and radius are replaced with the variables h and r. Part (c) asks to find an expression for the height of the cylinder, in terms of the radius. This is actually very similar to the straight forward part (a), just using h and r instead of the numbers.

Part (d) asks to find an expression for the total volume of the shape, in terms of the radius. This is a challenging question, asking to initially find the expression in terms of both r and h, then substituting the expression from part (c) to remove the h term. This type of mathematical model question is a common, challenging, end of Paper 2, IB Maths Studies Past Paper question.

Part (e) asks to find the value of the radius that maximizes the volume. The expression from part (d) can be graphed using your calculator and use the maximum analysis function to determine this.

Part (f) is an interesting question, asking to justify if the new shape (presented in part (c)), is more or less than 40% greater in volume than the original shape (in part (a)).

2018 Mathematics Studies Paper 2 May TZ1 Question 6 – 18M.2.studies.TZ1.6

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