Direct and inverse proportionIB MYP Maths Extended: Subtopic test

1. 1
   $y$ is directly proportional to $x$, and $y=18$ when $x=4$.

   (a)

   Which equation connects $y$ and $x$?

   [1 mark]

   • A$y=x+14$
   • B$y=\frac{72}{x}$
   • C$y=4.5x$
   • D$y=\frac{x}{4.5}$

   (b)

   Find $y$ when $x=10$.

   [1 mark]

   • A$24$
   • B$7.2$
   • C$40$
   • D$45$

   (c)

   Find the value of $x$ when $y=63$.

   [2 marks]

   Total for question 1: 4 marks

2. 2
   $p$ is inversely proportional to $q$, and $p=6$ when $q=5$.

   (a)

   Write $p=\frac{k}{q}$. Find the constant $k$.

   [1 mark]

   • A$1.2$
   • B$30$
   • C$11$
   • D$\frac{5}{6}$

   (b)

   Which statement describes the graph of $p$ against $q$ for $q>0$?

   [1 mark]

   • Aa curve that falls as $q$ increases and never touches either axis
   • Ba straight line through the origin with positive gradient
   • Ca straight line with negative gradient
   • Da curve that starts at the origin and rises

   (c)

   Find the value of $q$ when $p=4$.

   [2 marks]

   Total for question 2: 4 marks

3. 3
   A currency exchange in Doha gives USD $68.50$ for QAR $250$, at a fixed rate with no commission.

   (a)

   Find how many USD are given for QAR $1800$.

   [3 marks]

   (b)

   A tourist wants USD $150$ at the same rate. (i) Find how many QAR she must pay, to the nearest riyal. (ii) Her friend works out $0.274\times150=41.10$ QAR. Explain the mistake and why $41.10$ cannot be right.

   [4 marks]

   Total for question 3: 7 marks

4. 4
   A school kitchen in Mumbai prepares biryani for a festival. The rice needed is directly proportional to the number of guests: $9$ kg of rice is needed for $60$ guests. The time needed to prepare the meal is inversely proportional to the number of cooks: $5$ cooks need $8$ hours.

   (a)

   (i) Find the amount of rice needed for $200$ guests. (ii) Find the time taken by $8$ cooks. (iii) Find the number of cooks needed to finish in $2$ hours.

   [6 marks]

   (b)

   The head cook plans for $300$ guests. (i) Find the amount of rice needed. (ii) Find the time taken if she uses $12$ cooks. (iii) She suggests using $40$ cooks to finish more quickly. Use the model to find the time for $40$ cooks and comment on whether the model is realistic.

   [6 marks]

   Total for question 4: 12 marks

End of questions