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# 2018 November Maths SL – Paper 1

### Paper 1 – Question 1

Topic: Trigonometry

Difficulty: Easy

Marks: 6

Question 1 (6 marks) in the 2018 November Maths SL Paper 1 Exam is a basic Trigonometry Questions where the shaded region of a circle sector is shown. The radius and the angle of the sector is given.

This is a standard Question 1 when comparing to other IB Math SL Past Papers.

## 2018 Mathematics SL Paper 1 November TZ0 Question 1 – 18N.1.sl.TZ0.1 – N18/5/MATME/SP1/ENG/TZ0/XX

### Paper 1 – Question 2

Topic: Functions

Difficulty: Medium

Marks: 5

Question 2 (6 marks) in the 2018 November Maths SL Paper 1 Exam is a Functions Question that shows you a table of values with respect to functions f(x) and g(x).

Part (a) asks to write down the value of f(1)

Part (b) asks to find f(g(1)).

Part (c) asks to find the inverse of g(x) when x=-2.

This question is similar in difficulty when comparing to other IB Math SL Past Paper Questions 2-5.

## 2018 Mathematics SL Paper 1 November TZ0 Question 2 – 18N.1.sl.TZ0.2 – N18/5/MATME/SP1/ENG/TZ0/XX

### Paper 1 – Question 3

Topic: Sequences & Series

Difficulty: Easy

Marks: 6

Question 3 (6 marks) in the 2018 November Maths SL Paper 1 Exam is a Sequences & Series Question where an arithmetic sequence is defined with the first term and common difference given.

Part (a) asks to find the eighth term in the sequence.

Part (b) asks to find the value of n for which un=67.

This question is slightly easier in difficulty when comparing to other IB Math SL Past Paper Questions 2-4.

## 2018 Mathematics SL Paper 1 November TZ0 Question 3 – 18N.1.sl.TZ0.3 – N18/5/MATME/SP1/ENG/TZ0/XX

### Paper 1 – Question 4

Topic: Logs

Difficulty: Medium

Marks: 6

Question 4 (6 marks) in the 2018 November Maths SL Paper 1 Exam is a Logs Question where b=log2(a) and you are asked to write the following expression in terms of b.

Part (a), log2(a)^3

Part (b), Log2(8a)

Part (c), Log8(a)

This question is a tricky question that requires knowledge of your log laws. It is similar in difficulty when comparing to other IB Math SL Past Paper Questions 3-5.

## 2018 Mathematics SL Paper 1 November TZ0 Question 4 – 18N.1.sl.TZ0.4 – N18/5/MATME/SP1/ENG/TZ0/XX

### Paper 1 – Question 5

Topic: Vectors

Difficulty: Medium

Marks: 6

Question 5 (6 marks) in the 2018 November Maths SL Paper 1 Exam is a Vector Question where vectors a and b are defined (containing the variable p). The question then asks to find the possible values of p for which the vectors a and b are parallel.

This is a challenging question and hasn’t been seen before in an IB Math SL Exam. This question is slightly more difficult when comparing to other IB Math SL Past Paper Questions 4-6.

## 2018 Mathematics SL Paper 1 November TZ0 Question 5 – 18N.1.sl.TZ0.5 – N18/5/MATME/SP1/ENG/TZ0/XX

### Paper 1 – Question 6

Topic: Calculus

Difficulty: Hard

Marks: 8

Question 6 (8 marks) in the 2018 November Maths SL Paper 1 Exam is an Integration Question where a function f(x) is given. The sketch of the function is also given and the area enclosed by the function and the x/y axis is shaded. The question then asks students to calculate the area of the shaded region. Integartion by substitution is needed for the question.

This is a standard question when comparing to other IB Math SL Past Paper Questions 6-7.

## 2018 Mathematics SL Paper 1 November TZ0 Question 6 – 18N.1.sl.TZ0.6 – N18/5/MATME/SP1/ENG/TZ0/XX

### Paper 1 – Question 7

Topic: Trig (Circular Functions)

Difficulty: Hard

Marks: 6

Question 7 (6 marks) in the 2018 November Maths SL Paper 1 Exam is a Trig (Circular Functions) Question where it is given that sin(x)=1/3.  The question asks students to find the value of cos(4x). Multiple trigonometric identites are needed.

This is a difficult question when comparing to other IB Math SL Past Paper Questions 6-7.

## 2018 Mathematics SL Paper 1 November TZ0 Question 7 – 18N.1.sl.TZ0.7 – N18/5/MATME/SP1/ENG/TZ0/XX

### Paper 1 – Question 8

Difficulty: Medium

Marks: 16

Question 8 (16 marks) in the 2018 November Maths SL Paper 1 Exam is a Functions (Quadratics) Question. A function f(x) is given.

