IB Maths Past Paper Overviews

 

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2018 May Time Zone 2 Maths SL – Paper 1

 

Paper 2 (Click here to scroll down)

Paper 1 – Question 1

Topic: Vectors

Difficulty: Medium

Marks: 5

Link to Video Solution

Question 1 (5 marks) in the 2018 May TZ2 Maths SL Paper 1 Exam is a basic vectors question where two vectors are given.

Part (a) asks to find the vector equation of a line that passes through two points.

Part (b) introduces a second vector which is perpendicular to our line. It asks you to solve for an unknown variable by using the scalar product.

2018 Mathematics SL Paper 1 May TZ2 Question 1 – 18M.1.sl.TZ2.1

Paper 1 – Question 2

Topic: Calculus

Difficulty: Easy

Marks: 6

Link to Video Solution

Question 2 (6 marks) in the 2018 May TZ2 Maths SL Paper 1 Exam shows a quadratic function with a diagram (function given).

Part (a) asks to find the indefinite integral of the function.

Part (b) asks to find the area under the quadratic function with given limits. This is a simple definite integral of the original function.

2018 Mathematics SL Paper 1 May TZ2 Question 2 – 18M.1.sl.TZ2.2

Paper 1 – Question 3

Topic: Statistics

Difficulty: Medium

Marks: 6

Link to Video Solution

Question 3 (6 marks) in the 2018 May TZ2 Maths SL Paper 1 Exam is a common IB Descriptive Statistics question. Information about a data set is provided.

Part (a) asks to find the number of items in the original data set.

Part (b) asks to find the new mean and variance after the original data set is changed. This type of question appears frequency in IB Mathematics SL Past Papers and should be practised by IB students.

2018 Mathematics SL Paper 1 May TZ2 Question 3 – 18M.1.sl.TZ2.3

Paper 1 – Question 4

Topic: Trigonometry

Difficulty: Medium

Marks: 7

Link to Video Solution

Question 4 (7 marks) in the 2018 May TZ2 Maths SL Paper 1 Exam is a very common IB Maths SL Exam Question (Trigonometry) where a circle sector diagram is provide with a shaded sector.

Information about the shaded sector is given (area and arc length given) and the question asks to find the radius of the sector. A very frequent IB Maths SL Past Paper Question and one to practice by students.

2018 Mathematics SL Paper 1 May TZ2 Question 4 – 18M.1.sl.TZ2.4

Paper 1 – Question 5

Topic: Functions

Difficulty: Medium

Marks: 6

Link to Video Solution

Question 5 (6 marks) in the 2018 May TZ2 Maths SL Paper 1 Exam is a functions question with a given diagram.

Part (a) asks to sketch the reflection of the function in the y-axis.

Part (b) is a difficult transformations question (4 marks) where a transformed function is given and you have to write down the transformations that have taken place. This type of question is typically seen in 20% – 30% of IB Maths SL Paper 1 Exams.

2018 Mathematics SL Paper 1 May TZ2 Question 5 – 18M.1.sl.TZ2.5

Paper 1 – Question 6

Topic: Quadratics

Difficulty: Hard

Marks: 7

Link to Video Solution

Question 6 (7 marks) in the 2018 May TZ2 Maths SL Paper 1 Exam is a tricky Quadratics problem involving the number of roots for the equations when it is made equal to zero. The question is short and the solution can be obtained with only a few steps however a deep understanding of functions and the discriminant test is needed. Discriminant test questions are very common towards the end of Section A Paper 1 Exams so students should practice lots of IB Maths SL Paper Paper Questions (Q5-Q7) to get a feel for the layout of these tricky questions.

2018 Mathematics SL Paper 1 May TZ2 Question 6 – 18M.1.sl.TZ2.6

Paper 1 – Question 7

Topic: Logs / Sequences & Series

Difficulty: Hard

Marks: 8

Link to Video Solution

Question 7 (8 marks) in the 2018 May TZ2 Maths SL Paper 1 Exam is a Sequences & Series question that involves logs.

Part (a) asks you to find the common difference, d, in terms of the logarithms provided in the question.

