Straight linesAQA A-Level Maths: Subtopic test

1. 1
   The line $l_1$ passes through $A(1,2)$ and $B(5,12)$.

   (a)

   Find the gradient of $l_1$.

   [1 mark]

   • A$\frac{2}{5}$
   • B$\frac{5}{2}$
   • C$\frac{7}{3}$
   • D$-\frac{5}{2}$

   (b)

   Which of these is an equation of $l_1$?

   [1 mark]

   • A$5x-2y-1=0$
   • B$2x-5y+8=0$
   • C$5x+2y-9=0$
   • D$5x-2y+1=0$

   (c)

   Find the coordinates of the point where $l_1$ crosses the $y$-axis.

   [2 marks]

   Total for question 1: 4 marks

2. 2
   The line $m$ has equation $3x+4y-12=0$.

   (a)

   Find the gradient of $m$.

   [1 mark]

   • A$\frac{3}{4}$
   • B$-3$
   • C$-\frac{4}{3}$
   • D$-\frac{3}{4}$

   (b)

   A line is perpendicular to $m$. What is its gradient?

   [1 mark]

   • A$-\frac{3}{4}$
   • B$\frac{3}{4}$
   • C$\frac{4}{3}$
   • D$-\frac{4}{3}$

   (c)

   Find the equation of the line parallel to $m$ that passes through the point $(8,-1)$. Give your answer in the form $ax+by+c=0$, where $a$, $b$ and $c$ are integers.

   [2 marks]

   Total for question 2: 4 marks

3. 3
   The points $A(2,1)$ and $B(6,3)$ are given.

   (a)

   Find an equation of the perpendicular bisector of $AB$, giving your answer in the form $ax+by+c=0$ where $a$, $b$ and $c$ are integers.

   [3 marks]

   (b)

   The perpendicular bisector of $AB$ meets the $x$-axis at $D$. Find the coordinates of $D$ and the area of triangle $ABD$.

   [4 marks]

   Total for question 3: 7 marks

4. 4
   A taxi company charges a fixed fee plus a constant rate for each kilometre travelled. A 4 km journey costs £9.50 and a 10 km journey costs £20.00. The cost £$C$ of a journey of $d$ km is modelled by a straight line.

   (a)

   Find the equation of the model in the form $C=a+bd$. Interpret the values of $a$ and $b$ in this context, and use the model to find the cost of a 15 km journey.

   [6 marks]

   (b)

   A rival company charges £4.00 plus £1.50 per kilometre. Find the journey length for which the two companies charge the same. A customer says that the rival is always the cheaper company for journeys of more than 6 km. Justify this claim, and state one limitation of using a linear model for very long journeys.

   [6 marks]

   Total for question 4: 12 marks

End of questions