PA.3B, SEC 3, Practical Applications (44)

Question 1 of 44

1. Question
Topic: Practical Applications

Please have pen and paper handy to show workings out. 📝

🛠️ The following formula is used to calculate the time ( $T$ ) in hours to assemble a machine:

$T = 4 \cdot m + 2$

a) 🕒 How long does it take to assemble 3 machines?

b) ⚙️ How many machines can be assembled in 18 hours?
- a)
  
  t =
  
  hours
  
  b)
  
  m =
  
  Machines
  
  ⌨️ Type your answer in the fields provided.
Correct

Incorrect

Hint

Hint: A formula works like a number-machine—run the steps forward for an output, or reverse them to recover the input.

Example – Formula: M = 3x + 5

If x = 4, find M

Forwards Number Machine (symbols):

x → × 3 → + 5 → M

Forwards Number Machine (values):

4 → × 3 → 12 → + 5 → 17

So, M = 17.

If M = 17, find x

Backwards Number Machine (symbols):

x ← ÷ 3 ← − 5 ← M

Backwards Number Machine (values):

4 ← ÷ 3 ← 12 ← − 5 ← 17

So, x = 4.

💡 To reverse a number-machine, undo each operation in the opposite order: adding undoes subtraction, multiplying undoes division, squaring undoes square-rooting, and so on.
Question 2 of 44

2. Question
Topic: Practical Applications

Please have pen and paper handy to show workings out. 📝

🚧 The following formula is used to calculate the total cost ( $C$ ) in pounds for renting equipment for $d$ days:

$C = 50 d + 20$

a) 🚧 What is the cost for renting equipment for 5 days?

b) 💷 How many days can the equipment be rented for £320?
- a)
  
  c =
  
  £
  
  b)
  
  d =
  
  days
  
  ⌨️ Type your answer in the fields provided.
Correct

Incorrect

Hint

Hint: A formula works like a number-machine—run the steps forward for an output, or reverse them to recover the input.

Example – Formula: M = 3x + 5

If x = 4, find M

Forwards Number Machine (symbols):

x → × 3 → + 5 → M

Forwards Number Machine (values):

4 → × 3 → 12 → + 5 → 17

So, M = 17.

If M = 17, find x

Backwards Number Machine (symbols):

x ← ÷ 3 ← − 5 ← M

Backwards Number Machine (values):

4 ← ÷ 3 ← 12 ← − 5 ← 17

So, x = 4.

💡 To reverse a number-machine, undo each operation in the opposite order: adding undoes subtraction, multiplying undoes division, squaring undoes square-rooting, and so on.
Question 3 of 44

3. Question
Topic: Practical Applications

Please have pen and paper handy to show workings out. 📝

💊 The following formula is used to calculate the dosage ( $D$ ) in milligrams of a medication, where $W$ is the weight of the patient in kilograms:

$D = 5 \sqrt{W} + 15$

a) 💊 What is the dosage for a patient weighing 36kg?

b) ⚕️ What is the weight of a patient if the dosage is 55mg?
- a)
  
  d =
  
  mg
  
  b)
  
  w =
  
  kg
  
  ⌨️ Type your answer in the fields provided.
Correct

Incorrect

Hint

Hint: A formula works like a number-machine—run the steps forward for an output, or reverse them to recover the input.

Example – Formula: M = 3x + 5

If x = 4, find M

Forwards Number Machine (symbols):

x → × 3 → + 5 → M

Forwards Number Machine (values):

4 → × 3 → 12 → + 5 → 17

So, M = 17.

If M = 17, find x

Backwards Number Machine (symbols):

x ← ÷ 3 ← − 5 ← M

Backwards Number Machine (values):

4 ← ÷ 3 ← 12 ← − 5 ← 17

So, x = 4.

💡 To reverse a number-machine, undo each operation in the opposite order: adding undoes subtraction, multiplying undoes division, squaring undoes square-rooting, and so on.
Question 4 of 44

4. Question
Topic: Practical Applications

Please have pen and paper handy to show workings out. 📝

💧 The following formula is used to calculate the amount of water ( $W$ ) in litres filled in a tank:

$W = 50 \cdot h + 100$

a) 💦 How much water is in the tank after 4 hours?

b) 🛁 How many hours does it take to fill 450 litres of water?
- a)
  
  w =
  
  Liters
  
  b)
  
  h =
  
  Hours
  
  ⌨️ Type your answer in the fields provided.
Correct

Incorrect

Hint

Hint: A formula works like a number-machine—run the steps forward for an output, or reverse them to recover the input.

Example – Formula: M = 3x + 5

If x = 4, find M

Forwards Number Machine (symbols):

x → × 3 → + 5 → M

Forwards Number Machine (values):

4 → × 3 → 12 → + 5 → 17

So, M = 17.

If M = 17, find x

Backwards Number Machine (symbols):

x ← ÷ 3 ← − 5 ← M

Backwards Number Machine (values):

4 ← ÷ 3 ← 12 ← − 5 ← 17

So, x = 4.

