Linear functions and graphsIB MYP Maths Extended: Subtopic test

1. 1
   A straight line has equation $y=-2x+6$.

   (a)

   What is the gradient of the line?

   [1 mark]

   • A$-2$
   • B$2$
   • C$6$
   • D$-\frac12$

   (b)

   At which point does the line cross the $x$-axis?

   [1 mark]

   • A$(0,6)$
   • B$(6,0)$
   • C$(3,0)$
   • D$(-3,0)$

   (c)

   The line, the $x$-axis and the $y$-axis form a triangle. Find the area of this triangle.

   [2 marks]

   Total for question 1: 4 marks

2. 2
   A straight line passes through the points $A(1,3)$ and $B(5,11)$.

   (a)

   Find the gradient of the line $AB$.

   [1 mark]

   • A$\frac12$
   • B$2$
   • C$4$
   • D$8$

   (b)

   Which is the equation of the line $AB$?

   [1 mark]

   • A$y=2x+3$
   • B$y=2x-1$
   • C$y=\frac12x+\frac52$
   • D$y=2x+1$

   (c)

   Determine whether the point $C(10,20)$ lies on the line $AB$.

   [2 marks]

   Total for question 2: 4 marks

3. 3
   A swimming pool is being filled at a constant rate. After 2 minutes it holds 150 litres of water, and after 6 minutes it holds 450 litres. The volume $V$ litres after $t$ minutes follows a linear relationship.

   (a)

   Find the gradient of the line and hence write down the equation for $V$ in terms of $t$.

   [3 marks]

   (b)

   (i) Explain what the gradient and the $y$-intercept mean in this situation.
   (ii) The pool holds 3000 litres when full. How long does it take to fill?

   [4 marks]

   Total for question 3: 7 marks

4. 4
   A gym in Cairo offers membership plans. Plan A has a joining fee of 300 Egyptian pounds (EGP) plus 100 EGP per month. Plan B has no joining fee and costs 160 EGP per month.

   (a)

   (i) Write an equation for the total cost $y$ EGP of each plan after $m$ months.
   (ii) Find the number of months for which the two plans cost the same, and find that cost.
   (iii) A member joins for one year (12 months). Which plan is cheaper, and by how much?

   [6 marks]

   (b)

   The gym introduces Plan C. A member who stays for 3 months pays a total of 540 EGP, and a member who stays for 6 months pays a total of 870 EGP. The total cost is a linear function of the number of months.
   (i) Find the gradient and the equation of the line for Plan C.
   (ii) Find the number of months for which Plan A and Plan C cost the same.
   (iii) Justify which of Plan A or Plan C is better value for a member who stays 12 months.

   [6 marks]

   Total for question 4: 12 marks

End of questions