Algebra

In Year 7 you learned that a letter can stand for a number, and you collected like terms to tidy up an expression. In this topic you'll take algebra further: substituting negative numbers and fractions into formulas, multiplying and dividing terms, simplifying longer expressions, and using the distributive law to expand brackets and to factorise. These are the skills you'll need to solve equations and draw graphs in the next topic.

What you'll learn

• 5.01 Substitution: finding the value of expressions and formulas, including with negative numbers and fractions, and checking whether a value solves an equation.
• 5.02 Add and subtract algebraic terms: collecting like terms with negative coefficients, powers and terms like $xy$ and $yx$.
• 5.03 Multiply and divide algebraic terms: simplifying products like $3a \times 4ab$ and quotients like $\frac{12mn}{4n}$, using the index laws.
• 5.04 Simplify algebraic expressions: the order of operations with algebra, and adding and subtracting algebraic fractions such as $\frac{x}{2} + \frac{x}{5}$.
• 5.05 The distributive law: expanding brackets like $3(2x - 5)$, then collecting like terms.
• 5.06 Numeric factors: factorising by taking out the highest common factor, such as $12x + 18 = 6(2x + 3)$.

Which level should I pick?

Every worksheet comes in three levels. Each one covers the same skills.

• Level 1 · Warm-up: simpler expressions and more help along the way. A good place to start.
• Level 2 · Core: the main worksheet for the lesson.
• Level 3 · Challenge: longer expressions, fractions and problems with more steps, for when the Core level feels easy.

Not sure? Start with Level 2. If the first few questions feel tricky, drop to Level 1. If you finish quickly and get them right, try Level 3. Download the worksheet, print it, and write your answers in the boxes.

Practice tests

When you've finished the lessons, try the three practice tests. Each one is like the real topic test: 45 minutes, 40 marks, a section without a calculator and a section with one. Write your working under each question, then copy your final answers onto the answer sheet on the last page, just like you will in the real test.