Mathematics in the 1st grade vwo Solids (chapter 1) We learn about the net of a solid, the top, side and front view. That are views of a solid. The view-line is view-line is an imaginary line from your eye to an object. This is a net of net of a solid. ↓
Angels and distances (chapter 2) In the Netherlands we learn how to calculate the distance between two lines by using a geo-triangle. We learn what parallel lines, point of o f intersection and perpendicular lines are. The right, acute and the obtuse angle and we know how to draw them.
Graphs(chapter 3) We learn about the falling, rising and constant graphs. That the graph haves units and variables. We know how to make and use them and to read the point of intersection. We also know how to make graphs from a table.
Negative numbers (chapter 4) We learn about the negative coordinates and about the rule that we use when you multiply and divide numbers; - positive x positive = positive - positive x negative =negative - negative x positive = negative - negative x negative = positive
or
-positive : positive= positive - positive: positive : negative =negative - negative : positive = negative - negative x negative = positive
Numbers(chapter 5) Adding, subtracting, multiplying and dividing. We learned about the calculation order: 1. Work out what is in the brackets 2. Then raise the powers. 3. Multiplying and dividing from left to right. 4. Add and subtract from left to right.
We also learned about powers, the exponent and base. For example: 53. 5 is the base and 3 is the exponent.
Ratio(chapter 6) We learn about the ratio tables, that are tables that represent the relationships relationships between different ratios. How to calculate a ratio table: 1. Make a ratio table and fill in the given numbers. 2. Write the number 1 and then the given amount in the top row. Find the numbers that should be written by the arrows. 3. Use the arrows to calculate the numbers in the row below. 4. Write down the answer of the question.
Formulas in words(chapter 7) First we learned how to make a formula. Then we learned how to make the formula shorter. Then step three plotting a graph from a formula. You can do that by making a table from the formula. Then you have to choose an appropriate scale for each axis. We also learned how to make a formula from a graph. You just make a table from the points that you can accurately read off from the graph.
Working with formulas (chapter 8) We learn about the calculation order, so we know now what we must calculate first. ↓ 1. Brackets 2. Exponents 3. Multiply and divide 4. Adding and subtract
Plane figures (chapter 9) In this chapter wel learn about symmetry. You can use a mirror to find out if a figure is symmetrical or not. You have a axes of symmetry and rotation symmetry.Every figure with a rotation symmetry has axes. Two equals side are isosceles triangles. The triangles. The equal angles of a isosceles triangle are called base angles.
Area and volume(chapter 10) In this chapter we learn about the units of length ↓
Equations(chapter11) Claculate the unknown value in a formula when the outcome is known: ↓ 1. Write down the formula 2. Fill in the outcome in the correct place 3. Calculate backwords and you find the unknown value We learned about rounding off. You can round up and round down.
Chapter 12 was repeating the hole book.
2 vwo Mathematics Our mathematics book is called: Modern Mathematics. Mathematics. You have 2 parts, A and B, in each part you have 6 chapters, so in total you have 12 chapters. It consist of a textbook, a workbook and ICT, but we don’t do the ICT exercises. The textbook is divided into three blocks. Each block consist of two chapters, sections with more exercises, VWO-sections and projects. In the second year, we learn different subjects about math. We are going to learn about:
Book A ( how to make them and to use them) Linear formulas : 1. Graphs and formulas 2. Gradient and y-intercept 3. Making linear formulas 4. Directly proportional 5. Making exercises Square roots 1. Square roots 2. Adding square roots 3. Multiplying square roots 4. Square roots formulas Similarity 1. Making figures larger 2. Scale factor 3. Similar figures 4. Similar triangles 5. Calculating Similarity Pythagoras theorem 1. Pythagoras theorem 2. Calculating a side 3. Applying the theorem 4. Cubes and cuboids 5. Pythagoras and pyramids Quadratic formulas 1. Quadratic formulas 2. Removing brackets 3. Negative factors 4. Formulas with double brackets 5. Quadratic equations Exponential growth 1. 100% and more 2. From percentage to factor 3. Exponential formulas 4. Standard notation
