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MCAT Summaries

This resource outlines essential methods for simplifying algebraic expressions, tailored for MCAT success. It covers four main operations: adding and subtracting like terms, multiplying, dividing, and handling powers. The document explains how to expand expressions using single and double brackets, including methods like FOIL and long multiplication. Additionally, it details factorization techniques and solving equations, focusing on moving variables and constants, simplifying, and solving normal and quadratic equations. Perfect for students seeking to reinforce their algebra skills for the MCAT.

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MCAT Summaries

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  1. MCAT Summaries

  2. Simplifying Simplifying has 4 methods: • Adding and Subtracting Only if letters and powers are the same Only add or subtract the big numbers • Multiplying Multiply numbers Write all letters (use powers if you can) • Dividing Simplify any numbers just like a fraction Cancel out letters that are on both top and bottom • Powers Write as a multiplication then solve.

  3. Expanding There are two main types of expanding: • Single Bracket Multiply EACH thing in the bracket by whatever is outside the bracket. • Double Bracket (3 methods) Long (Split the first bracket) FOIL (Front, outside, inside and last) Fast (x2, add with an x, multiply) Some questions might need more than one step.

  4. Factorising Single Brackets or Double Brackets • Single Brackets Outside the brackets write the highest dividing number and any common letters. Inside the brackets write the leftover numbers and letters. • Double Brackets Find numbers that multiply to make the last number but add to make the middle number. Write them in the brackets

  5. Solving For normal equations or quadratics. Normal • Move the letters to the left of the = Do this by swapping, adding or subtracting. • Simplify • Move the numbers to the right of the = Do this by doing the opposite of what the number is doing to the letter. • Simplify

  6. Quadratics • Make the equation equal zero. • Factorise • Solve 2 equations by making each bracket equal zero. • Both answers are usually the answer but be careful that they make sense in word equations.

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