Syllabus for MYP years 4 and 5 (grades 9 and 10)

1. Surveys and experiments

• carry out a project in data handling.
• make frequency tables,
• draw bar charts or pie charts and use scatter diagrams.
• write an effective questionnaire
• carry out experiments to get data

2. The tangent function

• Understand the relationship between lengths and angles in right triangles.

3. Fractions

• calculate with fractions, including: addition, subtraction and multiplication reciprocals and division
•  work with powers and positive indices, including prime factorisation
• find lowest common multiples and highest common factors using prime factorisation
• use the rules for multiplying and dividing powers
• work with negative indices
• simplify algebraic expressions that involve indices

4.Indices

5. Forming and solving equations

• solve equations with the unknown on both sides, and with brackets
• form simple equations and solving them
• solve equations involving algebraic fractions
• form more complex equations and solve them

6. Rates

• the relationships between speed, time and distance
• distance—time graphs
• solve problems involving various rates.

7. Distributions and averages

• median and range
• calculating or estimating the mean of a frequency distribution
• stem-and-leaf tables
• group continuous data and represent it graphically by a bar chart or frequency polygon
• calculate a moving average and use it to detect a trend

8. Changing the subject 1

• Rearrange a formula where the new subject appears only once.

9. Increase and decrease

• write percentages as decimal equivalents
• express one quantity as a percentage of another
• express a percentage increase as a multiplier
• calculate the overall percentage change given two successive percentage changes
• calculate the final amount when money is invested at a given rate of interest
• calculate the original value given a percentage change and the final value

10. Using area and volume

• find the area of any rectangle, triangle or parallelogram
• find the volume of a simple object
• use Pythagoras’s theorem
• find and use the area of a trapezium
• find and use density
• convert between units of area and volume

11. Sine and cosine

• Find sides and angles in right-angled triangles.

12. Large and little

• write large and small numbers in standard form
• calculate with numbers in standard form

13. Gradients and equations

• plot points and draw the graph of a straight line, given its equation
• rearrange simple formulas
• calculate and use gradients
• understand and use the gradient—intercept form of the equation of a line

14. Loci and constructions

• the loci of points equidistant from two points or two lines
• constructions using a straight edge and compasses
• solve problems using loci.

15. Cumulative frequency

• calculate an estimate of the mean of a frequency distribution
• make a cumulative frequency table and draw a cumulative frequency graph
• find and interpret the median, quartiles and interquartile range
• interpret and draw a box-and-whisker plot

16. Combining transformations

• describe and carry out rotations, reflections, translations and enlargements on shapes.
• understand negative enlargements
• find a centre of enlargement
• recognise and carry out a one-way stretch
• recognise combinations of transformations

17. Probability

• calculate a probability using equally likely outcomes
• estimate a probability from data
• calculate probabilities in the case of mutually exclusive events independent events and dependent events

18. Simultaneous equations

• draw the graph of a straight line, given its equation
• rearrange simple formulas
• form and solve a variety of linear simultaneous equations, using elimination and substitution
• interpret the solution of simultaneous equations as the point of intersection of two graphs

19 Solving inequalities

• Understand simple and combined inequalities, and how to represent them on a number line.
• Solve inequalities.

20. Brackets and quadratic equations 1

• multiply powers by adding indices
• multiply simple expressions
• add, subtract and multiply simple fractions
• multiply out brackets and simplify
• factorise expressions
• solve quadratic equations such by factorising
• solve problems by forming and solving quadratic equations

21. Sampling

• carry out surveys.
• Know a range of sampling methods to collect data
• Use random numbers to select a sample

22. Direct and inverse proportion

• recognise direct and inverse proportion
• do calculations involving direct and inverse proportion
• solve problems involving other types of proportionality -

23. Graphing inequalities

• Graph and interpret inequalities in two variables.

24. Handling secondary data

• Interpret tabulated secondary data.

25. Length, area and volume

• calculate the length of an arc
• calculate the area of a sector and a segment of a circle
• calculate the surface area of a cylinder, a cone and a sphere
• calculate the volume of a cylinder, a pyramid, a cone and a sphere

26. Quadratic graphs

• plot graphs of linear functions
• rearrange simple formulas
• multiply out brackets like
• substitute into and interpret quadratic functions
• draw the graphs of quadratic functions and use them to solve simple problems
• use quadratic graphs and straight lines to solve related equations

27. Algebraic fractions

• use the four operations on number fractions
• multiplying out brackets and factorise
• manipulate and simplify fractions with letters in them.

