**Purpose of the Test**

The Mathematics Placement Test is a pass-fail test!

The placement test gives a measure of a student's mathematical skills and knowledge of specific concepts at the time, and the results are used to determine eligibility for enrollment in MATH1510 (Calculus for Engineers) in order to complete one of the graduation requirements for an Engineering programme.

A student will take the placement test only once on 11^{th} August 2017.__ Any student who fails the test must take both MATH1020 (General Mathematics) and MATH1510 (Calculus for Engineers) in Term 1, 2017-18. Any student who passes the test will only have to take MATH1510.__

__There are no exemptions made for the placement test!__

**Placement Test Schedule**

The placement test is now scheduled for __ 11:30a.m. - 12:30p.m. on Friday, 11^{th} August 2017__. Alternate seating will be arranged.

**Please arrive at 10:30a.m. at Lecture Theatre 1, Yasumoto International Acadmic Park to complete the test registration before the start of the test. **

**General Characteristics of the Test**

- The paper and pencil test consists entirely of multiple choice questions, each with six choices.
- There are 25 multiple-choice questions worth 4 points each for a total of 100 points. Each item has only one acceptable answer. There is no penalty for any question if you pick the choice “I don’t know” for your answer. But there is a penalty for incorrectly guessing the answer.
__Calculators are NOT permitted during the test.__with a #2 pencil.**Bring a valid, physical photo ID such as HKID or passport (not expired)****Please also get your JUPAS / Non-JUPAS Application Number ready in case Mathematics Department may ask such number for further verification.**- The Mathematics Placement Test is designed as a test of skill and concepts and not speed. Sixty (60) minutes are allowed to complete the test. Ample time is allowed for most students to answer all 25 questions.
- You are NOT allowed to use the followings during the test:

- Cell phones, smart phones, and other electronic devices.

- Any clocks, timers, or watches that beep or have audible alarms.

- A make-up placement test will be provided only when documentation of hospitalization, major illness, family death, or emergency is provided. In order to be considered for permission to take the make-up placement test, you must send us an e-mail notice with a written explanation of your absence within 2 days of the placement test, i.e. on either 11
^{th}or 12^{th}August 2017 at: math1510@math.cuhk.edu.hk

No late request or request without explanation and supporting documents will be considered.

Absence from a placement test for any other reasons – including minor illnesses, family obligations, summer jobs, job interviews, trips or any other unexpected events – will result in a fail grade for that placement test.

Only one make-up placement test, if approved, will be held at 5:30-6:30 p.m. on Monday, 4^{th} September 2017, which is at the exact first tutorial class of MATH1510 while the test venue is to be announced.

**Test Description**

The Mathematics Placement Test consists of 25 multiple-choice questions covering five main areas: arithmetic & algebra, trigonometry, calculus (differentiation and integration), probability and complex analysis.

Below is a list of topics covered in the Mathematics Placement Test, which can be used as a study guide.

__Arithmetic____&____Algebra__

**Inequalities**

- Inequalities involving absolute value
- Table of signs for polynomial and rational inequalities

**Functions**

- Domain
- Operations including compositions
- Inverses
- Graphs
- Symmetry
- Transformations: shifts, reflections, stretching and shrinking`
- Systems of Linear Equations

**Quadratic functions and equations**

- Applications involving quadratic equations
- Parabolas
- Finding local/global extrema
- Solving quadratic equations involving radicals

**Polynomials**

- Long division
- Factorization
- Multiplicities of roots
- Shape of graph
- Writing polynomial functions with given properties

**Rational functions**

- Finding intercepts and asymptotes
- Graphs sketching without calculator

**Conic sections**

- Standard equations for parabolas, circles, ellipses, and hyperbolas, shift of center

**Exponential and Logarithmic functions**

- Definition
- Graphs
- Exponent rules
- Laws of logarithms
- Exponential and logarithmic equations
- Exponential growth and decay

__Trigonometry__

**Basic Trigonometry**

- Converting between radian and degree
- Arc length, sector area and angular speed

**Trigonometric functions**

- Definition using right-triangle
- Definition using unit circle
- Graphs of standard trigonometric functions
- Sinusoidal graphs
- Definitions of secant, cosecant and cotangent

**Solving triangles**

- Right triangles
- Law of cosines
- Law of sines

**Trigonometric identities**

- Reciprocal identities
- Pythagorean identities
- Negative-angle identities
- Periodicity identities
- Angle sum and difference identities
- Double-angle identities
- Half-angle identities

**Trigonometric equations**

- Finding general solutions

__Calculus____(____differentiation and integration)__

**Limits and Continuity**

- Limit of a function
- Limit laws
- Limits at infinity, horizontal asymptotes
- Determining continuity

**Derivatives**

- Definition of the derivative
- The product rule and quotient rule
- The chain rule
- Derivatives of power functions, polynomials, exponential, logarithmic and trigonometric functions

**Applications of the Derivative**

- Tangent lines and velocity
- Increasing and decreasing functions
- Local extrema
- The second derivative, concavity and points of inflection
- Curve sketching
- Indeterminate forms and L’Hôpital’s rule
- Global extrema
- Implicit differentiation
- Related rates

**Integration**

- Definite and indefinite integrals
- Estimating area with finite sums
- Finding exact area
- Sigma notation and infinite sums
- Fundamental theorem of calculus
- Integration by substitution
- Integration by parts
- Integrals of power, polynomials, trigonometric, exponential and natural logarithmic functions

__Probability__

- Tree diagram
- Venn diagram
- Conditional probability
- Bayes’ theorem
- Counting principle: permutation and combination

__Complex Analysis__

- Definition of complex numbers
- Basic arithmetic : addition, subtraction, multiplication and division
- Complex conjugate
- Argand diagram
- Euler’s formula