Solving quadratic equationsIB MYP Maths Standard: Subtopic test

1. 1
   A quadratic equation is $x^2-5x-14=0$.

   (a)

   Which of the following is the correct factorised form of $x^2-5x-14$?

   [1 mark]

   • A$(x+7)(x-2)$
   • B$(x-7)(x+2)$
   • C$(x-7)(x-2)$
   • D$(x+14)(x-1)$

   (b)

   What is the sum of the two solutions of the equation?

   [1 mark]

   • A$-5$
   • B$9$
   • C$-14$
   • D$5$

   (c)

   Write down the coordinates of the points where the graph of $y=x^2-5x-14$ crosses the $x$-axis.

   [2 marks]

   Total for question 1: 4 marks

2. 2
   A ball is thrown upwards from a platform. Its height $h$ metres above the ground after $t$ seconds is modelled by $h=-5t^2+10t+15$.

   (a)

   Find the height of the ball when $t=1$.

   [1 mark]

   • A$20$ m
   • B$30$ m
   • C$10$ m
   • D$25$ m

   (b)

   Which equation must be solved to find when the ball is 10 m above the ground?

   [1 mark]

   • A$t^2-2t-3=0$
   • B$t^2-2t-5=0$
   • C$t^2-2t-1=0$
   • D$t^2+2t-1=0$

   (c)

   Solve $-5t^2+10t+15=0$ by factorising, and hence state how long the ball takes to hit the ground.

   [2 marks]

   Total for question 2: 4 marks

3. 3
   Consider the quadratic equation $3x^2-4x-5=0$.

   (a)

   Use the quadratic formula to solve the equation. Give your answers correct to 3 significant figures.

   [3 marks]

   (b)

   (i) The equation $3x^2-4x+k=0$ has exactly one solution. Find the value of $k$.
   (ii) Hence solve $3x^2-4x+k=0$.

   [4 marks]

   Total for question 3: 7 marks

4. 4
   A community school in Nairobi is marking out a rectangular vegetable garden. The length of the garden is 3 m more than its width.

   (a)

   The garden must have an area of $54$ m$^2$. Let the width be $x$ m. Form a quadratic equation in $x$, solve it, and state the width and length of the garden. Explain why one of the solutions is rejected.

   [6 marks]

   (b)

   The school plans a second, larger garden of the same shape with an area of $100$ m$^2$ and width $w$ m.
   (i) Show that $w^2+3w-100=0$.
   (ii) Use the quadratic formula to find the width and length of the garden, to 3 significant figures.
   (iii) Fencing is sold in rolls of 5 m. How many rolls are needed to fence the whole perimeter? Justify your answer.

   [6 marks]

   Total for question 4: 12 marks

End of questions