National Course modification summary: Mathematics - SQA

National Course modification
summary: Mathematics
National 5, Higher and Advanced Higher
course assessment in session 2020–21

The Deputy First Minister has announced that National 5 exams will not take place in session
2020–21. SQA is working with stakeholders to develop an alternative certification model for
National 5 that is based on teacher and lecturer estimates.

At present, Higher and Advanced Higher exams are still planned for 2021 and this will remain
under review. We continue to work with stakeholders to put contingency plans in place to
respond to any changes in public health advice, or local or national lockdowns, that may
result in further changes to the 2021 exam diet — including changes to the timetable.

For up-to-date information on arrangements for National Courses in session 2020–21,
including timetable information and guidance on estimates, please visit our website at
www.sqa.org.uk/nq2021.

Modifications to assessment
Following our public consultation on proposed modifications to National 5 to Advanced
Higher course assessment, which closed on 24 August 2020, we are making changes to
course assessment for session 2020–21. The changes detailed on the following pages are
intended to support the delivery of learning and teaching, while maintaining the validity,
credibility and standard of the courses.

We have published a high-level report on the outcomes of the consultation, which is available
from www.sqa.org.uk/nq2021. This includes details of the modifications to National 5 course
assessment, which were planned prior to the 2021 National 5 exams being cancelled.

National 5 course assessment 2020–21
There will be no external assessment for National 5 courses in session 2020–21.
Candidates will not be required to sit exams and SQA will not assess coursework.
Instead, we are working with stakeholders to develop an alternative certification model for
National 5 that is based on teacher and lecturer estimates.

Centres need to gather evidence of candidates’ attainment and use this to determine
estimate grades and bands. We have published separate guidance on gathering evidence
and producing estimates and there is an SQA Academy course available to support teachers
and lecturers.

We are also developing subject-specific guidance for teachers and lecturers on gathering
evidence and producing estimates. This will include how the previously-intended National 5
modifications could be used to support with gathering evidence and producing estimates in
session 2020–21. This guidance will be published from the end of October.

Details of the modifications we had previously intended to make to National 5 course
assessment in session 2020–21 are included in our high-level report on the outcomes of the
consultation.

To view the high-level report, and to access the guidance on gathering evidence and
producing estimates, visit www.sqa.org.uk/nq2021.

Higher course assessment 2020–21
 Component                                     Marks            Duration
 Question paper 1 (non-calculator)             55 marks         1 hour and 15 minutes
 Question paper 2                              65 marks         1 hour and 30 minutes

To reduce the volume of learning and teaching required, the duration of both question papers
will be reduced and limited optionality will be introduced. The duration of question paper 1
will be reduced by 15 minutes and it will contain 15 marks fewer. The duration of question
paper 2 will be reduced by 15 minutes and it will contain 15 marks fewer.

Candidates will be assessed on either option A or option B as outlined below.

Option A

 Skills                          Explanation
 Modelling situations using       determining a recurrence relation from given information
 sequences                         and using it to calculate a required term
                                  finding and interpreting the limit of a sequence, where it
                                   exists
 Determining vector               determining the resultant of vector pathways in three
 connections                       dimensions
                                  working with collinearity
                                  determining the coordinates of an internal division point
                                   of a line
 Working with vectors             evaluating a scalar product given suitable information
                                   and determining the angle between two vectors
                                  applying properties of the scalar product
                                  using and finding unit vectors including i, j, k as a basis

Option B

 Skills                           Explanation
 Solving algebraic equations       solving logarithmic and exponential equations
                                   using the laws of logarithms and exponents
                                   solving equations of the following forms for a and b,
                                    given two pairs of corresponding values of x and y:
                                    log y = b log x + log a, y = axb and
                                      log y = x log b + log a, y = ab x
                                   using a straight-line graph to confirm relationships of the
                                    form y = ax , y = ab
                                                 b         x

                                   mathematically modelling situations involving the
                                    logarithmic or exponential function
 Identifying and sketching         sketching the inverse of a logarithmic or an exponential
 related functions                  function
 Applying algebraic skills to      determining and using the equation of a circle
 circles and graphs                using properties of tangency in the solution of a problem
                                   determining the intersection of circles or a line and a
                                    circle

Question paper 1 (non-calculator)
11 marks out of 55 will be available for each optional section.