💡 To reverse a number-machine, undo each operation in the opposite order: adding undoes subtraction, multiplying undoes division, squaring undoes square-rooting, and so on.
Question 5 of 44

5. Question
Topic: Practical Applications

Please have pen and paper handy to show workings out. 📝

⚡ The following formula is used to calculate the electrical power ( $P$ ) in watts of a circuit:

$P = I V + 5$

a) ⚡ What is the power if the current is 3A and the voltage is 12V?

b) 💡 What is the current if the power is 53W and the voltage is 10V?
- a)
  
  p =
  
  W
  
  b)
  
  i =
  
  voltage
  
  ⌨️ Type your answer in the fields provided.
Correct

Incorrect

Hint

Hint: A formula works like a number-machine—run the steps forward for an output, or reverse them to recover the input.

Example – Formula: M = 3x + 5

If x = 4, find M

Forwards Number Machine (symbols):

x → × 3 → + 5 → M

Forwards Number Machine (values):

4 → × 3 → 12 → + 5 → 17

So, M = 17.

If M = 17, find x

Backwards Number Machine (symbols):

x ← ÷ 3 ← − 5 ← M

Backwards Number Machine (values):

4 ← ÷ 3 ← 12 ← − 5 ← 17

So, x = 4.

💡 To reverse a number-machine, undo each operation in the opposite order: adding undoes subtraction, multiplying undoes division, squaring undoes square-rooting, and so on.
Question 6 of 44

6. Question
Topic: Practical Applications

Please have pen and paper handy to show workings out. 📝

🔥 The following formula is used to calculate the water pressure ( $P$ ) needed to extinguish a fire, where $h$ is the height of the fire in metres:

$P = 4 h^{2} - 20$

a) 🚒 What is the pressure needed for a fire 5m high?

b) 💦 What is the height of the fire if the required pressure is 124 units?
- a)
  
  p =
  
  units
  
  b)
  
  h =
  
  m
  
  ⌨️ Type your answer in the fields provided.
Correct

Incorrect

Hint

Hint: A formula works like a number-machine—run the steps forward for an output, or reverse them to recover the input.

Example – Formula: M = 3x + 5

If x = 4, find M

Forwards Number Machine (symbols):

x → × 3 → + 5 → M

Forwards Number Machine (values):

4 → × 3 → 12 → + 5 → 17

So, M = 17.

If M = 17, find x

Backwards Number Machine (symbols):

x ← ÷ 3 ← − 5 ← M

Backwards Number Machine (values):

4 ← ÷ 3 ← 12 ← − 5 ← 17

So, x = 4.

💡 To reverse a number-machine, undo each operation in the opposite order: adding undoes subtraction, multiplying undoes division, squaring undoes square-rooting, and so on.
Question 7 of 44

7. Question
Topic: Practical Applications

Please have pen and paper handy to show workings out. 📝

🍰 The following formula is used to calculate the total cost ( $C$ ) of ordering $n$ cakes:

$C = 12 n + 5$

a) 🎂 How much does it cost to order 6 cakes?

b) 🍰 How many cakes can be ordered for £101?
- a)
  
  c =
  
  £
  
  b)
  
  n =
  
  cakes
  
  ⌨️ Type your answer in the fields provided.
Correct

Incorrect

Hint

Hint: A formula works like a number-machine—run the steps forward for an output, or reverse them to recover the input.

Example – Formula: M = 3x + 5

If x = 4, find M

Forwards Number Machine (symbols):

x → × 3 → + 5 → M

Forwards Number Machine (values):

4 → × 3 → 12 → + 5 → 17

So, M = 17.

If M = 17, find x

Backwards Number Machine (symbols):

x ← ÷ 3 ← − 5 ← M

Backwards Number Machine (values):

4 ← ÷ 3 ← 12 ← − 5 ← 17

So, x = 4.

💡 To reverse a number-machine, undo each operation in the opposite order: adding undoes subtraction, multiplying undoes division, squaring undoes square-rooting, and so on.
Question 8 of 44

8. Question
Topic: Practical Applications

Please have pen and paper handy to show workings out. 📝

🛠️ The following formula is used to calculate the torque ( $τ$ ) in newton-metres:

$τ = F r + 2$

a) 🔩 What is the torque if the force is 50N and the radius is 0.8m?

b) 🚀 What is the force if the torque is 82Nm and the radius is 1.6m?
- a)
  
  t =
  
  Nm
  
  b)
  
  f =
  
  N
  
  ⌨️ Type your answer in the fields provided.
Correct

Incorrect

Hint

Hint: A formula works like a number-machine—run the steps forward for an output, or reverse them to recover the input.

Example – Formula: M = 3x + 5

If x = 4, find M

Forwards Number Machine (symbols):

x → × 3 → + 5 → M

Forwards Number Machine (values):

4 → × 3 → 12 → + 5 → 17

So, M = 17.

If M = 17, find x

Backwards Number Machine (symbols):

x ← ÷ 3 ← − 5 ← M

Backwards Number Machine (values):

4 ← ÷ 3 ← 12 ← − 5 ← 17

So, x = 4.

💡 To reverse a number-machine, undo each operation in the opposite order: adding undoes subtraction, multiplying undoes division, squaring undoes square-rooting, and so on.
Question 9 of 44

9. Question
Topic: Practical Applications

Please have pen and paper handy to show workings out. 📝

🛫 The following formula is used to calculate the lift force ( $F$ ) in newtons generated by an aircraft, where $v$ is the speed in metres per second:

$F = 2 v^{2} + 50$

a) 🛫 What is the lift force if the aircraft speed is 10m/s?

b) ✈️ What is the aircraft speed if the lift force is 850N?
- a)
  
  f =
  
  N
  
  b)
  
  v =
  
  m/s
  
  ⌨️ Type your answer in the fields provided.
Correct

Incorrect

Hint

Hint: A formula works like a number-machine—run the steps forward for an output, or reverse them to recover the input.

