Variations: practice questions

6 questions · 12 marks · free, no account · Read the notes first

1. Question 1Multiple choice · 1 mark

   $y$ varies directly as $x$, and $y = 12$ when $x = 4$. Find $y$ when $x = 10$.

   A

   $40$

   B

   $15$

   C

   $30$

   D

   $3$

2. Question 2Multiple choice · 1 mark

   $y$ varies inversely as $x^2$. If $x$ is doubled, then $y$ is

   A

   halved

   B

   decreased by 75%

   C

   decreased by 25%

   D

   multiplied by 4

3. Question 3Multiple choice · 1 mark

   $z$ varies jointly as $x$ and $y$. If $x$ increases by 20% and $y$ decreases by 20%, then $z$

   A

   is unchanged

   B

   increases by 4%

   C

   decreases by 4%

   D

   decreases by 40%

4. Question 4Multiple choice · 1 mark

   If $y$ varies inversely as $x$, which of the following must be a constant?

   A

   $x + y$

   B

   $\dfrac{y}{x}$

   C

   $x - y$

   D

   $xy$

5. Question 54 marks

   $y$ is partly constant and partly varies as $x$. When $x = 2$, $y = 7$; when $x = 5$, $y = 13$. Find $y$ when $x = 8$.

   Show worked solution

   Let $y = a + bx$, where $a$ and $b$ are non-zero constants. 1M

   $a + 2b = 7$ and $a + 5b = 13$ 1M

   Solving, $a = 3$ and $b = 2$. 1A

   When $x = 8$, $y = 3 + 2(8) = 19$. 1A

6. Question 64 marks

   The time $T$ hours needed to finish a job varies directly as the number of tasks $n$ and inversely as the number of workers $w$. 6 workers can finish 30 tasks in 10 hours. How many workers are needed to finish 45 tasks in 9 hours?

   Show worked solution

   Let $T = \dfrac{kn}{w}$, where $k$ is a non-zero constant. 1M

   $10 = \dfrac{k(30)}{6}$, so $k = 2$. 1A

   $9 = \dfrac{2(45)}{w}$ 1M

   $w = 10$, so 10 workers are needed. 1A