The mathematics combined placement test for MA1200 (Calculus and Basic Linear Algebra I) and MA1201 (Calculus and Basic Linear Algebra II) aims to help academic units under College of Science manage the consistency of the basic knowledge in mathematics of their students of cohort 2021 and hence contribute in effective teaching and student learning. The test is designed to allow students to demonstrate their abilities and skills in the basic mathematics requirement at university level. It is optional and plays no role in admission.

If a student does not pass the combined test, he or she is advised to enroll in MA1200 and MA1201.

Prospective students of Advanced Standing I/II admitted in 2021 meeting the following requirements can register to take the test subject to a recommendation from the student's Programme/Major Leader or Admission Officer:

- without HKALE A-Level Applied Mathematics or Pure Mathematics, but with grade C or above in HKALE AS-Level Mathematics and Statistics, or equivalent

Students who have taken exams of MA1006, MA1200, MA1201, MA1300, MA1301, MA1508, MA2176, MA2182 or MA2183 previously are NOT eligible to take the test.

The level of the test is equivalent to the syllabuses of MA1200 and MA1201. The test consists of two sections and will cover the following mathematical areas:

- Polynomials; Mathematical induction; Binomial theorem
- Coordinate geometry and conic sections; Basic trigonometry
- Functions and inverses; Limits, continuity and differentiability
- Techniques of differentiation, implicit, logarithmic and parametric differentiation; Successive differentiation
- Applications of differentiation: rate of change, local extrema, optimization problems, Taylor series, l'Hôpital rule

- Definite and indefinite integrals; Techniques of integration, integration of rational functions, integration by substitution, integration by parts
- Physical and geometric applications of integration
- Functions and inverses; Limits, continuity and differentiability
- Vectors in
**R**^{2}and**R**^{3}; Scalar products, cross products, triple scalar products; Linear (in)dependence - Matrices; Determinants, cofactor expansion; Systems of linear equations, Gaussian elimination, Cramer's rule; Matrix inverses, Gauss-Jordan elimination method
- Arithmetic of complex numbers; Polar and Euler forms; De Moivre's theorem and its applications

Sample questions and solutions

Duration of the test: | 1.5 hours for Section A and 1.5 hours for Section B |

Test style: | Written |

Test format: | 80 multiple choice questions. Each section consists of 40 questions |

Grading pattern: | Pass/Fail |

Passing grade: | A minimum standard of 70% must be achieved in each section |

Students must get approval from their Programme/Major Leaders or Admission Officers in order to take the test. **Pre-registration must be completed 5 working days prior to the test date. **A completed application form must reach the Department of Mathematics by hand.

Application form without endorsement of Programme/Major Leader or Admission Officer and departmental stamp of the student's home department will **NOT** be processed further. Students should ensure that the form has been completed and signed before sending to the Department of Mathematics.

Date: | 23 August 2021 (Monday) |

Time: | 2:00pm – 5:30pm (3 hours, including a short break in between the 2 tests) |

Venue: | Online (details will be emailed to participants) |

- Please pay attention to the instructions provided in our emails and during the start of the tests.

Test results will be released to individual students and the relevant Programme/Major Leaders or Admission Officers within five working days after the test. If a student does not pass the combined test, he or she is advised to enroll in MA1200 and MA1201.

If a student passes the combined placement test, s/he will be exempted from taking the related course(s) and cannot take such course(s) thereafter.

General Office

Department of Mathematics

Y6524, 6/F, Yeung Kin Man Academic Building

City University of Hong Kong

Email: maserv@cityu.edu.hk

Tel: +852 3442-8404

Fax: +852 3442-0250

Last update: 27 July 2021