## 15 Points

Faculty of Computing and Mathematical Sciences
Rorohiko me ngā Pūtaiao Pāngarau
Department of Mathematics and Statistics

### Staff

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#### Lecturer(s)

: rachael.foote@waikato.ac.nz

#### Librarian(s)

You can contact staff by:

• Calling +64 7 838 4466 select option 1, then enter the extension.
• Extensions starting with 4, 5 or 9 can also be direct dialled:
• For extensions starting with 4: dial +64 7 838 extension.
• For extensions starting with 5: dial +64 7 858 extension.
• For extensions starting with 9: dial +64 7 837 extension.
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### Paper Description

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This paper is provided for students who have not attained the entry standard for MATH101 or MATH102. A clear pass of at least C- in this paper can be used to gain entry to MATH101 and MATH102, but it has no direct sequel at 200 Level.

If you have done sufficiently well at school, you should consider enrolling in MATH101 Introduction to Calculus and MATH102 Introduction to Algebra.

This paper provides passing students with sufficient understanding and proficiency in basic mathematical concepts and skills to enable them to handle the mathematical aspects of their undergraduate studies (if this paper is their terminating mathematics paper) or to advance into the mainstream papers MATH101 (a grade of at least B- is required) and MATH102 (just a pass is required).

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### Paper Structure

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Three lectures and one 50 minute tutorial per week.
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### Learning Outcomes

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Students who successfully complete the course should be able to:

• manipulate mathematical equations to solve for unknown quantities
• simplify mathematical expressions involving brackets and fractions
• understand the properties of powers and logarithms and be able to apply them
• understand the formula for a linear function and be able to find the slope of a given line
• find the equation of a line given the slope and a point or given two points
• know how to complete the square for a quadratic and be able to find its maximum/minimum
• know the conditions under which a quadratic has zero, one, or two distinct real solutions
• know what a Polynomial is
• solve systems of linear equations
• understand the use of matrices
• use matrix algebra and find the inverse of a square matrix
• know the definition of the ‘trig’ ratios
• understand the uses of Pythagoras’ theorem and Sine & Cosine Rules
• know angles in degrees & radians
• work with angles of any magnitude
• use compound angle formulae
• understand permutations and combinations
• know about the binomial coefficients and be able to use the binomial theorem to expand powers
• know what a geometric series is and how to apply the simplified formula for such a series
• understand the definition of the derivative and be able to use it to work out derivatives
• understand and be able to apply differentiation rules such as the product rule and quotient rule
• find tangent lines and find local extrema of functions by finding turning points
• apply the second derivative test to find the type of extremum a turning point is
• know about some of the applications of differentiation
• understand how the fundamental theorem of calculus relates integration and differentiation
• understand the concept of antiderivatives and be able to apply them to calculate definite integrals
• apply simple methods of integration
• know about some of the applications of integration
• understand how the natural logarithm arises in integration and be able to calculate such integrals
• know about the exponential function and its properties
• use natural logarithms to solve simple equations involving the exponential function
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### Assessment

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In answers to questions in the assessed work, students are expected to show sufficient working so that the markers can see how the answer was obtained. Numerical answers with no working will NOT get full marks.

The internal assessment mark will consist of TWO Tests (worth a total of 40%) as follows:

Tuesday 27 March 6.00-8.00pm PWC & ELT.G.01 & MSB.1.01 (20%)

Thursday 24 May 6.00-8.00pm PWC & ELT.G.01 & MSB.1.01 (20%)

plus the total tutorial quiz component (10%).

Please ensure you take your ID CARD to tests – if you do not, your test script and mark will be withheld until you present this to the Maths Reception (G.3.19) the following day.

An UNRESTRICTED pass (i.e. C- or better) will only be awarded to students who achieve both a final overall mark of at least 50% and an Examination mark of at least 40%. A final overall grade of RP (Restricted pass) will not be accepted as a prerequisite for entry into any higher level Maths paper.

CALCULATORS will be required (any basic scientific calculator, but NO graphics or more advanced calculators). You are strongly advised to purchase a suitable calculator at the beginning of the paper so that you have time to become familiar with it. Suggested Calculator: “Casio” FX82 - available from most stationery shops.

COPYING of other students’ Quizzes/Tests will receive zero (this will include all students involved) and also be reported to the Disciplinary Committee.

#### Assessment Components

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The internal assessment/exam ratio (as stated in the University Calendar) is 50:50. There is no final exam. The final exam makes up 50% of the overall mark.

The internal assessment/exam ratio (as stated in the University Calendar) is 50:50 or 0:0, whichever is more favourable for the student. The final exam makes up either 50% or 0% of the overall mark.

Component DescriptionDue Date TimePercentage of overall markSubmission MethodCompulsory
1. 10x Tutorial quizzes (only the best 8 out of 10 marks are counted)
10
2. Test 1
27 Mar 2018
6:00 PM
20
3. Test 2
24 May 2018
6:00 PM
20
4. Exam
50
 Assessment Total: 100
Failing to complete a compulsory assessment component of a paper will result in an IC grade
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A PDF copy of the Lecture notes and Exercises booklet will be posted on Moodle - they will NOT be available from Campus Printery.

You will need a copy of these notes to work from.

### Online Support

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All information relating to this paper including your internal assessment marks will be posted on Moodle.
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Three lectures and one 50 minute tutorial per week.

Corresponding Papers: MATH166 Management Mathematics

Restricted Papers: This paper may not be taken concurrently with or subsequent to obtaining a pass in: MATH101 Introduction to Calculus or MATH102 Introduction to Algebra.

Other Information: Entry to this paper is guaranteed for those students with 18 credits from NCEA Level 2 Mathematics or 10 credits from NCEA Level 3 Mathematics.

Others without this criterion may be advised to take MATH168 Preparatory Mathematics before attempting MATH165.

Experience in this and similar papers indicates strongly that students who miss a significant number of sessions, and those who do not keep up with the exercises are unlikely to pass. You are strongly advised not to take the paper lightly. You will find that it requires the same diligence and commitment as other papers.

#### Prerequisite(s)

Prerequisite papers: 18 credits at Level 2 in NCEA Mathematics, or 10 credits at Level 3 in NCEA Calculus, or 14 credits at Level 3 in NCEA Mathematics, or at least a B- in MATH168 or MATHS168, or equivalent.

#### Restriction(s)

Restricted papers: MATH165