1. 1
   A gym charges a joining fee of $£x$ plus $£y$ per month. Priya's total cost after 6 months can be written as $x + 6y$.

   (a)

   (a) If $x = 20$ and $y = 15$, what is Priya's total cost?

   [1 mark]

   • A£110
   • B£90
   • C£125
   • D£210

   (b)

   (b) Which expression correctly represents simplifying $3x + 5y - x + 2y$?

   [1 mark]

   • A$3x + 7y$
   • B$4x + 7y$
   • C$2x + 3y$
   • D$2x + 7y$

   (c)

   (c) The gym also offers a discount so the monthly cost is expressed as $\frac{2y}{5}$. What is $\frac{2y}{5}$ when $y = 15$?

   [1 mark]

   • A3
   • B7.5
   • C6
   • D30

   Total for question 1: 3 marks

2. 2
   A rectangular garden has width $w$ metres and length $(w + 5)$ metres.

   (a)

   (a) Write an expanded expression, in terms of $w$, for the area of the garden.

   [2 marks]

   (b)

   (b) Factorise fully the expression $2w^2 + 10w$, which represents twice the area of the garden.

   [2 marks]

   Total for question 2: 4 marks

3. 3
   A phone plan charges a fixed monthly fee plus a rate per gigabyte (GB) of data. Tom claims that the expression $3(2g + 4) - 2(g - 1)$ for the monthly cost (where $g$ is GB used) simplifies to $4g + 14$.

   (a)

   (a) Show that Tom's simplification is correct by expanding and simplifying $3(2g+4) - 2(g-1)$.

   [3 marks]

   (b)

   (b) Prove that the expression $4g + 14$ (from part (a)) can never equal $4g + 10$ for any value of $g$, and explain what this means about the two expressions.

   [3 marks]

   Total for question 3: 6 marks

4. 4
   A market trader sells apples and oranges. Let $a$ be the price of an apple in pence and $o$ be the price of an orange in pence. A customer buys 3 apples and 2 oranges for a total expression of $3a + 2o$ pence, and the trader also offers a bulk box priced using the expression $2(3a + 2o) - (a + o)$.

   (a)

   (a) Expand and fully simplify the expression $2(3a + 2o) - (a + o)$.

   [4 marks]

   (b)

   (b) If $a = 25$ and $o = 40$, calculate the value of the simplified expression $5a + 3o$ (from part (a)), in pence.

   [4 marks]

   (c)

   (c) The trader wants to factorise the general bulk box expression $5a + 3o$ pence to check for a common factor, but also wants to compare it with a different bundle costing $10a + 6o$ pence. Show that the second bundle's expression can be written as a multiple of the first, and state the multiplier.

   [5 marks]

   Total for question 4: 13 marks

End of questions