Rearranging formulaeIB MYP Maths Extended: Subtopic test

1. 1
   A car accelerates in a straight line with constant acceleration $a$ m/s². It starts at speed $u$ m/s and has speed $v$ m/s after $t$ seconds, where $v=u+at$.

   (a)

   Make $a$ the subject of the formula.

   [1 mark]

   • A$a=\frac{v-u}{t}$
   • B$a=\frac{v+u}{t}$
   • C$a=\frac{v}{t}-u$
   • D$a=(v-u)t$

   (b)

   Make $u$ the subject of the formula.

   [1 mark]

   • A$u=at-v$
   • B$u=v+at$
   • C$u=v-at$
   • D$u=\frac{v-a}{t}$

   (c)

   A car starts at $7$ m/s and reaches $25$ m/s with acceleration $3$ m/s². Rearrange the formula to make $t$ the subject and find $t$.

   [2 marks]

   Total for question 1: 4 marks

2. 2
   The area $A$ of a trapezium with parallel sides $a$ and $b$ and perpendicular height $h$ is $A=\frac{1}{2}(a+b)h$.

   (a)

   Make $h$ the subject of the formula.

   [1 mark]

   • A$h=\frac{A}{2(a+b)}$
   • B$h=\frac{2A}{a+b}$
   • C$h=2A-(a+b)$
   • D$h=\frac{A(a+b)}{2}$

   (b)

   Make $a$ the subject of the formula.

   [1 mark]

   • A$a=\frac{2A}{h}+b$
   • B$a=\frac{2A-b}{h}$
   • C$a=\frac{A}{2h}-b$
   • D$a=\frac{2A}{h}-b$

   (c)

   A trapezium has area $44$ cm$^2$, height $8$ cm and one parallel side $a=7$ cm. Make $b$ the subject of the formula and find $b$.

   [2 marks]

   Total for question 2: 4 marks

3. 3
   The volume $V$ of a cone with base radius $r$ and height $h$ is $V=\frac{1}{3}\pi r^2h$.

   (a)

   Make $r$ the subject of the formula.

   [3 marks]

   (b)

   A cone has height $8$ cm and volume $96\pi$ cm$^3$. Find its radius. A second cone has the same radius and volume $192\pi$ cm$^3$. Find the height of the second cone.

   [4 marks]

   Total for question 3: 7 marks

4. 4
   A stone is dropped from a bridge. The distance $d$ metres it has fallen after $t$ seconds is modelled by $d=5t^2$, ignoring air resistance.

   (a)

   (i) Make $t$ the subject of the formula.
   (ii) The bridge is $80$ m above a river. Find the time the stone takes to reach the river.
   (iii) Show that a stone that falls for twice as long as another stone falls four times as far.

   [6 marks]

   (b)

   On another planet the model is $d=\frac{1}{2}gt^2$, where $g$ m/s² is the acceleration due to gravity.
   (i) Make $g$ the subject of the formula.
   (ii) A stone falls $20$ m in $2.5$ s on this planet. Find $g$.
   (iii) On Earth the model $d=5t^2$ corresponds to $g=10$. Justify which planet has the weaker gravity, and give one limitation of the model.

   [6 marks]

   Total for question 4: 12 marks

End of questions