Part (b) is a sigma notation question where the arithmetic series formula is needed.

When comparing to other IB Maths SL Past Papers, this question is a similar level of difficulty to other Question 7’s. You must know your log laws and how to find the value of an arithmetic series sum using sigma notation (see video for more details).

2018 Mathematics SL Paper 1 May TZ2 Question 7 – 18M.1.sl.TZ2.7

Paper 1 – Question 8

Topic: Probability

Difficulty: Medium

Marks: 14

Link to Video Solution

Question 8 (14 marks) in the 2018 May TZ2 Maths SL Paper 1 Exam is a Probability question with a tree diagram. Information is provided and half of the tree diagram is completed.

Part (a) asks to complete the tree diagram.

Part (b) asks to find the probability of an outcome where you simply need to multiply branches of the tree.

Part (c) asks to find the probability of an outcome where you need to add the multiplication of multiple branches. Not too difficult and a common IB Maths SL Past Paper Question.

Part (d) is a conditional probability question. Once again, not too difficult and a common IB Maths SL Past Paper Question.

Part (e) is a tricky 3 mark question where it asks to find the probability of an outcome occurring ‘at least once’ out of two days. The complement probability is needed to find the answer (see video for more details).

This is a fairly common Question 8 / Question 9 when comparing to other IB Mathematics Standard Level Paper 1 Exams. This is an opportunity for a student to start Section B with 14/14 marks.

2018 Mathematics SL Paper 1 May TZ2 Question 8 – 18M.1.sl.TZ2.8

Paper 1 – Question 9

Topic: Calculus

Difficulty: Hard

Marks: 15

Link to Video Solution

Question 9 (15 marks) in the 2018 May TZ2 Maths SL Paper 1 Exam is Calculus & Optimisation Question involving a cylindrical can with known and unknown dimensions.

Part (a) asks to express the height of the can in terms of the radius.

Part (b) asks find the cost equation (surface area) for the materials needed to make the can.

Part (c) asks to find the minimum cost (optimisation) for the materials needed to make the can.

This question is a very common IB Maths SL Optimisation question. If students have practised Optimisation Questions in IB Maths SL Past Papers, they shouldn’t find this too difficult.

2018 Mathematics SL Paper 1 May TZ2 Question 9 – 18M.1.sl.TZ2.9

Paper 1 – Question 10

Topic: Calculus & Functions

Difficulty: Very Hard

Marks: 16

Link to Video Solution

Question 10 (16 marks) in the 2018 May TZ2 Maths SL Paper 1 Exam is a very challenging Calculus question to finish. Up to this point, Section B has been kind to students and this question will separate IB students. An unknown function is defined and a tangent equation is given at a known point.

Part (a) asks you to write down the value of the gradient at the known point using the tangent equation and it also asks for the y value at the known point. These 4 marks aren’t too difficult to get.

Part (b) introduces a new function (g(x) which is a transformation of the original function f(x). A different point is given on g(x) but is related to the given point in part (a). Part (b) then asks the gradient of g(x) at the given point. Many students will make mistakes here and lose marks as you firstly need to use the correct deriving laws to find g'(x) (see video for details).

Part (c) introduces and new tangent line (tangent to g(x)). The two tangent lines in the question intersect at an unknown point and the question asks to find the y coordinate of this intersection point.

This question is difficult and slightly more challenging than the typical Section B IB Maths SL Question. Watch the video solution twice to fully grasp part (b) as you need it for part (c). Only students aiming for a 6 or a 7 will get 12+ out of 16 for this question.

2018 Mathematics SL Paper 1 May TZ2 Question 10 – 18M.1.sl.TZ2.10

2018 May Time Zone 2 Maths SL – Paper 2

 

Paper 2 – Question 1

Topic 1: Bivariate Statistics

Difficulty: Easy

Marks: 6

Link to Video Solution

Question 1 (6 marks) in the 2018 May TZ2 Maths SL Paper 2 Exam is a simple Bivariate Statistics question where a table of values is provided.

