Early Algebra
Early algebra introduces using letters to represent unknown numbers, including simplifying expressions by collecting like terms, substituting numbers into expressions, expanding brackets, and solving simple equations. In 11+ maths papers these skills are often applied to word problems, number puzzles and shape problems where an equation must be formed and then solved.
Before you start
Make sure you're comfortable with these topics first:
Method
- Collect like terms by adding or subtracting the numbers in front of identical letters, such as 3a + 5a = 8a; different letters cannot be combined.
- To substitute values, replace each letter with its given number and then calculate carefully, remembering that a negative number squared is positive.
- To expand brackets, multiply everything inside the bracket by the number (or term) directly outside it.
- To solve a simple equation, do the same operation to both sides to isolate the letter: undo addition or subtraction first, then multiplication or division.
- When the letter appears on both sides, collect all the letter terms on one side and all the number terms on the other before solving.
- Check your solution by substituting it back into the original equation to see that both sides match.
Worked example
Solve the equation 4(x + 3) = 2(3x - 1).
- Expand the brackets on both sides: 4x + 12 = 6x - 2.
- Subtract 4x from both sides: 12 = 2x - 2.
- Add 2 to both sides: 14 = 2x.
- Divide both sides by 2: x = 7.
- Check: 4(7 + 3) = 40 and 2(3 x 7 - 1) = 40, so both sides match.
Practice questions
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Exam-style questions
Written in the style of a 11+ exam paper, with a full mark scheme.
Expand and simplify 4(x + 3) + 2(x - 1).
A rectangle has length (x + 6) cm and width (x - 1) cm. The perimeter of the rectangle is 30 cm. (a) Show that 4x + 10 = 30. (b) Solve the equation to find x. (c) Find the length and width of the rectangle.
A pattern is made from triangles. Pattern 1 has 5 triangles, pattern 2 has 8 triangles and pattern 3 has 11 triangles. The number of triangles increases by 3 for each new pattern. (a) Calculate the number of triangles in pattern 6. (b) Find an expression, in terms of n, for the number of triangles in pattern n. (c) A pattern in the sequence has 74 triangles. Calculate which pattern number this is.
Free printable worksheet
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