Part (a) asks to find the x-intercepts of the graph of f.

Part (b) asks to find the equation of the axis of symmetry of f.

Part (c) asks to find the values of h and k when the function is converted to the vertext form of a quadratic.

Part (d) is a transformations question where the function undegoes a reflection followed by a tranlsation.

This is a very common Question 8-9 when comparing to other IB Math SL Past Papers.

## 2018 Mathematics SL Paper 1 November TZ0 Question 8 – 18N.1.sl.TZ0.8 – N18/5/MATME/SP1/ENG/TZ0/XX

### Paper 1 – Question 9

Topic: Probability

Difficulty: Hard

Marks: 15

Question 9 (15 marks) in the 2018 November Maths SL Paper 1 Exam is a Probability Question involving a bag containing n marbles, 2 of which are blue. Haylye is playing a game which ends when she draws a blue marble.

Part (a) asks to find the probability (in terms of n) that the game will end on her (i) first draw. (ii) second draw.

now n=5. Part (b) asks to find the probability the game will end on her (i) third draw. (ii) fourth draw.

Part (c) introduces a probability distribution table where money is earned depending on how many draws it takes for the game to end. The question asks to find the value of k (unknown variabe) such that the game is fair.

This is a challenging but common Question 8-9 when comparing to other IB Math SL Past Papers.

## 2018 Mathematics SL Paper 1 November TZ0 Question 9 – 18N.1.sl.TZ0.9 – N18/5/MATME/SP1/ENG/TZ0/XX

### Paper 1 – Question 10

Topic: Calculus & Functions

Difficulty: Very Hard

Marks: 16

Question 10 (16 marks) in the 2018 November Maths SL Paper 1 Exam is a Calculus Question. A function f(x) is given.

Part (a) asks to find the y-intercept of the function (Point P).

Part (b) asks to find the first derivative of f(x) and then to find the equation of the tangent at point P.

Part (c) asks to find the value of ‘a’ (unknown variable) using information given about the function (diagram given, watch video solution for more details).

This is a very challenging when compared to other IB Math SL Past Paper Questions 8-10.

# 2018 November Maths SL – Paper 2

### Paper 2 – Question 1

Topic 1: Probability

Difficulty: Easy

Marks: 6

Question 1 (6 marks) in the 2018 November Maths SL Paper 2 Exam is a Probability Question where infomation about students in a class taking Art and Music is given on a Venn diagram.

Part (a) asks to write down the number of students who take Art.

Part (b) asks to find the probability that (i) a student does not take Art. (ii) a student takes either Art or Music, but not both.

This is a standard Question 1 when comparing to other IB Math SL Past Papers.

## 2018 Mathematics SL Paper 2 November TZ0 Question 1 – 18N.2.sl.TZ0.1 – N18/5/MATME/SP2/ENG/TZ0/XX

### Paper 2 – Question 2

Topic: Bivariate Statistics

Difficulty: Easy

Marks: 6

Question 2 (6 marks) in the 2018 November Maths SL Paper 2 Exam is a Bivariate Statistics Question where the relationship of hand length and height is given in a table.

Part (a) asks to find the values of a and b from the regression line y=ax+b. Calculator is needed. (ii) asks to write down the correlation coefficicent.

Part (b) asks to estimate the height of an athlete who has a hand length of 21.5cm. The regression line equation from part (a) is needed.

This is a very common Question 1-3 when comparing to other IB Math SL Past Papers.

## 2018 Mathematics SL Paper 2 November TZ0 Question 2 – 18N.2.sl.TZ0.2 – N18/5/MATME/SP2/ENG/TZ0/XX

### Paper 2 – Question 3

Topic: Rational Functions

Difficulty: Medium

Marks: 7

Question 3 (7 marks) in the 2018 November Maths SL Paper 2 Exam is a Rational Functions Question. A function f(x) is given.

Part (a) asks to find the (i) y-intercept. (ii) Vertical asymptote. (iii) Horizontal asymptote.

Part (b) asks to ‘hence’ find the limit of the function f(x) as x approaches infinity.

This is a standard Question 3-5 when comparing to other IB Math SL Past Papers.

## 2018 Mathematics SL Paper 2 November TZ0 Question 3 – 18N.2.sl.TZ0.3 – N18/5/MATME/SP2/ENG/TZ0/XX

### Paper 2 – Question 4

Topic: Kinematics

Difficulty: Medium

Marks: 7

Question 4 (7 marks) in the 2018 November Maths SL Paper 2 Exam is a Kinematics Question. A particle is moving along a straight line and the velocity function is given.

Part (a) asks to find when the particle is at rest.

Part (b) asks to find the acceleration of the particle when t=2.

Part (c) asks to find the total distance travelled by the particle in the first 5 seconds.