Book B (how to make them and how to use them ) Statistics 1. Pie chart 2. Bar chart and frequency polygon 3. Mean, mode and median 4. Stem-and-leaf diagram Probability 1. Calculating probabilities 2. Tree diagram 3. Probabilities and powers 4. Replacing and powers Linear equations 1. Using a balance 2. Solving equations 3. Interesting lines 4. Break-even points 5. Solving inequalities Factorising 1. Factorising 2. Factorising binomials 3. A x B = 0 4. Factorising trinomials 5. Quadratic equations Area 1. Triangles 2. Parallelograms 3. Circumference of a circle 4. Area of a circle Constructing and reasoning 1. Constructing figures 2. Mid-parallel 3. Perpendicular bisector 4. Altitude 5. Angle bisector
3rd grade mathematics vwo The major math subjects are number sense and operations, algebra, geometry and spatial sense, measurement, and data analysis and probability. I am not sure in what order you learn as it could be different from every school. There is a major difference in level between the second and the third year and thus a third year student has to work way harder than what they used to remember. You are supposed to make a whole chapter in 2 weeks time and then you get a test about it. In the same year they learn about mathematics A and Mathematics B. Third Graders get subjects divided in blocks; Geometry, Algebra, Mathematics A and Mathematics B. Under the block Geometry they get the subjects: Trigonometry and Solids. Take Trigonometry for example; under that Geometric subject t hey learn about tangents, Sine and Cosine. Under Solids they have: Drawing, Enlarging and shapes. So the whole curriculum is divided in 6 blocks. All of those Blocks contain 2 smaller subjects (which are called chapters) and those smaller subjects have even samller subjects attached to them. Each 2-3 a chapter must be finished and so every 4-6 weeks a block is finshed. Chapter 1: Subjects are: Functions, Domain and Range, Functions and parameters, Directly and inversely proportional, Fractional functions Chapter 2: Subjects are: Quadratic Functions, Parabolas, Symmetry and vertex, plotting parabolas, the shape of a parabola Chapter 3: Subjects are: Statistics, Absolute and relative, distribution in classes, measures of spread, box plot, cumulative frequencies. Chapter 4: Subjects are: Probability, samples, simulations, probability experiments, calculating probabilities Chapter 5: Subjects are: Quadratic formula, solving by factorizing, quadratic equations, finding the vertex Chapter 6: Subjects are: New graphs, periodic grahps, addition, multiplication, combinations. Chapter 7: Subjects are: Trigonometry, tangent, using tangent, sine and cosine, calculating in right-angled triangles. Chapter 8: Subjects are: Solids, drawing, enlarging, cuboid, prism, cylinder, pyramid, cone, sphere, compound solids. Chapter 9: Subjects are: Calculating with functions, f unctions, parallel and coinciding lines, calculating with exponents, calculating with powers, calculating with square roots.
Chapter 10: Subjects are: Graphs, equations and inequalities, quadratic inequali ties, parabola and line, intersect, touch and no common point, families of lines, working with parameters. Chapter 11A: Subjects are: Calculations, without a calculator, fractions and percentages, ratios, calculating time, standard notation. Chapter 12A: Subjects are: Fractions and functions, calculating with fractions, fractional functions, power functions, solving equations. Chapter 11B: Subjects are: Reasoning in geometry, Properties and definitions, Proofs, Theorems, Tales’ theorem, Angles in a circle. Chapter 12B: Subjects are: Calculating with fractions, f ractions, fractional functions, graphs of fractional functions, solving equations.
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Mathematics A in the 4 grade vwo
Block 1 Analyse Chapter 1 Functions and the graphic calculator Chapter 2 Algebra or calculator
Block 2 Analyse Chapter 3 Exponentia l functions.
Chapter 4 Power functions.
Block 3 Statistics Chapter 5 Counting problems Chapter 6 Counting with chances Chapter 7 Chance distripution
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2
3
4
5
6
7
1-1 Plotting, sketching and drawing. 2-1 Solving with the calculator.
