# Akriel Development Plan 2019

**Topics in years 6-10, which have been prepared:**

- prime factorisation of composite numbers
- finding the greatest common divisor
- finding the least common multiple
- multiplying and dividing powers with identical bases
- raising powers to powers
- collecting like terms in algebraic expressions
- multiplying monomials
- dividing monomials
- multiplication monomials with multi-term expressions
- expanding brackets
- factorisation
- simplifying algebraic fractions (year 7)
- linear equations
- linear fractional equations
- multiplication multi-term algebraic expressions
- square of a sum and square of a difference
- product of the sum and difference of two terms
- factorising with the help of the special square products
- algebraic fractional equations
- factorisation with grouping
- powers of product and fraction
- square of a trinomial
- third power of a sum and a difference
- factorisation with the help of special products involving cubes
- quadratic formula
- algebraic fractional quadratic equations

## Future Plans

**2019, Spring: March-May**

deadline: 31st May 2019

Year 5:

- simplifying fractions
- finding equivalent fractions with multiplying the numerator and the denominator with the same number
- addition and subtraction of fractions with identical denominators
- addition and subtraction of fractions with different denominators
- multiplying fractions with natural numbers
- dividing fractions with natural numbers
- addition and subtraction of integers

Year 6:

- multiplying integers
- dividing integers
- raising to powers
- powers of negative numbers
- simplifying fractions using GCD
- finding the common denominator using LCM
- addition and subtraction of negative fractions
- multiplying and dividing fractions with whole numbers
- multiplying fractions with fractions
- dividing with fraction
- multiplying and dividing negative fractions
- simplifying complex fractions

Year 8:

- addition and subtraction of fractions containing variables as well
- simplifying algebraic fractions (year 8)
- equations with multiple solutions
- solving equations with factorisation

Year 9:

- operations of powers with negative exponents
- multi step factoring
- simplifying algebraic fractions (year 9)
- addition and division of algebraic fractions
- multiplication and division of algebraic fractions
- linear simultaneous equations

Year 10:

- identities of square roots
- putting under and taking out under the radical
- rationalise the denominator of a fraction
- identities of n-th roots
- putting under and taking out under the radical (n-th root)
- rationalise the denominator of a fraction (n-th root)
- further identities of n-th root

Year 11:

- operation of powers with fractional exponents
- exponential equations
- operations with logarithmic expressions, logarithmic identities
- logarithmic equations

Year 12:

- revision algebraic exercises for the final exam

**2019, Summer: June-August**

Topics of primary schools (years 1-4)

Deadline: 31st August 2019

Year 1:

- addition up to 5
- subtraction up to 5
- addition and subtraction up to 10
- addition and subtraction up to 20 without carrying
- addition up to 20 with carrying
- subtraction up to 20 with carrying

Year 2:

- addition and subtraction up to 100 with whole tens
- addition and subtraction up to 100 without carrying
- addition up to 100 with carrying
- subtraction up to 100 with carrying
- addition and subtraction of two-digit numbers up to 100
- using brackets
- multiplication and division up to 10
- multiplication and division up to 20

Year 3:

- addition and subtraction up to 1000 with whole tens and hundreds
- addition up to 1000 with carrying hundreds
- written addition up to 1000
- subtraction up to 1000
- written subtraction up to 1000
- multiplication up to 1000
- written multiplication up to 1000
- division up to 1000

Year 4:

- oral addition and subtraction up to 10.000
- written addition and subtraction up to 10.000
- oral multiplication up to 10.000
- written multiplication up to 10.000
- oral division up to 10.000
- written division up to 10.000
- written multiplication with multi-digits multiplier
- written division with multi-digits divisor
- written addition and subtraction up to 100.000
- written multiplication and division up to 100.000

**2019, autumn: September-November**

Deadline: 30th November 2019

Year 9:

- linear inequalities
- absolute value equations
- absolute value inequalities

Year 10:

- factorising using the factored form of a quadratic equation
- simplifying algebraic fractions (year 10)
- higher degree equations which can be solved as a quadratic equation
- quadratic inequalities
- simple quadratic simultaneous equations
- square root equations
- square root inequalities

Year 11:

- exponential inequalities
- exponential simultaneous equations
- logarithmic inequalities
- logarithmic simultaneous equations

**2019, December- 2020, January**

Deadline: 31st January 2020

Year 5:

- rewriting improper fractions as mixed numbers
- addition and subtraction of mixed numbers
- rewriting fractions as decimals
- addition and subtraction of decimals
- multiplication and division of decimals with natural numbers
- simplifying decimals and expanding decimals

Year 6:

- merging decimals
- multiplication decimals with decimals
- division decimals with decimals

**Further Planned Topics from 2020 (there is no deadline):**

- word problems (practising equations and simultaneous equations)
- parametric linear equations
- parametric quadratic equations
- square root simultaneous equations
- trigonometric equations
- trigonometric inequalities
- limits if functions
- limits of sequences
- derivatives of composite functions
- derivatives of different types of functions
- definite integral: Riemann –integral
- methods of integration (integration by partial fractions and rational fraction)
- indefinite integral

The bigger topics are prepared in many different topics in Akriel, therefore the expected number of future topics will be much more than it is in the development plan. You can calculate with the following minimum number of topics per year group:

- Year 1: 6 topics
- Years 2-4: 10-10 topics
- Years 5-12: 20-20 topics

The complete learning material of Akriel will contain more than 200 algebraic topics in total.