IB myp 4-5 MATHEMATICS – Practice Questions- All Topics
Topic :Geometry–Gradients of perpendicular lines
Topic :Geometry- Weightage : 21 %
All Questions for Topic : Volume and capacity (additional shapes),Enlargement around a given point,Enlargement by a rational factor,Gradients of perpendicular lines,Identical representation of transformations
Question (a)
Robot 1 is at point $S$. It moves following the vector $3 a-c-2 b$. Label the grid to show the path of Robot 1.
▶️Answer/Explanation
Ans:
Question (b)
Robot 2 is at point $\mathrm{M}$. It must collect books from point $\mathrm{P}$ and then deliver them to the conveyor belt. Determine the vector of path of Robot 2, in terms of $\boldsymbol{a}, \boldsymbol{b}$ and $\boldsymbol{c}$, in its simplest form.
▶️Answer/Explanation
Ans:
$–2b + 3.5a – 4b$ or $4a – 2b – 0.5a – 4b$
Question (c)
4 robots can prepare 15 orders in 3 minutes. Calculate how many minutes it would take 10 robots to prepare 300 orders.
▶️Answer/Explanation
Ans:
Given that 4 robot can prepare 15 orders in 3 minutes
So, 1 robot can prepare 3.75 orders $\frac{14}{4}$
and 10 robots can prepare 37.5 orders, the ratio of orders to robots is the same. Therefore:
\[\frac{300}{37.5} = 8\]
This means that with 10 robots, it would take 8 units of time to prepare 300 orders. Since each unit of time corresponds to 3 minutes (as given in the problem), the total time would be:
\[8 \times 3 = 24\]
So, it would take 24 minutes for 10 robots to prepare 300 orders.