This is a standard Question 3-5 when comparing to other IB Math SL Past Papers.

## 2018 Mathematics SL Paper 2 November TZ0 Question 4 – 18N.2.sl.TZ0.4 – N18/5/MATME/SP2/ENG/TZ0/XX

### Paper 2 – Question 5

Topic: Sequences & Series

Difficulty: Medium

Marks: 6

Question 5 (6 marks) in the 2018 November Maths SL Paper 2 Exam is a Sequences & Series Question where the sum of the infinite geometric sequence and the second term on the sequence are given. The question asks students to find the possible values of r (common ratio).

This is a standard Question 4-7 when comparing to other IB Math SL Past Papers.

## 2018 Mathematics SL Paper 2 November TZ0 Question 5 – 18N.2.sl.TZ0.5 – N18/5/MATME/SP2/ENG/TZ0/XX

### Paper 2 – Question 6

Topic: Binomial Expansion

Difficulty: Hard

Marks: 7

Question 6 (7 marks) in the 2018 November Maths SL Paper 2 Exam is a Binomial Expansion Question. It is given that the coefficient of the x^40 term is fives times the coefficient of the x^38 term. The question ask students to find k (the unknown variable).

This is a standard Question 6-7 when comparing to other IB Math SL Past Papers.

## 2018 Mathematics SL Paper 2 November TZ0 Question 6 – 18N.2.sl.TZ0.6 – N18/5/MATME/SP2/ENG/TZ0/XX

### Paper 2 – Question 7

Topic: Trigonometry

Difficulty: Hard

Marks: 6

Question 7 (6 marks) in the 2018 November Maths SL Paper 2 Exam is a Trigonometry Question. A diagram is given showing the location of a communication tower, T, and a road that runs through the tower signal range (circular).

Part (a) asks students to use the cosine rule to show a given equation (see video solution for more details).

Part (b) asks to find the total distance along the road where the signal from the tower can reach cellular phones.

This is a standard Question 6-7 when comparing to other IB Math SL Past Papers.

## 2018 Mathematics SL Paper 2 November TZ0 Question 7 – 18N.2.sl.TZ0.7 – N18/5/MATME/SP2/ENG/TZ0/XX

### Paper 2 – Question 8

Topic: Vectors

Difficulty: Medium / Hard

Marks: 16

Question 8 (16 marks) in the 2018 November Maths SL Paper 2 Exam is a Vectors Question. Two points, A and B, are given.

Part (a) asks to find the vector AB (ii) find the magnitude of the vector AB.

Part (b) introduces a line with a vector equation and tells students that a point C lies on the line. (i) find the value of y (unknown variable from point C). (ii) Find the vector AC.

Part (c) asks to find the angle between AB and AC.

Part (d) asks to find the area of the triangle ABC.

This is a standard Question 8-9 when comparing to other IB Math SL Past Papers.

## 2018 Mathematics SL Paper 2 November TZ0 Question 8 – 18N.2.sl.TZ0.8 – N18/5/MATME/SP2/ENG/TZ0/XX

### Paper 2 – Question 9

Topic: Probability (Normal/Binomial Distribution)

Difficulty: Hard

Marks: 15

Question 9 (15 marks) in the 2018 November Maths SL Paper 2 Exam is a Probability Question. A study has been conducted on the reaction time of participants from 2 different age groups, Group X (less than 40yrs old) and Group Y (40 yrs and older). The reaction times for Groups X and Y are normally distributed.

Part (a) asks to find the probability a participant from Group X has a reaction time greater than 0.65sec.

Part (b) gives you some information about Group Y and asks students to find the standard deviation of participants in Group Y.

Part (c) is a conditional probability question (see video solution for more details).

Part (d) is a Binomial Distribution question that leads on from parts (a)-(c). (see video solution for more details).

This is a standard Question 8-9 when comparing to other IB Math SL Past Papers.

## 2018 Mathematics SL Paper 2 November TZ0 Question 9 – 18N.2.sl.TZ0.9 – N18/5/MATME/SP2/ENG/TZ0/XX

### Paper 2 – Question 10

Topic: Calculus & Trigonometry

Difficulty: Hard

Marks: 14

Question 10 (14 marks) in the 2018 November Maths SL Paper 2 Exam is a Calculus & Trigonometry Question. A function f(x) is given.

Part (a) asks to find the volume of the solid formed when the area (seen in the diagram) is rotated 360deg around the x-axis.

The function f(x) represents the shape of a container and the rate of change of the volume of water in the container is given as g'(x).

Part (b) asks to find the period of time when the volume of the water in the container is increasing. (ii) asks to find the increase in volume during this period.

Part (c) asks to find the minimum volume of empty space in the container during the 4h period.

This is a challenging question and similar in difficulty when comparing to other IB Math SL Past Paper Questions 9-10.