Algebra and Sequences

Algebra is the part of maths where we use letters to stand for unknown numbers. In the CEM 11+ exam, algebra questions can appear in many forms — from simple "find the missing number" puzzles to function machines and number sequences. CEM papers sometimes present algebra in unfamiliar layouts, so it is important to understand the underlying ideas, not just memorise methods.

---

Using Letters for Numbers

In algebra, letters like a, b, n, and x represent numbers we do not know yet:

• 3a means 3 × a
• ab means a × b
• a² means a × a
• 2a + 5 means "double a, then add 5"

CEM Tip: CEM questions may not always use x. They might use shapes, blanks, or other symbols to represent the unknown. The method is exactly the same.

---

Simplifying Expressions

Collect like terms (terms with the same letter) together:

Worked Example

Simplify: 3a + 5b + 2a - b

• Collect the a terms: 3a + 2a = 5a
• Collect the b terms: 5b - b = 4b

Answer: 5a + 4b

More Examples