1-2 Sorts of graphs.
1-3 Setting window.
1-4 Edge points and asymtotes.
1-5 Domain and range.
1-6 Mixed exercises.
N.V.T N.V.T
2-2 Solving with algebra.
2-3 Compare with quadratic algebra.
2-4 Calculate or compute exactly.
2-5 Inequalities.
2-6 Chain calculation.
2-7 Mixed exercises.
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2
3
4
5
6
3-1 Draw exponenti al functions. 4-1 Power fumctions
3-2 Negative and broken exponents 4-2 Negative exponent
3-3 Count with growth factors. 4-3 Broken exponents
3-4 Equations and inqualities
3-5 Mixed exercises
N.V.T N.V.T
4-4 Solving equations
4-5 Functions and combining
4-6 Mixed exercise
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2
3
4
5
5-1 Power trees and faculty trees
5-2 Permutations and combinations
5-3 Counting with a grid
5-4 Choose a good counting model
5-5 Mixed exercise
6-1 Chances
6-2 Calculating chances
6-3 Multiplying chances
6-4 Counting chances
7-1 Frequentie distripution
7-2 Random variables
7-3 Chance distribution
7-4 Expectations value
6-5 With en without replacements 7-5 Tennis tournament
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6-6 Conditionl chances
6-7 Mixed exercises
7-6 Mixed exercise
Blok 4 Matrices Chapter 8 Calculating and matrices
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2
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8-1 Graphs
8-2 Matrices
8-3 Direct weighing matrices
8-4 Som and diffreence matrix
8-5 Multiplying matrices
8-6 Matrix product
8-7 Mixed exercices
Chapter 9 Transitions matrices
9-1 Transitions matrices
9-2 Multisteps ways
9-3 Caunt back
9-4 Stable distrbution
9-5 Population Prediction matrix
9-6 Mixed exercices
VWO 4th Grade Mathematics B.
Block 1
Block 1
Refresh
§1
§2
§3
§4
§5
§6
Chapter1 Functions and calculator Chapter2 Algebra or calculator
functions
plotting and drawing sketches solved using the calculator
types of charts
Setting window
edge points and asymptotes
domain and range
mixed contracts
solve algebra
calculate or calculate exactly
inequalities
root compare present solve
mixed contracts
quadratic equations
Block 2
Block 2
Refresh
§1
§2
§3
§4
§5
§6
Chapter3 exponential functions
growth factors
graphs and exponential functions
arithmetic and powers
graphs and exponential inequalities
functions different writing
mixed contracts
Chapter4 powerfunctions
functions and symmetry
power functions
negative exponents and broken negative exponents
broken exponents
exactly solve
sum and difference of power functions
mixed contracts
Block 3
Block 3
Refresh
§1
§2
§3
§4
§5
§6
§7
§8
Chapter5 geometry and analysis
special characters
similarity
theorems and definitions
congruent triangles
evidence addressing
equivalent definitions
evidence suggests
with the computer
mixed contracts
Chapter6 Working with algebra
xxxxxxx
resolve dissolve
algebra with fractions
count with roots
sets of equations
equivalent formulas
geometric applications
mixed exercises
xxxxxxx
Block4 Blok 4
Refresh
§1
§2
§3
§4
§5
§6
§7
§8
Chapter7 Periodic functions
trigonometric ratios
periodic motion
properties of sinusoids
Solving Equations
shift and deform
General shape of sinusoid
mixed exercises
xxxxxxx xxxxxxx
Chapter8 of the derivative
Linear functions
increase diagrams
mean change
slopes approaching
Slopes exactly
the derivative function
differentiate
power functions
mixed orders
Dutch program (5 VWO mathematics A) Chapter 1 rows
Chapter 2 changes
Chapter 3 the derivative function
Chapter 4 Periodic functions
Chapter 5 binomial
Chapter 6 Static processing
Chapter 7 Logarithmic functions
Chapter 8 transformations
1-1 Formulas by rows 1-2 Time graphs
2-1 Increase diagrams 2-2 Inflection points
3-1 Calculate slopes
7-1 Growth times
8-1 Shifting graphs
6-2 Classification
7-2 Logarithms
8-2 Translations
2-3 Average changes
6-3 Cumulative frequency
7-3 Calculating logarithms
1-4 Geometric sequences
2-4 Speed and slopes