28. Further graphs

• solve equations by trial and improvement methods.
• extend your understanding of cubic and quadratic graphs
• use graphs to solve equations involving x
• use graphs of functions such as y
• solve problems involving graphs that model real-life situations

29. Angles and circles

• understand what is meant by proving a statement
• know relationships between angles connected with circles, and how they are proved

30. Changing the subject 2

• rearrange a formula where the new subject appears once
• rearrange a formula where the new subject appears more than once
• rearrange more complex formulas
• Work out your own formulas from a given situation

31. Accuracy

• find the upper and lower bounds of the interval within which a number must lie when you are given an approximate value
• find the upper and lower bounds of the result of a calculation involving approximate values

32. Dimensions

• work out the dimension of an expression
• use dimensions to check that an expression is sensible

33. Similarity and enlargement

• finding and using the scale factor of an enlargement
• solve problems involving similar triangles
• see how the scale factor, area factor and volume factor of an enlargement are related

34. Brackets and quadratic equations 2

• multiply out brackets and factorise quadratic expressions
• solve quadratic equations such as x + 4x + 3 = 0
• solve quadratic equations by factorising, using perfect squares and using the formula
• solve problems by forming and solving a quadratic equation
• solve simultaneous equations, one linear and one quadratic

35. Trigonometric graphs

• use sines, cosines and tangents of angles greater than 900 and negative angles
• work with trigonometric graphs
• relate trigonometric graphs to real-life situations

36. Pattern and proof

• find and use a rule for the nth term of a linear or quadratic sequence
• find a rule for the nth term of a sequence generated from a context and prove it
• prove a general statement is false using a counter-example
• prove a general statement is true using algebra

37. Histograms

• read and draw histograms
• understand frequency density

38. Algebraic fractions and equations

• simplify expressions involving straightforward algebraic fractions
• solve equations involving fractions with numerical denominators
• simplify more complex expressions with algebraic fractions
• solve equations involving fractions with algebraic denominators

39. Indices 2

• understand fractional indices
• exponential growth and decay

40. Vectors

• use vector notation
• express positions and lines in terms of a combination of vectors
• solve simple geometrical problems using vectors

41. Transforming graphs

• sketch the graph of a quadratic function
• draw and interpret trigonometric graphs
• solve a quadratic equation by completing the square
• find and use the completed-square form of a quadratic expression
• transform graphs and find their equations
• use function notation
• sketch graphs of y = af(x), f(ax), f(x) + a and f(x + a) given the graph of y = f(x)
• fit a function to a non-linear set of data

42. Congruent triangles

• decide from given information whether two triangles are congruent
• use congruent triangles to prove geometrical statements

43. Circles and equations

• write quadratic expressions in completed square form
• solve quadratic equations
• sketch the graph of a quadratic equation
• solve simultaneous equations (one linear, one quadratic)
• find the equation of a circle
• sketch a circle given its equation
• solve simultaneous equations (one linear, one circle equation)

44. Exactly so

• find the circumference and area of a circle
• using Pythagoras
• Understand why and how to leave exact values in answers instead of numerical approximations.

45. Rational and irrational numbers

• write recurring decimals as fractions
• understand the distinction between rational and irrational numbers
• manipulate irrational numbers in surd form

46. Further trigonometry

• use sine, cosine and tangent in right-angled triangles
• using Pythagoras’ rule
• find lengths and angles in any triangle
• find the area of any triangle

47. Three dimensions

• Pythagoras and trigonometry to solve three-dimensional problems
• Use three-dimensional coordinates

48. Sets and Venn Diagrams

• language, notation and Venn diagrams to describe sets and represent relationships between sets

49. Networks

• Use network to diagrams to represent and solve simple optimisation problems.
• Use matrices to represent networks.

50. Logic

• Solve problems and puzzles using systematic and intuitive logic

• Represent worded statements using logical symbols

51. Algebra

• Linear equations: form, solve and illustrate graphically.
• Linear inequalities: form, solve and illustrate graphically.
• Simultaneous linear equations: form, solve and illustrate graphically.
• Use graphical calculator software to solve simultaneous linear equations
• Use factorisation to solve quadratic equations.
• The quadratic formula to solve quadratic equations (2.6)
• Use graphical calculator software to solve quadratic equations
• Use of the discriminant to solve problems involving the number of solutions (2.6)
• Sketch graphs of quadratic functions, and use these as a problem solving tool
• Simplify algebraic fractions

52. Circular functions and trigonometry

• The circle: radian measure of angles; length of an arc; area of a sector (3.1)
• The circular functions sin x, cos x and tan x (3.4)
• Solution of triangles. The cosine rule. The sine rule (3.6)
• Area of a triangle as absinC (3.6)

53. Functions and equations

• Concept of function: domain, range; image (value) (2.1)
• Composite functions fog; identity function (2.1)
• Inverse function f (2.1)
• The graph of a function; its equation y = ax). Function graphing skills (2.2)
• use of a graphic display calculator to graph a variety of functions (2.2)
• investigation of key features of graphs (2.2)
• solution of equations graphically (2.2)
• Transformations of graphs: translations; stretches; reflections in the axes. The graph of f^-1(x)as a reflection in the line y=x of f(x) (2.3)
• The reciprocal function: its graph; its self-inverse nature. (2.4)

54. Sequences and series

• Arithmetic sequences and series; sum of finite arithmetic series; geometric sequences and series; sum of finite and infinite geometric series (1.1)
• Sigma notation (1.1)
• The binomial theorem (1.3)