Example – Formula: M = 3x + 5

If x = 4, find M

Forwards Number Machine (symbols):

x → × 3 → + 5 → M

Forwards Number Machine (values):

4 → × 3 → 12 → + 5 → 17

So, M = 17.

If M = 17, find x

Backwards Number Machine (symbols):

x ← ÷ 3 ← − 5 ← M

Backwards Number Machine (values):

4 ← ÷ 3 ← 12 ← − 5 ← 17

So, x = 4.

💡 To reverse a number-machine, undo each operation in the opposite order: adding undoes subtraction, multiplying undoes division, squaring undoes square-rooting, and so on.
Question 10 of 44

10. Question
Topic: Practical Applications

Please have pen and paper handy to show workings out. 📝

🚌 The following formula is used to calculate the total number of passengers ( $P$ ) on a bus route after $t$ stops:

$P = 15 t - 10$

a) 🕒 How many passengers are there after 4 stops?

b) 🚌 How many stops are required for 95 passengers?
- a)
  
  p =
  
  passengers
  
  b)
  
  t =
  
  stops
  
  ⌨️ Type your answer in the fields provided.
Correct

Incorrect

Hint

Hint: A formula works like a number-machine—run the steps forward for an output, or reverse them to recover the input.

Example – Formula: M = 3x + 5

If x = 4, find M

Forwards Number Machine (symbols):

x → × 3 → + 5 → M

Forwards Number Machine (values):

4 → × 3 → 12 → + 5 → 17

So, M = 17.

If M = 17, find x

Backwards Number Machine (symbols):

x ← ÷ 3 ← − 5 ← M

Backwards Number Machine (values):

4 ← ÷ 3 ← 12 ← − 5 ← 17

So, x = 4.

💡 To reverse a number-machine, undo each operation in the opposite order: adding undoes subtraction, multiplying undoes division, squaring undoes square-rooting, and so on.
Question 11 of 44

11. Question
Topic: Practical Applications

Please have pen and paper handy to show workings out. 📝

💊 The following formula is used to calculate the total dosage ( $D$ ) of medicine in milligrams:

$D = 2 W + 10$

a) 💊 What is the dosage for a person weighing 70kg?

b) ⚕️ What is the weight of a person who receives a dosage of 90mg?
- a)
  
  d =
  
  mg
  
  b)
  
  w =
  
  kg
  
  ⌨️ Type your answer in the fields provided.
Correct

Incorrect

Hint

Hint: A formula works like a number-machine—run the steps forward for an output, or reverse them to recover the input.

Example – Formula: M = 3x + 5

If x = 4, find M

Forwards Number Machine (symbols):

x → × 3 → + 5 → M

Forwards Number Machine (values):

4 → × 3 → 12 → + 5 → 17

So, M = 17.

If M = 17, find x

Backwards Number Machine (symbols):

x ← ÷ 3 ← − 5 ← M

Backwards Number Machine (values):

4 ← ÷ 3 ← 12 ← − 5 ← 17

So, x = 4.

💡 To reverse a number-machine, undo each operation in the opposite order: adding undoes subtraction, multiplying undoes division, squaring undoes square-rooting, and so on.
Question 12 of 44

12. Question
Topic: Practical Applications

Please have pen and paper handy to show workings out. 📝

✈️ The following formula is used to calculate the distance ( $D$ ) travelled by a plane in kilometres, where $t$ is the time in hours:

$D = 300 t - 100$

a) ✈️ What is the distance travelled in 4 hours?

b) 🕒 How long does it take to travel 800km?
- a)
  
  d =
  
  km
  
  b)
  
  t =
  
  hours
  
  ⌨️ Type your answer in the fields provided.
Correct

Incorrect

Hint

Hint: A formula works like a number-machine—run the steps forward for an output, or reverse them to recover the input.

Example – Formula: M = 3x + 5

If x = 4, find M

Forwards Number Machine (symbols):

x → × 3 → + 5 → M

Forwards Number Machine (values):

4 → × 3 → 12 → + 5 → 17

So, M = 17.

If M = 17, find x

Backwards Number Machine (symbols):

x ← ÷ 3 ← − 5 ← M

Backwards Number Machine (values):

4 ← ÷ 3 ← 12 ← − 5 ← 17

So, x = 4.

💡 To reverse a number-machine, undo each operation in the opposite order: adding undoes subtraction, multiplying undoes division, squaring undoes square-rooting, and so on.
Question 13 of 44

13. Question
Topic: Practical Applications

Please have pen and paper handy to show workings out. 📝

☕ The following formula is used to calculate the cost ( $C$ ) in pounds for serving $n$ coffees:

$C = 1.5 n + 10$

a) ☕ What is the cost for serving 20 coffees?

b) 💷 How many coffees can be served for £55?
- a)
  
  c =
  
  £
  
  b)
  
  n =
  
  coffees
  
  ⌨️ Type your answer in the fields provided.
Correct

Incorrect

Hint

Hint: A formula works like a number-machine—run the steps forward for an output, or reverse them to recover the input.

