International Mathematics for the middle years 5

Chapter 1. Review of Year 9

1:01 Basic number skills

1:01A Order of operations

1:01B Fractions

1:01C Decimals

1:01D Percentages

1:01E Ratio

1:01F Rates

1:01G Significant figures

1:01H Approximations

1:01I Estimation

1:02 Algebraic expressions

How do mountains hear?

1:03 Probability

1:04 Geometry

1:05 Indices

1:06 Surds

1:07 Measurement

1:08 Equations, inequations and formulae

1:09 Consumer arithmetic

1:10 Coordinate geometry

1:11 Statistics

1:12 Simultaneous equations

1:13 Trigonometry

1:14 Graphs of physical phenomena

Working mathematically

Chapter 2. Consumer Arithmetic

2:01 Saving money

Financial spreadsheets

2:02 Simple interest

Why not buy a tent?

2:03 Solving simple interest problems

2:04 Compound interest

What is the difference between a book and a bore?

2:05 Depreciation

2:06 Compound interest and depreciation formulae

Compound interest tables

2:07 Reducible interest

Reducible home loan spreadsheet

2:08 Borrowing money

A frightening formula

2:09 Home loans

Mathematical terms • Diagnostic test • Revision assignment • Working mathematically

Chapter 3. Quadratic equations

3:01 Solution using factors

3:02 Solution by completing the square

3:03 The quadratic formula

How many solutions?

3:04 Choosing the best method

What is an Italian referee?

3:05 Problems involving quadratic equations

Temperature and altitude

Did you know that 2 = 1?

Mathematical terms • Diagnostic test • Revision assignment • Working mathematically

Chapter 4. Number Plane Graphs

4:01 The parabola

The graphs of parabolas

4:02 Parabolas of the form y = ax² + bx + c

Why didn’t the bald man need his keys?

4:03 The hyperbola: y = k/x

4:04 Exponential graphs: y = aˣ

The tower of Hanoi

4:05 The circle

4:06 Curves of the form y = ax³ + d

What is HIJKLMNO?

4:07 Miscellaneous graphs

4:08 Using coordinate geometry to solve problems

Mathematical terms • Diagnostic test • Revision assignment • Working mathematically

Chapter 5. Further Algebra

5:01 Simultaneous equations involving a quadratic equation

5:02 Literal equations: Pronumeral restrictions

What small rivers flow into the Nile?

Fibonacci formula

5:03 Understanding variables

Number patterns and algebra

Mathematical terms • Diagnostic test • Revision assignment • Working mathematically

Chapter 6. Curve Sketching

6:01 Curves of the form y = axⁿ and y = axⁿ + d

6:02 Curves of the form y = axⁿ and y = a(x − r)ⁿ

6:03 Curves of the form y = a(x − r)(x − s)(x − t)

6:04 Circles and their equations

6:05 Finding of graphs

A parabola and a circle

Mathematical terms • Diagnostic test • Revision assignment • Working mathematically

Chapter 7. Polynomials

7:01 Polynomials

7:02 Sum and difference of polynomials

7:03 Multiplying and dividing polynomials by linear expressions

7:04 Remainder and factor theorems

7:05 Solving polynomial equations

7:06 Sketching polynomials

How do you find a missing hairdresser?

7:07 Sketching curves related to y = P(x)

Mathematical terms • Diagnostic test • Revision assignment • Working mathematically

Chapter 8. Functions and Logarithms

8:01 Functions

8:02 Inverse functions

Quadratic functions and inverses

8:03 The graphs of y = f(x), y = f(x) + k and y = f(x − a)

Where would you get a job playing a rubber trumpet?

8:04 Logarithms

8:05 Logarithmic and exponential graphs

8:06 Laws of logarithms

Logarithmic scales

8:07 Simple exponential equations

Solving harder exponential equations by “guess and check”

8:08 Further exponential equations

Logarithmic scales and the history of calculations

Mathematical terms • Diagnostic test • Revision assignment • Working mathematically

Chapter 9. Matrices

9:01 Defining a matrix, and some matrix operations

9:02 Matrix multiplication

9:03 Matrix operations and the GDC

Inverses and the GDC

9:04 The determinant and inverse of a 2 × 2 matrix

9:05 Solving matrix equations

9:06 Solving simultaneous equations using matrices

Mathematical terms • Diagnostic test • Revision assignment • Working mathematically

Chapter 10. Surface Area and Volume

10:01 Review of surface area

10:02 Surface area of a pyramid

10:03 Surface area of a cone

The surface area of a cone

10:04 Surface area of a sphere

The surface area of a sphere

How did the rains win the war against the nuts?

10:05 Volume of a pyramid

The volume of a pyramid

10:06 Volume of a cone

10:07 Volume of a sphere

Estimating your surface area and volume

10:08 Practical applications of surface area and volume

Mathematical terms • Diagnostic test • Revision assignment • Working mathematically

Chapter 11. Similarity

11:01 Review of similarity

11:02 Similar triangles

A. Matching angles

B. Ratios of matching sides

Drawing enlargements

11:03 Using the scale factor to find unknown sides

What happened to the mushroom that was double parked?

11:04 Similar triangle

11:05 Sides and areas of similar figures

11:06 Similar solids

King Kong — Could he have lived?

Mathematical terms • Diagnostic test • Revision assignment • Working mathematically

Chapter 12. Further Trigonometry

12:01 Trigonometric ratios of obtuse angles

12:02 Trigonometric relationships between acute and obtuse angles

Why are camels terrible dancers?

12:03 The sine rule

12:04 The sine rule: The ambiguous case

12:05 The cosine rule

Why did Tom’s mother feed him Peter’s ice-cream?

12:06 Area of a triangle

12:07 Miscellaneous problems

12:08 Problems involving more than one triangle

Mathematical terms • Diagnostic test • Revision assignment • Working mathematically

Chapter 13. Circle Geometry

13:01 Circles

Circles in space

13:02 Chord properties of circles (1)

Locating the epicentre of earthquakes

13:03 Chord properties of circles (2)

13:04 Angle properties of circles (1)

13:05 Angle properties of circles (2)

The diameter of a circumcircle

13:06 Tangent properties of circles

13:07 Further circle properties

How do you make a bus stop?

13:08 Deductive exercises involving the circle

How many sections?

Mathematical terms • Diagnostic test • Revision assignment • Working mathematically

Chapter 14. Transformations and Matrices

14:01 Translations

14:02 Enlargement

14:03 Reflection

14:04 Rotation

Matrix methods

14:05 Transformations and matrices

Mathematical terms • Diagnostic test • Revision assignment • Working mathematically

Chapter 15. Statistics

15:01A Review: Representing data

15:01B Review: Analysing data

Comparing sets of data

15:02 Using the standard deviation

15:03 The normal distribution

15:04 Statistics with two variables

Mathematical terms • Diagnostic test • Revision assignment

Chapter 16. Probability

16:01 Probability review

This AND that OR something else

16:02A Simultaneous events

16:02B Successive events

16:03 Independent events and conditional probability

Mathematical terms • Diagnostic test • Revision assignment

Chapter 17. An Introduction to Algorithms and Number Theory

17:01 Algorithms

Sorting it out

17:02 Absolute value and the division algorithm

17:03 Divisibility, greatest common divisor and the Euclidean algorithm

Common divisors

17:04 Properties of gcd(a, b)

Mathematical terms • Diagnostic test • Revision assignment

Answers

Answers to ID Cards