3-3 Polynomial function differentiate 3-4 Slopes and tangents
5-1 The triangle of Pascal 5-2 Binomial distribution 5-3 Working with binomial distribution 5-4 Cumulative binomial distribution
6-1 Frequencies
1-3 Arithmetic rows
4-1 Periodic movement 4-2 Degrees and radians 4-3 The sine function
6-4 Data in image
7-4 Graphs of logarithmic functions
8-3 Vertical elongation and contraction 8-4 Horizontal elongation and contraction
1-5 Sum of a geometric sequences
2-5 Work with the slopes
6-5 Dispersion
7-5 Calculation rules for logarithms
6-6 Standard deviation
7-6 Logarithmic scales
3-2 Power Calculus
3-5 Extreme values
4-4 The cosine function
4-5 Stretching and shrinking
4-6 Vertically shifting
5-5 Expectation value
8-5 Combining transformations
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5 grade Mathematics B Chapter 1 summary: It’s about logarithmic function. It tells about exponents and powers. It also teaches us aout how to calculate logarithms with certain rules.
Chapter 2 summary:
It tells us about the transformations of graphs. For example the shifting of graphs horizontally and vertically but also making it steeper or wider.
Chapter 3 summary:
Differentiating. It’s about powers and negative and broken exponents. F urthermore, it talks about the chain-rule and chain-functions. but also about bending points.
Chapter 4 summary:
Integrals. It teaches us about area and the ways of calculating differ shapes’ areas as accurate as possible.
Chapter 5 summary:
It informs us about Geographical areas (Shapes, figures), and it will teach us how to draw the inner circle and outer circle of a triangle. It also tells us about the construction of lines, figures, -mainly circular shapes-.
Chapter 6 Summary:
It teaches us about the the Circle, mainly, its properties: The constant angle, chord-triangle, circle bows. Also, the geographical area of a constant angle.
Chapter 7 summary:
Chapter 7 Subjects the trigonometric functions, frequencies and phase differences, usage of the ‘sine’ and ‘cosine’ functions (squared).
Chapter 8 Summary:
Is about the product and Quotient-rule and formula, and also rewinds Asymptotes, this chapter focuses of the economical usage of math, mainly.
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These are the subjects we get in the 6 grade VWO at mathematics A ( So the highest form on middle/high school )
Chapter 1: calculus
Chapter 2: chainrule
Chapter 3: distributions
Chapter 4: Normal distributions
Chapter 5: Hypothesis tests
Broken functions
Chain functions
Standard deviation for a probability distributions
The normal distributions
True or not true
Power calculus
The chainrule
Binomial distribution
Count back
Tests for significance
Product rule
Using the chainrule
Divisions, continuous and discrete
Normal or nonnormal
Binomial tests
Ratio rule
Inflection points
Calculation rules for random variables
Normal distributions with discrete values
Double sided binomial tests
The root-n-law
Approach by normal distributions
The calculation test
The conduct of functions
A test for the mean
VWO 6th grade Mathematics B Chapter 1
Subject Exponential and logaritmic functions
What to learn?
2
Perodic movements
3
Conflict lines
4
Conic section
5
Goniometric formulas
6
Applied analyse
Another base Number e Natural logarithm Devirative functions Primatives Mixed exercises (all the previous exercises together) Parameter introduction Special points Lissajous figures Reforming Speed Mixed exercises Distance to an area Iso-distance lines Distance to an edge Conflict lines Conflict Lines with GeoGebra Parabol Ellips and hyperbola Mixed exercises Conic section Parabols Ellips Hyperbolas Mixed exercise Symmetry properties Sum formulas Formulas of Simpson How to use formulas? Mixed exercises Upper most values and bendingpoints Intergral and content Rotation albodies Length of a curve Applications of intergral Mixed exercise
