Factorising quadratics with leading coefficient not 1IB MYP Maths Extended: Subtopic test

1. 1
   Consider the quadratic equation $6x^2+7x-3=0$.

   (a)

   Find the value of the discriminant $b^2-4ac$.

   [1 mark]

   • A$25$
   • B$-23$
   • C$121$
   • D$67$

   (b)

   Which is the fully factorised form of $6x^2+7x-3$?

   [1 mark]

   • A$(3x-1)(2x+3)$
   • B$(3x+1)(2x-3)$
   • C$(6x-1)(x+3)$
   • D$(6x+3)(x-1)$

   (c)

   Solve the equation, using your factorised form.

   [2 marks]

   Total for question 1: 4 marks

2. 2
   A rectangular garden has area $(2x^2+5x-12)$ m$^2$ and length $(x+4)$ m, where $x>0$.

   (a)

   Find an expression for the width of the garden, in metres.

   [1 mark]

   • A$(2x+3)$
   • B$(2x-3)$
   • C$(x-3)$
   • D$(2x-12)$

   (b)

   The area of the garden is $63$ m$^2$. Which value of $x$ gives valid dimensions?

   [1 mark]

   • A$x=-7.5$
   • B$x=7$
   • C$x=9$
   • D$x=5$

   (c)

   Find the perimeter of the garden when the area is $63$ m$^2$.

   [2 marks]

   Total for question 2: 4 marks

3. 3
   A ball is thrown upwards from a platform. Its height above the ground, $h$ metres, after $t$ seconds is modelled by $h=12+4t-5t^2$, for $t\geq0$.

   (a)

   Find the time at which the ball hits the ground, by factorising.

   [3 marks]

   (b)

   Use the quadratic formula to find when the ball is $10$ m above the ground. Give your answer to 3 significant figures and explain why only one solution is valid.

   [4 marks]

   Total for question 3: 7 marks

4. 4
   A bakery in Nairobi models its weekly profit, $P$ thousand Kenyan shillings, by $P=-2x^2+11x-12$, where $x$ is the number of hundreds of loaves sold that week and $1\leq x\leq5$.

   (a)

   (i) Factorise $-2x^2+11x-12$ and hence find the numbers of loaves at which the bakery breaks even ($P=0$).
   (ii) State the numbers of loaves for which the bakery makes a profit.
   (iii) Find the greatest profit predicted by the model.

   [6 marks]

   (b)

   (i) Use the quadratic formula to find the values of $x$ for which $P=2$.
   (ii) The owner claims that selling $500$ loaves gives the best result. Evaluate this claim using the model, and state one limitation of the model.

   [6 marks]

   Total for question 4: 12 marks

End of questions