Part (a) asks you to find the regression line equation as well as the correlation coefficient.

Part (b) asks you to estimate a ‘y’ value using your regression line equation found in part (a).

This is a very common IB Maths SL Exam Question and appears in 60% – 80% of IB Maths SL Past Papers (Paper 2).

2018 Mathematics SL Paper 2 May TZ2 Question 1 – 18M.2.sl.TZ2.1

Paper 2 – Question 2

Topic: Trigonometry

Difficulty: Easy

Marks: 6

Link to Video Solution

Question 2 (6 marks) in the 2018 May TZ2 Maths SL Paper 2 Exam is a triangle trigonometry question. A diagram of two connected triangles is shown.

Part (a) asks you to find a side length (use sine rule).

Part (b) asks you to find another side length (use cosine rule).

This is a common IB Maths SL Exam Question and appears in 25% – 30% of IB Maths SL Past Papers (Paper 2).

2018 Mathematics SL Paper 2 May TZ2 Question 2 – 18M.2.sl.TZ2.2

Paper 2 – Question 3

Topic: Functions & Calculus

Difficulty: Medium

Marks: 5

Link to Video Solution

Question 3 (5 marks) in the 2018 May TZ2 Maths SL Paper 2 Exam is Functions and Calculus question where a function and a sketch is given.

Part (a) asks you to find the x-intercept of the function (use GDC).

Part (b) says that the region enclosed by the function and the x-axis is rotated around the x-axis. The question then asks to find the volume of the solid formed.

This is a common IB Mathematics Standard Level Exam Question and appears in 20% – 25% of IB Maths SL Past Papers (Paper 1 or Paper 2).

2018 Mathematics SL Paper 2 May TZ2 Question 3 – 18M.2.sl.TZ2.3

Paper 2 – Question 4

Topic: Sequences & Series

Difficulty: Medium

Marks: 7

Link to Video Solution

Question 4 (7 marks) in the 2018 May TZ2 Maths SL Paper 2 Exam is Geometric Sequences & Series question. The first term and the infinite sum are given.

Part (a) asks you to find the common ration, r.

Part (b) asks you to find the sum of the first 8 terms in the sequence.

Part (c) is quite challenging where it asks you to find the the least value of terms such that the sum exceeds a certain value. You will need your GDC to solve this.

This is a common IB Mathematics Standard Level Exam Question and appears in 15% – 25% of IB Maths SL Past Papers (mostly Paper 2). You will need calculator skills to solve part (c).

2018 Mathematics SL Paper 2 May TZ2 Question 4 – 18M.2.sl.TZ2.4

Paper 2 – Question 5

Topic: Binomial Expansion

Difficulty: Hard

Marks: 6

Link to Video Solution

Question 5 (6 marks) in the 2018 May TZ2 Maths SL Paper 2 Exam is Binomial Expansion question. The expansion is given with an unknown coefficient ‘k’. The question says that the coefficient of two of the terms (x^3 and x^5) are equal and you have to find k.

This questions is a difficult IB Mathematics Standard Level Exam Question. Similar questions appears in 40% – 70% of IB Maths SL Past Papers (mostly Paper 2) however this question is slightly different in that you have to pair up two terms in order to solve for the unknown ‘k’. Quite challenging for a Question 5.

2018 Mathematics SL Paper 2 May TZ2 Question 5 – 18M.2.sl.TZ2.5

Paper 2 – Question 6

Topic: Circular Functions

Difficulty: Hard

Marks: 8

Link to Video Solution

Question 6 (8 marks) in the 2018 May TZ2 Maths SL Paper 2 Exam is Circular Functions Ferris wheel question. The diameter of the Ferris wheel is given and the rotation time is also given.

Part (a) asks you to find the initial height of the Ferris wheel, ‘k’.

Part (b) asks you to complete the trigonometric function by finding the amplitude.

Part (c) asks you to find the third time when the seat will reach a certain height. You will need to graph the curve and solve.

This question is a fairly common IB Mathematics Standard Level Exam Question. Circular function question like this appear in 30% – 40% of IB Maths SL Past Papers (mostly Paper 2). Calculator skills required.