Example – Formula: M = 3x + 5

If x = 4, find M

Forwards Number Machine (symbols):

x → × 3 → + 5 → M

Forwards Number Machine (values):

4 → × 3 → 12 → + 5 → 17

So, M = 17.

If M = 17, find x

Backwards Number Machine (symbols):

x ← ÷ 3 ← − 5 ← M

Backwards Number Machine (values):

4 ← ÷ 3 ← 12 ← − 5 ← 17

So, x = 4.

💡 To reverse a number-machine, undo each operation in the opposite order: adding undoes subtraction, multiplying undoes division, squaring undoes square-rooting, and so on.
Question 14 of 44

14. Question
Topic: Practical Applications

Please have pen and paper handy to show workings out. 📝

🚀 The following formula is used to calculate the final velocity ( $v$ ) of an object:

$v = u + a t$

a) 🚀 What is the final velocity if the initial velocity is 5m/s, acceleration is 3m/s², and time is 4 seconds?

b) 🕒 What is the time taken if the final velocity is 29m/s, the initial velocity is 5m/s, and acceleration is 4m/s²?
- a)
  
  t =
  
  4m/s²
  
  b)
  
  v =
  
  seconds
  
  ⌨️ Type your answer in the fields provided.
Correct

Incorrect

Hint

Hint: A formula works like a number-machine—run the steps forward for an output, or reverse them to recover the input.

Example – Formula: M = 3x + 5

If x = 4, find M

Forwards Number Machine (symbols):

x → × 3 → + 5 → M

Forwards Number Machine (values):

4 → × 3 → 12 → + 5 → 17

So, M = 17.

If M = 17, find x

Backwards Number Machine (symbols):

x ← ÷ 3 ← − 5 ← M

Backwards Number Machine (values):

4 ← ÷ 3 ← 12 ← − 5 ← 17

So, x = 4.

💡 To reverse a number-machine, undo each operation in the opposite order: adding undoes subtraction, multiplying undoes division, squaring undoes square-rooting, and so on.
Question 15 of 44

15. Question
Topic: Practical Applications

Please have pen and paper handy to show workings out. 📝

⚡ The following formula is used to calculate the resistance ( $R$ ) in ohms of a circuit, where $V$ is the voltage in volts and $I$ is the current in amperes:

$R = \frac{V}{I} - 3$

a) ⚡ What is the resistance if the voltage is 24V and the current is 6A?

b) 🔋 What is the voltage if the resistance is 7Ω and the current is 5A?
- a)
  
  r =
  
  Ω
  
  b)
  
  v =
  
  V
  
  ⌨️ Type your answer in the fields provided.
Correct

Incorrect

Hint

Hint: A formula works like a number-machine—run the steps forward for an output, or reverse them to recover the input.

Example – Formula: M = 3x + 5

If x = 4, find M

Forwards Number Machine (symbols):

x → × 3 → + 5 → M

Forwards Number Machine (values):

4 → × 3 → 12 → + 5 → 17

So, M = 17.

If M = 17, find x

Backwards Number Machine (symbols):

x ← ÷ 3 ← − 5 ← M

Backwards Number Machine (values):

4 ← ÷ 3 ← 12 ← − 5 ← 17

So, x = 4.

💡 To reverse a number-machine, undo each operation in the opposite order: adding undoes subtraction, multiplying undoes division, squaring undoes square-rooting, and so on.
Question 16 of 44

16. Question
Topic: Practical Applications

Please have pen and paper handy to show workings out. 📝

📦 The following formula is used to calculate the total weight ( $W$ ) in kilograms of a parcel containing $n$ items:

$W = 2.5 n + 3$

a) 📦 What is the weight of a parcel containing 8 items?

b) 📬 How many items can be packed for a parcel weighing 28 kilograms?
- a)
  
  w =
  
  kg
  
  b)
  
  n =
  
  items
  
  ⌨️ Type your answer in the fields provided.
Correct

Incorrect

Hint

Hint: A formula works like a number-machine—run the steps forward for an output, or reverse them to recover the input.

Example – Formula: M = 3x + 5

If x = 4, find M

Forwards Number Machine (symbols):

x → × 3 → + 5 → M

Forwards Number Machine (values):

4 → × 3 → 12 → + 5 → 17

So, M = 17.

If M = 17, find x

Backwards Number Machine (symbols):

x ← ÷ 3 ← − 5 ← M

Backwards Number Machine (values):

4 ← ÷ 3 ← 12 ← − 5 ← 17

So, x = 4.

💡 To reverse a number-machine, undo each operation in the opposite order: adding undoes subtraction, multiplying undoes division, squaring undoes square-rooting, and so on.
Question 17 of 44

17. Question
Topic: Practical Applications

Please have pen and paper handy to show workings out. 📝

🌡️ The following formula is used to convert temperature from Celsius ( $C$ ) to Fahrenheit ( $F$ ):

$F = 1.8 C + 32$

a) 🌡️ What is the Fahrenheit temperature for 25°C?

b) ❄️ What is the Celsius temperature for 95°F?
- a)
  
  f =
  
  °F
  
  b)
  
  c =
  
  °C
  
  ⌨️ Type your answer in the fields provided.
Correct

Incorrect

Hint

Hint: A formula works like a number-machine—run the steps forward for an output, or reverse them to recover the input.