Question paper 2
13 marks out of 65 will be available for each optional section.

Questions will be selected to ensure that whichever option a candidate chooses, the balance
of the question paper overall will remain at 65% level C and 35% level A.

Advanced Higher course assessment 2020–21
 Component                                       Marks             Duration
 Question paper 1 (non-calculator)               35 marks          1 hour
 Question paper 2                                60 marks          2 hours

To reduce the volume of learning and teaching required, the duration of question paper 2 will
be reduced and limited optionality will be introduced. The duration of question paper 2 will be
reduced by 30 minutes and it will contain 20 marks fewer. There will be no changes to the
duration or mark allocation of question paper 1.

Candidates will be assessed on either option A or option B as outlined below.

Option A

Skills                           Explanation
Finding the general term and      applying the rules of sequences and series to find:
summing arithmetic and              — the nth term
geometric progressions
                                    — the sum to n terms
                                    — common difference of arithmetic sequences
                                    — common ratio of geometric sequences
                                  determining the sum to infinity of geometric series
                                  determining the condition for a geometric series to
                                   converge
Applying summation formulae       knowing and using sums of certain series, and other
                                   straightforward results and combinations of these
Using the Maclaurin               using the Maclaurin expansion to find a power series for
expansion to find specified        simple functions
terms of the power series for     combining Maclaurin expansions to find a power series
simple functions
Disproving a conjecture by        disproving a conjecture by providing a counterexample
providing a counterexample        knowing and using the symbols  (there exists) and
                                    (for all)
                                  giving the negation of a statement
Using indirect or direct proof    proving a statement by contradiction
in straightforward examples       using proof by contrapositive
                                  using direct proof in straightforward examples
Using proof by induction          using proof by induction

Option B

Skills                           Explanation
Calculating a vector product      using a vector product method in three dimensions
                                  evaluating the scalar triple product a. ( b  c )
Working with lines in three       finding the equation of a line in parametric, symmetric,
dimensions                         or vector form, given suitable defining information
                                  finding the angle between two lines in three dimensions
                                  determining whether or not two lines intersect and,
                                   where possible, finding the point of intersection
Working with planes               finding the equation of a plane in vector, parametric, or
                                   Cartesian form
                                  finding the point of intersection of a plane with a line that
                                   is not parallel to the plane
                                  determining the intersection of two or three planes
                                  finding the angle between a line and a plane, or between
                                   two planes

Skills                           Explanation
 Performing geometric              plotting complex numbers in the complex plane (an
 operations on complex              Argand diagram)
 numbers                           knowing the definition of modulus and argument of a
                                    complex number
                                   converting a given complex number from Cartesian to
                                    polar form and vice-versa
                                   using de Moivre’s theorem with integer and fractional
                                    indices
                                   applying de Moivre’s theorem to multiple angle
                                    trigonometric formulae
                                   applying de Moivre’s theorem to find the nth roots of a
                                    complex number
                                   interpreting geometrically certain equations or
                                    inequalities in the complex plane by sketching or
                                    describing a straight line or circle that represents the
                                    locus of points that satisfy a given equation or inequality

Question paper 1 (non-calculator)
There is no change to this component. Given the duration and mark allocation of the
non-calculator paper, there is no scope for optionality.

Question paper 2
15 marks out of 60 will be available for each optional section.

Questions will be selected to ensure that whichever option a candidate chooses, the balance
of the question paper overall will remain at 65% level C and 35% level A.

If you have any questions about these changes, please email NQ2020@sqa.org.uk.