Equations

An equation says that two things are equal. It is like a balance: whatever is on one side weighs the same as whatever is on the other. In this topic you'll learn to tell equations from expressions, check whether a number is a solution, write rules that link the numbers in a table or a growing pattern, and solve equations by undoing operations step by step. Solving equations is one of the most useful skills in algebra, and you'll keep using it for the rest of high school.

What you'll learn

• 9.01 Introduction to equations: the difference between an equation and an expression, checking a solution by substituting it, and writing equations from words.
• 9.02 Write rules for relationships: finding the rule that links x and y in a table of values or a growing pattern, such as y = 3*x* + 2, and using it to predict.
• 9.03 One-step equations: solving equations like x + 7 = 15 and 4*x* = 36 with inverse operations, keeping both sides balanced.
• 9.04 Two-step equations: solving equations like 3*x* + 5 = 26 by backtracking, and writing and solving equations for word problems.

Which level should I pick?

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

• Level 1 · Warm-up: smaller numbers and more help along the way. A good place to start.
• Level 2 · Core: the main worksheet for the lesson.
• Level 3 · Challenge: bigger numbers, brackets, 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.