Example – Formula: M = 3x + 5

If x = 4, find M

Forwards Number Machine (symbols):

x → × 3 → + 5 → M

Forwards Number Machine (values):

4 → × 3 → 12 → + 5 → 17

So, M = 17.

If M = 17, find x

Backwards Number Machine (symbols):

x ← ÷ 3 ← − 5 ← M

Backwards Number Machine (values):

4 ← ÷ 3 ← 12 ← − 5 ← 17

So, x = 4.

💡 To reverse a number-machine, undo each operation in the opposite order: adding undoes subtraction, multiplying undoes division, squaring undoes square-rooting, and so on.
Question 18 of 44

18. Question
Topic: Practical Applications

Please have pen and paper handy to show workings out. 📝

🛠️ The following formula is used to calculate the mechanical advantage ( $MA$ ) of a machine, where $F$ is the output force in newtons and $e$ is the effort force in newtons:

$MA = \frac{F}{e} + 2$

a) 🛠️ What is the mechanical advantage if the output force is 40N and the effort force is 10N?

b) ⚙️ What is the output force if the mechanical advantage is 8 and the effort force is 8N?
- a)
  
  MA =
  
  b)
  
  f =
  
  N
  
  ⌨️ Type your answer in the fields provided.
Correct

Incorrect

Hint

Hint: A formula works like a number-machine—run the steps forward for an output, or reverse them to recover the input.

Example – Formula: M = 3x + 5

If x = 4, find M

Forwards Number Machine (symbols):

x → × 3 → + 5 → M

Forwards Number Machine (values):

4 → × 3 → 12 → + 5 → 17

So, M = 17.

If M = 17, find x

Backwards Number Machine (symbols):

x ← ÷ 3 ← − 5 ← M

Backwards Number Machine (values):

4 ← ÷ 3 ← 12 ← − 5 ← 17

So, x = 4.

💡 To reverse a number-machine, undo each operation in the opposite order: adding undoes subtraction, multiplying undoes division, squaring undoes square-rooting, and so on.
Question 19 of 44

19. Question
Topic: Practical Applications

Please have pen and paper handy to show workings out. 📝

🎟️ The following formula is used to calculate the total cost ( $C$ ) in pounds of buying $n$ tickets:

$C = 8 n + 4$

a) 🎫 What is the total cost for 5 tickets?

b) 💷 How many tickets can be bought for £68?
- a)
  
  c =
  
  £
  
  b)
  
  n =
  
  tickets
  
  ⌨️ Type your answer in the fields provided.
Correct

Incorrect

Hint

Hint: A formula works like a number-machine—run the steps forward for an output, or reverse them to recover the input.

Example – Formula: M = 3x + 5

If x = 4, find M

Forwards Number Machine (symbols):

x → × 3 → + 5 → M

Forwards Number Machine (values):

4 → × 3 → 12 → + 5 → 17

So, M = 17.

If M = 17, find x

Backwards Number Machine (symbols):

x ← ÷ 3 ← − 5 ← M

Backwards Number Machine (values):

4 ← ÷ 3 ← 12 ← − 5 ← 17

So, x = 4.

💡 To reverse a number-machine, undo each operation in the opposite order: adding undoes subtraction, multiplying undoes division, squaring undoes square-rooting, and so on.
Question 20 of 44

20. Question
Topic: Practical Applications

Please have pen and paper handy to show workings out. 📝

🎨 The following formula is used to calculate the total area ( $A$ ) of a wall in square metres, where $h$ is the height of the wall in metres:

$A = 2 h^{2} + 5$

a) 🎨 What is the area if the wall height is 4m?

b) 🛠️ What is the wall height if the area is 37m²?
- a)
  
  a =
  
  m²
  
  b)
  
  h =
  
  m
  
  ⌨️ Type your answer in the fields provided.
Correct

Incorrect

Hint

Hint: A formula works like a number-machine—run the steps forward for an output, or reverse them to recover the input.

Example – Formula: M = 3x + 5

If x = 4, find M

Forwards Number Machine (symbols):

x → × 3 → + 5 → M

Forwards Number Machine (values):

4 → × 3 → 12 → + 5 → 17

So, M = 17.

If M = 17, find x

Backwards Number Machine (symbols):

x ← ÷ 3 ← − 5 ← M

Backwards Number Machine (values):

4 ← ÷ 3 ← 12 ← − 5 ← 17

So, x = 4.

💡 To reverse a number-machine, undo each operation in the opposite order: adding undoes subtraction, multiplying undoes division, squaring undoes square-rooting, and so on.
Question 21 of 44

21. Question
Topic: Practical Applications

Please have pen and paper handy to show workings out. 📝

🌡️ The following formula is used to calculate the heat transfer rate ( $Q$ ) in watts, where $A$ is the area in square metres and $k$ is the thermal conductivity in watts per metre kelvin:

$Q = \frac{A}{k} - 1$

a) 🌡️ What is the heat transfer rate if the area is 20m² and the thermal conductivity is 4W/m·K?

b) 🔥 What is the area if the heat transfer rate is 9W and the thermal conductivity is 3W/m·K?
- a)
  
  q =
  
  W
  
  b)
  
  a =
  
  m²
  
  ⌨️ Type your answer in the fields provided.
Correct

Incorrect

Hint

Hint: A formula works like a number-machine—run the steps forward for an output, or reverse them to recover the input.

