Worksheets · Foundation and Higher

Algebraic language and notation

3 exam-style questions. Answers and the mark for each step are on the last page.

1. Question 1Non-calculator · 4 marks

   Simplify or write each expression.

   (a) Simplify $a + a + a + a$ (1)

   (b) Simplify $3 \times m \times n$ (1)

   (c) Pens cost $45$p each and rubbers cost $30$p each. Write an expression for the total cost, in pence, of $x$ pens and $y$ rubbers. (2)
2. Question 2Non-calculator · 4 marks

   A rectangle has length $(x+3)$ cm and width $x$ cm.

   (a) Write and simplify an expression for its perimeter. (2)

   (b) The perimeter is 30 cm. Find x. (2)
3. Question 3Non-calculator · 4 marks

   A rectangle has length $(2x + 3)$ cm and width $x$ cm. A square has sides of length $(x + 2)$ cm.

   (a) Show that the perimeter of the rectangle is $(2x - 2)$ cm more than the perimeter of the square. (3)

   (b) $x$ is a whole number. Explain why the perimeter of the rectangle is always a multiple of 6. (1)