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EFFECTIVE MATH & SCIENCE TUITION FOR SECONDARY STUDENTS

#### BlueTree Learning Resources

Our extensive collection of Math & Science resources which includesin-depth exam paper analysis and free cheat sheets, notes, study guides for Secondary Math & Science

## Secondary Science

Are you ready to unlock the secrets of secondary math? Whether you are a parent supporting your child’s learning journey or a student aiming to excel in mathematics, having the right tools at your disposal is essential.

That is why we have compiled a comprehensive cheat sheet covering crucial topics: real numbers, prime numbers, and estimation & approximation. This resource will not only enhance your understanding but also make tackling math problems a breeze. Do not wait any longer—download your free cheat sheet now to kickstart your mathematical success!

## Understanding Real Numbers: Foundation of Mathematics

Real numbers form the bedrock of mathematics, encompassing rational and irrational numbers. Rational numbers can be expressed as fractions, while irrational numbers cannot be written as fractions and include famous contestants like π and √2 (square root 2). Together, they populate the number line, providing a framework for solving a myriad of mathematical problems.

For example, imagine you are dividing a pizza among friends. Each slice represents a fraction of the whole, making fractions a part of real numbers.

1. Natural Numbers: These are the numbers we use for counting: 1, 2, 3, 4, and so on. They are called “natural” because they are the most basic numbers we encounter in the world around us.
2. Whole Numbers: They are like natural numbers but with the addition of zero. Whole numbers are used not only for counting but also for representing quantities.
3. Integers: These include all the positive and negative whole numbers, along with zero. They are a number line that stretches infinitely in both directions, including numbers like -3, -2, -1, 0, 1, 2, 3, and beyond.
4. Rational Numbers: These are numbers that can be expressed as fractions, where the numerator and denominator are both integers. For example, ½, – ¾, and 5 are all rational numbers.
5. Irrational Numbers: Irrational numbers cannot be expressed as fractions. They have decimal expansions that neither end nor repeat. For example, π and √2 (square root 2).

## Cracking the Code of Prime Numbers

Prime numbers, those elusive integers greater than 1 that are only divisible by 1 and themselves, have fascinated mathematicians for centuries. They serve as the building blocks for the integers, playing a fundamental role in number theory and cryptography.

What makes a prime? Prime numbers are special, they can only be divided by 1 and themselves e.g. 2, 3, 5, 7 and 11. Prime Factorisation is the process of breaking down a number into its smallest, indivisible parts. For example, 12 = 2 x 2 x 3.

## Mastering Estimation & Approximation

Estimation and approximation are indispensable skills, allowing us to make informed decisions and navigate the complexities of real-world problems. From calculating rough estimates to determining the reasonableness of solutions, these techniques empower us to tackle mathematical challenges with precision and efficiency. When numbers get too long or complicated, rounding makes them easier to work with.

Estimation involves making educated guesses, or approximations based on available information. For example, if you are at the grocery store and trying to estimate the total cost of your items before reaching the checkout counter, you might round the prices to the nearest dollar and add them up mentally.

Approximation, on the other hand, is about simplifying complex calculations by replacing exact values with simpler ones that are close enough for practical purposes. For instance, if you are calculating the area of a circle and you know the value of π is approximately 3.14, you can use this approximation to get a rough estimate of the area without having to use the exact value of π.