Example – Formula: M = 3x + 5

If x = 4, find M

Forwards Number Machine (symbols):

x → × 3 → + 5 → M

Forwards Number Machine (values):

4 → × 3 → 12 → + 5 → 17

So, M = 17.

If M = 17, find x

Backwards Number Machine (symbols):

x ← ÷ 3 ← − 5 ← M

Backwards Number Machine (values):

4 ← ÷ 3 ← 12 ← − 5 ← 17

So, x = 4.

💡 To reverse a number-machine, undo each operation in the opposite order: adding undoes subtraction, multiplying undoes division, squaring undoes square-rooting, and so on.
Question 22 of 44

22. Question
Topic: Practical Applications

Please have pen and paper handy to show workings out. 📝

🛠️ The following formula is used to calculate the time ( $T$ ) in hours required to paint $A$ square metres:

$T = 0.5 A + 2$

a) 🎨 How long does it take to paint 30 square metres?

b) 🛠️ How many square metres can be painted in 12 hours?
- a)
  
  t =
  
  hours
  
  b)
  
  a =
  
  square metres
  
  ⌨️ Type your answer in the fields provided.
Correct

Incorrect

Hint

Hint: A formula works like a number-machine—run the steps forward for an output, or reverse them to recover the input.

Example – Formula: M = 3x + 5

If x = 4, find M

Forwards Number Machine (symbols):

x → × 3 → + 5 → M

Forwards Number Machine (values):

4 → × 3 → 12 → + 5 → 17

So, M = 17.

If M = 17, find x

Backwards Number Machine (symbols):

x ← ÷ 3 ← − 5 ← M

Backwards Number Machine (values):

4 ← ÷ 3 ← 12 ← − 5 ← 17

So, x = 4.

💡 To reverse a number-machine, undo each operation in the opposite order: adding undoes subtraction, multiplying undoes division, squaring undoes square-rooting, and so on.
Question 23 of 44

23. Question
Topic: Practical Applications

Please have pen and paper handy to show workings out. 📝

🔧 The following formula is used to calculate the strength ( $S$ ) of a steel beam, where $l$ is the length of the beam in metres:

$S = 3 \sqrt{l} - 7$

a) 🔧 What is the strength if the length is 16m?

b) 🚧 What is the length if the strength is 5?
- a)
  
  s =
  
  b)
  
  l =
  
  m
  
  ⌨️ Type your answer in the fields provided.
Correct

Incorrect

Hint

Hint: A formula works like a number-machine—run the steps forward for an output, or reverse them to recover the input.

Example – Formula: M = 3x + 5

If x = 4, find M

Forwards Number Machine (symbols):

x → × 3 → + 5 → M

Forwards Number Machine (values):

4 → × 3 → 12 → + 5 → 17

So, M = 17.

If M = 17, find x

Backwards Number Machine (symbols):

x ← ÷ 3 ← − 5 ← M

Backwards Number Machine (values):

4 ← ÷ 3 ← 12 ← − 5 ← 17

So, x = 4.

💡 To reverse a number-machine, undo each operation in the opposite order: adding undoes subtraction, multiplying undoes division, squaring undoes square-rooting, and so on.
Question 24 of 44

24. Question
Topic: Practical Applications

Please have pen and paper handy to show workings out. 📝

🩺 The following formula is used to calculate the required heart rate ( $H$ ) for exercise, where $A$ is the age in years:

$H = 200 - 2 A$

a) 🏃‍♂️ What is the target heart rate for a 30-year-old?

b) ❤️ What is the age of a person with a target heart rate of 160 bpm?
- a)
  
  h =
  
  bpm
  
  b)
  
  a =
  
  years
  
  ⌨️ Type your answer in the fields provided.
Correct

Incorrect

Hint

Hint: A formula works like a number-machine—run the steps forward for an output, or reverse them to recover the input.

Example – Formula: M = 3x + 5

If x = 4, find M

Forwards Number Machine (symbols):

x → × 3 → + 5 → M

Forwards Number Machine (values):

4 → × 3 → 12 → + 5 → 17

So, M = 17.

If M = 17, find x

Backwards Number Machine (symbols):

x ← ÷ 3 ← − 5 ← M

Backwards Number Machine (values):

4 ← ÷ 3 ← 12 ← − 5 ← 17

So, x = 4.

💡 To reverse a number-machine, undo each operation in the opposite order: adding undoes subtraction, multiplying undoes division, squaring undoes square-rooting, and so on.
Question 25 of 44

25. Question
Topic: Practical Applications

Please have pen and paper handy to show workings out. 📝

📦 The following formula is used to calculate the total cost ( $C$ ) of delivering $n$ parcels:

$C = 3 n + 5$

a) 🚚 What is the cost of delivering 10 parcels?

b) 📦 How many parcels can be delivered for £26?
- a)
  
  c =
  
  £
  
  b)
  
  n =
  
  parcels
  
  ⌨️ Type your answer in the fields provided.
Correct

Incorrect

Hint

Hint: A formula works like a number-machine—run the steps forward for an output, or reverse them to recover the input.

Example – Formula: M = 3x + 5

If x = 4, find M

Forwards Number Machine (symbols):

x → × 3 → + 5 → M

Forwards Number Machine (values):

4 → × 3 → 12 → + 5 → 17

So, M = 17.

If M = 17, find x

Backwards Number Machine (symbols):

x ← ÷ 3 ← − 5 ← M

Backwards Number Machine (values):

4 ← ÷ 3 ← 12 ← − 5 ← 17

So, x = 4.

💡 To reverse a number-machine, undo each operation in the opposite order: adding undoes subtraction, multiplying undoes division, squaring undoes square-rooting, and so on.
Question 26 of 44

26. Question
Topic: Practical Applications

Please have pen and paper handy to show workings out. 📝

📦 The following formula is used to calculate the volume ( $V$ ) of a box in cubic metres, where $l$ is the length of the box in metres:

$V = l^{2} - 6$

a) 📦 What is the volume if the length is 5m?

b) 🚚 What is the length if the volume is 19m³?
- a)
  
  v =
  
  m³
  
  b)
  
  l =
  
  m
  
  ⌨️ Type your answer in the fields provided.
Correct

Incorrect

Hint

Hint: A formula works like a number-machine—run the steps forward for an output, or reverse them to recover the input.

Example – Formula: M = 3x + 5

If x = 4, find M

Forwards Number Machine (symbols):

x → × 3 → + 5 → M

Forwards Number Machine (values):

4 → × 3 → 12 → + 5 → 17

So, M = 17.

If M = 17, find x

Backwards Number Machine (symbols):

x ← ÷ 3 ← − 5 ← M

Backwards Number Machine (values):

4 ← ÷ 3 ← 12 ← − 5 ← 17

So, x = 4.

💡 To reverse a number-machine, undo each operation in the opposite order: adding undoes subtraction, multiplying undoes division, squaring undoes square-rooting, and so on.
Question 27 of 44

27. Question
Topic: Practical Applications

Please have pen and paper handy to show workings out. 📝

⚙️ The following formula is used to calculate the stress ( $S$ ) in pascals on a material, where $F$ is the force in newtons and $A$ is the area in square metres:

$S = \frac{F}{A} + 5$

a) ⚙️ What is the stress if the force is 50N and the area is 10m²?

b) 🛠️ What is the force if the stress is 20Pa and the area is 5m²?
- h
  
  a)
  
  s =
  
  pa
  
  b)
  
  f =
  
  N
  
  ⌨️ Type your answer in the fields provided.
Correct

Incorrect

Hint

Hint: A formula works like a number-machine—run the steps forward for an output, or reverse them to recover the input.

Example – Formula: M = 3x + 5

If x = 4, find M

Forwards Number Machine (symbols):

x → × 3 → + 5 → M

Forwards Number Machine (values):

4 → × 3 → 12 → + 5 → 17

So, M = 17.

If M = 17, find x

Backwards Number Machine (symbols):

x ← ÷ 3 ← − 5 ← M

Backwards Number Machine (values):

4 ← ÷ 3 ← 12 ← − 5 ← 17

So, x = 4.

💡 To reverse a number-machine, undo each operation in the opposite order: adding undoes subtraction, multiplying undoes division, squaring undoes square-rooting, and so on.
Question 28 of 44

28. Question
Topic: Practical Applications

Please have pen and paper handy to show workings out. 📝

🛠️ The following formula is used to calculate the total number of bricks ( $B$ ) required to build $W$ walls:

$B = 100 W + 50$

a) 🧱 How many bricks are required for 5 walls?

b) 🏗️ How many walls can be built using 950 bricks?
- a)
  
  b =
  
  bricks
  
  b)
  
  w =
  
  walls
  
  ⌨️ Type your answer in the fields provided.
Correct

Incorrect

Hint

Hint: A formula works like a number-machine—run the steps forward for an output, or reverse them to recover the input.

Example – Formula: M = 3x + 5

If x = 4, find M

Forwards Number Machine (symbols):

x → × 3 → + 5 → M

Forwards Number Machine (values):

4 → × 3 → 12 → + 5 → 17

So, M = 17.

If M = 17, find x

Backwards Number Machine (symbols):

x ← ÷ 3 ← − 5 ← M

Backwards Number Machine (values):

4 ← ÷ 3 ← 12 ← − 5 ← 17

So, x = 4.

💡 To reverse a number-machine, undo each operation in the opposite order: adding undoes subtraction, multiplying undoes division, squaring undoes square-rooting, and so on.
Question 29 of 44

29. Question
Topic: Practical Applications

Please have pen and paper handy to show workings out. 📝

🚜 The following formula is used to calculate the force ( $F$ ) exerted by a tractor in newtons, where $P$ is the power in kilowatts:

$F = P^{2} - 3$

a) 🚜 What is the force if the power is 4?

b) 💪 What is the power if the force is 61N?
- a)
  
  f =
  
  N
  
  b)
  
  p =
  
  kW
  
  ⌨️ Type your answer in the fields provided.
Correct

Incorrect

Hint

Hint: A formula works like a number-machine—run the steps forward for an output, or reverse them to recover the input.

Example – Formula: M = 3x + 5

If x = 4, find M

Forwards Number Machine (symbols):

x → × 3 → + 5 → M

Forwards Number Machine (values):

4 → × 3 → 12 → + 5 → 17

So, M = 17.

If M = 17, find x

Backwards Number Machine (symbols):

x ← ÷ 3 ← − 5 ← M

Backwards Number Machine (values):

4 ← ÷ 3 ← 12 ← − 5 ← 17

So, x = 4.

