# H1 MATH TUITION

(Syllabus 8865) 2017

## INTRODUCTION TO H1 MATH

The applications of mathematics extend beyond the sciences and engineering domains. A basic understanding of mathematics and statistics, and the ability to think mathematically and statistically are essential for an educated and informed citizenry. For example, social scientists use mathematics to analyse data, support decision making, model behaviour, and study social phenomena.

H1 Mathematics provides students with a foundation in mathematics and statistics that will support their business or social sciences studies at the university. It is particularly appropriate for students without O Level Additional Mathematics because it offers an opportunity for them to learn important mathematical concepts and skills in algebra and calculus that were taught in Additional Mathematics. Students will also learn basic statistical methods that are necessary for studies in business and social sciences.

## AIMS OF H1 MATH

The aims of H1 Mathematics are to enable students to:

(a) acquire mathematical concepts and skills to support their tertiary studies in business and the social sciences

(b) develop thinking, reasoning, communication and modelling skills through a mathematical approach to problem-solving

(c) connect ideas within mathematics and apply mathematics in the context of business and social sciences

(d) experience and appreciate the value of mathematics in life and other disciplines.

## ASSESSMENT OBJECTIVES OF H1 MATH

There are three levels of assessment objectives for the examination.

The assessment will test candidates’ abilities to:

AO1 Understand and apply mathematical concepts and skills in a variety of problems, including those that may be set in unfamiliar contexts, or require integration of concepts and skills from more than one topic.

AO2 Formulate real-world problems mathematically, solve the mathematical problems, interpret and evaluate the mathematical solutions in the context of the problems.

AO3 Reason and communicate mathematically through making deductions and writing mathematical explanations and arguments.

## USE OF A GRAPHING CALCULATOR (GC)

The use of an approved GC without computer algebra system will be expected. The examination papers will be set with the assumption that candidates will have access to GC. As a general rule, unsupported answers obtained from GC are allowed unless the question states otherwise. Where unsupported answers from GC are not allowed, candidates are required to present the mathematical steps using mathematical notations and not calculator commands. For questions where graphs are used to find a solution, candidates should sketch these graphs as part of their answers. Incorrect answers without working will receive no marks.

However, if there is written evidence of using GC correctly, method marks may be awarded. Students should be aware that there are limitations inherent in GC. For example, answers obtained by tracing along a graph to find roots of an equation may not produce the required accuracy.

## INTEGRATION AND APPLICATION OF H1 MATH

Notwithstanding the presentation of the topics in the syllabus document, it is envisaged that some examination questions may integrate ideas from more than one topic, and those topics may be tested in the contexts of problem solving and application of mathematics. Possible list of H1 Mathematics applications and contexts:

Applications and contexts | Some possible topics involved |
---|---|

Optimisation problems (e.g. maximising profits, minimising costs) | Inequalities; System of linear equations; Calculus |

Population growth, radioactive decay | Exponential and logarithmic functions |

Financial maths (e.g. profit and cost analysis, demand and supply, banking, insurance) | Equations and inequalities; Probability; Sampling distributions; Correlation and regression |

Games of chance, elections | Probability |

Standardised testing | Normal distribution; Probability |

Market research (e.g. consumer preferences, product claims) | Sampling distributions; Hypothesis testing; Correlation and regression |

Clinical research (e.g. correlation studies) | Sampling distributions; Hypothesis testing; Correlation and regression |

The list illustrates some types of contexts in which the mathematics learnt in the syllabus may be applied, and is by no means exhaustive. While problems may be set based on these contexts, no assumptions will be made about the knowledge of these contexts. All information will be self-contained within the problem.

## SCHEME OF H1 MATH EXAMINATION PAPERS

For the examination in H1 Mathematics, there will be one 3-hour paper marked out of 100 as follows:

**Section A** (Pure Mathematics – 40 marks) will consist of about 5 questions of different lengths and marks based on the Pure Mathematics section of the syllabus.

**Section B** (Probability and Statistics – 60 marks) will consist of 6 to 8 questions of different lengths and marks based on the Probability and Statistics section of the syllabus.

There will be at least two questions, with at least one in each section, in the application of Mathematics in real-world contexts, including those from business and the social sciences. Each question will carry at least 12 marks and may require concepts and skills from more than one topic.

Candidates will be expected to answer all questions.

## SYLLABUS FOR H1 MATH

### Section A (Pure Mathematics - 40 marks)

**Section A**(Pure Mathematics – 40 marks) will consist of about 5 questions of different lengths and marks based on the Pure Mathematics section of the syllabus. Candidates will be expected to answer all questions.

#### 1. Functions and Graphs

##### 1.1 Exponential and logarithmic functions and Graphing techniques

##### 1.2 Equations and inequalities

#### 2. Calculus

##### 2.1 Differentiation

##### 2.2 Integration

### Section B (Probability and Statistics - 60 marks)

#### 3. Probability and Statistics

##### 3.1 Probability

##### 3.2 Bionomial distribution

##### 3.3 Normal distribution

##### 3.4 Sampling

##### 3.5 Hypothesis testing

##### 3.6 Correlation and Linear regression

**Section B** (Probability and Statistics – 60 marks) will consist of 6 to 8 questions of different lengths and marks based on the Probability and Statistics section of the syllabus. Candidates will be expected to answer all questions.

For full syllabus, refer to Singapore Examinations and Assessment Board: Singapore–Cambridge General Certificate of Education Advanced Level Higher 1 (2023) Mathematics (Syllabus 8865)

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