### Long grammar schoolpreparation

Mathematics subject

- Place value, written arithmetic, rule of parentheses
- Understand the breakdown of the number in the decimal system, read off the place value, decimal point shift for multiplication / division by 10.
- Perform 100, apply basic operations to natural and decimal numbers, understand bracket rule and dot before dash.

- Divisor, multiple, cross sum and cross prod.
- Represent a natural number as a product of its divisors (in different ways), find the common divisor by trial and error.
- find natural numbers that satisfy certain conditions (concerning cross sum/cross product, even/odd, place value, divisor, etc.),
- solve simple sentence problems concerning divisors / multiples

- Understand and be able to calculate fractions and decimals
- Add, subtract, multiply with natural numbers, compare, expand, shorten, equate fractions, convert to decimals and mixed numbers (and vice versa).
- Order fractions, decimals, and mixed numbers by size.

- Length, hollow, time and weight measure
- Perform basic operations with different quantities and interpret the result.
- Convert units of length, volume, mass, and time.
- Perform basic operations with multiple units and specify the result in the desired form.

- Solve equations by calculating backwards
- Solve simple equations (with a placeholder/box), trace convoluted equations back to simple equations and solve by working backwards, form equations from sentence problems and solve them.

- Set tasks with multiple unknowns
- express two dependent unknowns by an equation, from sentence tasks (which contain at least two unknowns)
- form several equations and solve them by combining them, solve typical sentence tasks with mixing process, filling process etc.

- Proportionality and inverse proportionality
- solve simple two- and three-set tasks with proportional or inversely proportional quantities, solve typical set tasks on work, time, quantity, number, etc.

- Sentence tasks with fractions
- skillfully represent a given quantity as a fraction and calculate a specific fraction of it using a two- and three-step rule, subtract multiple fractions of a quantity from the quantity itself and calculate the initial or remainder quantity, calculate task types such as "fraction of a fraction of a quantity"

- Path - Time - Speed
- Learn and describe abbreviations of selected speed units, practice simple "lead" with a two or three sentence sentence, solve many sentence problems, perform speed-distance-time calculations, perform task types with "catch up, lap

- Counting, arranging and pairing
- Learn and describe abbreviations of selected speed units, perform simple speed-distance-time calculations using a two- or three-step rule, practice task types with "catch up, laps ahead," solve many sentence tasks

- In the triangle and quadrangle
- Perform perimeter and area calculations of triangles, quadrilaterals, and figures. Calculate a given area as a composition, given the perimeter of the rectangle and the dependence on length and width.

- Space and plane
- Draw views of a 3D figure, complete a given 3D figure into a cube, remove from a cube certain parts in the head and draw the result, systematically count number of cube faces of a given 3D figure (which consists of cubes), rotate a 3D figure along an axis(es) and draw or compare the result, flip a 3D figure to different directions and draw the result, rotate and flip 2D figures, draw and compare cube meshes.

- Numbers & Figures
- Recognize the evolution of given 2D and 3D figures and draw missing links. Express a sequence of patterns by a sequence of numbers and calculate quantities sought. Determine whether a sequence of numbers is finite or infinite and whether or not its members obey a rule. Form a given sequence from given digits. Calculate the members of a sequence of numbers.

- Length, angle/ bisector, perpendicular, parallel
- Learn different representations of distances, straight lines, rays and angles. Draw a line with a compass on a straight line/radius.
- Move a line parallel through a point with a triangle. Construct any parallel of a straight line without a set square.
- Construct a given length from given distances using a compass. Construct perpendiculars.
- Measure angles, add them together and measure them with the triangle. Construct angle bisectors. Construct special angles (such as 30º, 45º angles) without a triangle.
- Construct rhombus and rhomboid.

### Long grammar schoolpreparation

German subject

- Expand vocabulary, find words with similar (synonyms) or opposite meaning (antonyms), use synonyms/antonyms in text context, expand foreign word knowledge.

- Expand vocabulary, know superordinates and subordinates, form new words by derivation and composition, know common homonyms (words with different meanings), complete analogies, use appropriate terms.

- Expand vocabulary, distinguish word families from word fields, know and use common noun and adjective endings, form word families, modify verbs using prefixes, use word family terms appropriate to context.

- Expand vocabulary; know, correct, complete, and explain twin/pair formulas, idioms, and proverbs.

- Know four cases, determine the case of expressions, put terms in the correct case.

- Forms and times
- Know finite and infinite verb forms, determine and form tenses

- Distinguish five types of words, know specific characteristics of each type of word.

- Know and use displacement test; rephrase, shorten, extend and connect sentences.

- Know and apply common spelling rules, correct spelling errors, spell words correctly.

- Set punctuation marks, know and apply most common comma rules, set the marks in direct speech.

For more information on entrance exams to secondary schools in the Canton of Zurich, please visit the website of the Department of Education of the Canton of Zurich: