1. 1
   A straight line has equation $y = 2x - 5$.

   (a)

   What is the gradient of the line?

   [1 mark]

   • A5
   • B$-5$
   • C2
   • D$-2$

   (b)

   Which of the following lines is parallel to $y = 2x - 5$?

   [1 mark]

   • A$y = -2x - 5$
   • B$y = 2x + 3$
   • C$y = \frac{1}{2}x - 5$
   • D$y = 2 - 5x$

   (c)

   At what value of $x$ does the line $y = 2x - 5$ cross the $x$-axis?

   [1 mark]

   • A$x = 2$
   • B$x = -2.5$
   • C$x = 5$
   • D$x = 2.5$

   Total for question 1: 3 marks

2. 2
   A function is defined as $f(x) = 3x + 4$.

   (a)

   Calculate $f(5)$.

   [2 marks]

   (b)

   Find the inverse function $f^{-1}(x)$, and hence find $f^{-1}(19)$.

   [2 marks]

   Total for question 2: 4 marks

3. 3
   A quadratic function is given by $g(x) = x^2 - 6x + 5$.

   (a)

   Factorise $g(x)$ and hence find the roots of the equation $g(x) = 0$.

   [3 marks]

   (b)

   By completing the square, find the coordinates of the turning point of the graph of $g(x) = x^2 - 6x + 5$.

   [3 marks]

   Total for question 3: 6 marks

4. 4
   A cyclist's journey is modelled by $s = 5t^2$ for the first 4 seconds, where $s$ is the distance travelled in metres and $t$ is the time in seconds.

   (a)

   Calculate the average speed of the cyclist between $t = 1$ and $t = 3$ seconds.

   [4 marks]

   (b)

   Estimate the instantaneous speed of the cyclist at $t = 2$ seconds by calculating the gradient of the chord between $t = 1.9$ and $t = 2.1$ seconds.

   [4 marks]

   (c)

   After $t = 4$ seconds, the cyclist maintains a constant speed equal to her instantaneous speed at $t = 4$, estimated using the gradient of the chord between $t = 3.9$ and $t = 4.1$ seconds.
   
   Calculate this constant speed, then find the total distance she travels in a further 10 seconds at this speed.

   [5 marks]

   Total for question 4: 13 marks

End of questions