2018 Mathematics SL Paper 2 May TZ2 Question 6 – 18M.2.sl.TZ2.6

Paper 2 – Question 7

Topic: Rational Functions

Difficulty: Hard

Marks: 7

Link to Video Solution

Question 7 (7 marks) in the 2018 May TZ2 Maths SL Paper 2 Exam is a Rational Functions question. A function is given with an unknown coefficient.

Part (a) gives you the equation of the vertical asymptote and asks you to solve for the unknown coefficient,

Part (b) asks you to find the horizontal asymptote.

Part (c) is very challenging. The question asks when the modulus of the function will intersect with the line y=k at exactly one point, and to find the possible values of k (see video for more details). These 3 marks will be very difficult to get and will separate grade boundaries.

This question is a commonly seen IB Mathematics Standard Level Exam Question with an added twist (part c). Calculator skills are required and a deep understanding of functions is needed to get part (c). Part (c) doesn’t appear many times when going though IB Maths SL Past Papers.

2018 Mathematics SL Paper 2 May TZ2 Question 7 – 18M.2.sl.TZ2.7

Paper 2 – Question 8

Topic: Vectors

Difficulty: Medium / Hard

Marks: 13

Link to Video Solution

Question 8 (13 marks) in the 2018 May TZ2 Maths SL Paper 2 Exam is Vectors question where two points are given.

Part (a) asks you to find the vector connecting the two given points and to also find the magnitude of this vector.

Part (b) asks you to find the angle between the vector in part (a) and a new vector provided. Scalar product needed.

Part (c) asks to find the area of the triangle formed.

Part (d) asks to find the shortest distance from a point to our vector.

This is a common IB Mathematics Standard Level Exam Question and appears in 40% – 50% of IB Maths SL Past Papers (mostly Paper 2). Part (d) is quite challenging (see video for more details).

2018 Mathematics SL Paper 2 May TZ2 Question 8 – 18M.2.sl.TZ2.8

Paper 2 – Question 9

Topic: Kinematics

Difficulty: Hard

Marks: 15

Link to Video Solution

Question 9 (15 marks) in the 2018 May TZ2 Maths SL Paper 2 Exam is Kinematics (Calculus) question where the velocity function of a particle is given. A sketch is also provided.

Part (a) asks you to find the initial velocity.

Part (b) asks you to find the maximum speed (don’t be tricked into finding the maximum velocity… see video for details)

Part (c) asks to find the number of times the acceleration is zero.

Part (d) asks to find the acceleration when the particle changes direction.

Part (e) asks to find the total distance travelled by the particle.

This is a very common IB Mathematics Standard Level Exam Question and appears in 50% – 60% of IB Maths SL Past Papers (mostly Paper 2). Section B Kinematics questions like this can be the difference between achieving a 5 and a 6/7. Practice, practice, practice!

2018 Mathematics SL Paper 2 May TZ2 Question 9 – 18M.2.sl.TZ2.9

Paper 2 – Question 10

Topic: Probability (Distributions)

Difficulty: Hard

Marks: 17

Link to Video Solution

Question 10 (17 marks) in the 2018 May TZ2 Maths SL Paper 2 Exam is Probability question which involves Normal Distribution & Binomial Distribution. A probability distribution table is given.

Part (a) asks you to find an unknown value in the table and to find the mean of the data.

Part (b) is a normal distribution question where it asks to find the probability of our random variable (apples) weighing less than a given weight. This is straight forward on the GDC (see video).

Part (c) & Part (d) are Binomial Distribution questions that get progressively more challenging. Calculator skills are required.

This is a common IB Mathematics Standard Level Exam Question (Section B) and appears in 40% – 50% of IB Maths SL Past Papers (mostly Paper 2). Students might struggle getting started as part (a) is a little bit tricky. Parts (c) & (d) are quite challenging but top students will hopefully get 17/17 for this question.

2018 Mathematics SL Paper 2 May TZ2 Question 10 – 18M.2.sl.TZ2.10

IB Maths Past Paper Overviews

 

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