💡 To reverse a number-machine, undo each operation in the opposite order: adding undoes subtraction, multiplying undoes division, squaring undoes square-rooting, and so on.
Question 30 of 44

30. Question
Topic: Practical Applications

Please have pen and paper handy to show workings out. 📝

💡 The following formula is used to calculate the total energy consumption ( $E$ ) in kilowatt-hours for using $h$ hours of a device:

$E = 1.2 h + 0.5$

a) 💡 What is the energy consumption for 10 hours of usage?

b) ⚡ How many hours of usage corresponds to 15.7 kilowatt-hours?
- a)
  
  e =
  
  kilowatt-hours
  
  b)
  
  h =
  
  hours
  
  ⌨️ Type your answer in the fields provided.
Correct

Incorrect

Hint

Hint: A formula works like a number-machine—run the steps forward for an output, or reverse them to recover the input.

Example – Formula: M = 3x + 5

If x = 4, find M

Forwards Number Machine (symbols):

x → × 3 → + 5 → M

Forwards Number Machine (values):

4 → × 3 → 12 → + 5 → 17

So, M = 17.

If M = 17, find x

Backwards Number Machine (symbols):

x ← ÷ 3 ← − 5 ← M

Backwards Number Machine (values):

4 ← ÷ 3 ← 12 ← − 5 ← 17

So, x = 4.

💡 To reverse a number-machine, undo each operation in the opposite order: adding undoes subtraction, multiplying undoes division, squaring undoes square-rooting, and so on.
Question 31 of 44

31. Question
Topic: Practical Applications

Please have pen and paper handy to show workings out. 📝

💊 The following formula is used to calculate the required dose ( $D$ ) in milligrams for a patient based on their weight ( $W$ ) in kilograms:

$D = \sqrt{W} + 10$

a) 💊 What is the dose for a patient weighing 64kg?

b) ⚕️ What is the weight if the dose is 18mg?
- a)
  
  d =
  
  mg
  
  b)
  
  w =
  
  kg
  
  ⌨️ Type your answer in the fields provided.
Correct

Incorrect

Hint

Hint: A formula works like a number-machine—run the steps forward for an output, or reverse them to recover the input.

Example – Formula: M = 3x + 5

If x = 4, find M

Forwards Number Machine (symbols):

x → × 3 → + 5 → M

Forwards Number Machine (values):

4 → × 3 → 12 → + 5 → 17

So, M = 17.

If M = 17, find x

Backwards Number Machine (symbols):

x ← ÷ 3 ← − 5 ← M

Backwards Number Machine (values):

4 ← ÷ 3 ← 12 ← − 5 ← 17

So, x = 4.

💡 To reverse a number-machine, undo each operation in the opposite order: adding undoes subtraction, multiplying undoes division, squaring undoes square-rooting, and so on.
Question 32 of 44

32. Question
Topic: Practical Applications

Please have pen and paper handy to show workings out. 📝

🍞 The following formula is used to calculate the time ( $T$ ) in minutes required to bake $B$ loaves of bread:

$T = 20 B + 10$

a) 🍞 How long does it take to bake 4 loaves of bread?

b) ⏳ How many loaves of bread can be baked in 130 minutes?
- a)
  
  t =
  
  minutes
  
  b)
  
  b =
  
  loaves of bread
  
  ⌨️ Type your answer in the fields provided.
Correct

Incorrect

Hint

Hint: A formula works like a number-machine—run the steps forward for an output, or reverse them to recover the input.

Example – Formula: M = 3x + 5

If x = 4, find M

Forwards Number Machine (symbols):

x → × 3 → + 5 → M

Forwards Number Machine (values):

4 → × 3 → 12 → + 5 → 17

So, M = 17.

If M = 17, find x

Backwards Number Machine (symbols):

x ← ÷ 3 ← − 5 ← M

Backwards Number Machine (values):

4 ← ÷ 3 ← 12 ← − 5 ← 17

So, x = 4.

💡 To reverse a number-machine, undo each operation in the opposite order: adding undoes subtraction, multiplying undoes division, squaring undoes square-rooting, and so on.
Question 33 of 44

33. Question
Topic: Practical Applications

Please have pen and paper handy to show workings out. 📝

🧱 The following formula is used to calculate the total bricks ( $B$ ) needed to build a wall, where $h$ is the height in metres:

$B = 4 h^{2} + 12$

a) 🧱 How many bricks are needed for a wall 3m high?

b) 🛠️ What is the height of the wall if 76 bricks are needed?
- a)
  
  b =
  
  bricks
  
  b)
  
  h =
  
  m
  
  ⌨️ Type your answer in the fields provided.
Correct

Incorrect

Hint

Hint: A formula works like a number-machine—run the steps forward for an output, or reverse them to recover the input.

Example – Formula: M = 3x + 5

If x = 4, find M

Forwards Number Machine (symbols):

x → × 3 → + 5 → M

Forwards Number Machine (values):

4 → × 3 → 12 → + 5 → 17

So, M = 17.

If M = 17, find x

Backwards Number Machine (symbols):

x ← ÷ 3 ← − 5 ← M

Backwards Number Machine (values):

4 ← ÷ 3 ← 12 ← − 5 ← 17

So, x = 4.

💡 To reverse a number-machine, undo each operation in the opposite order: adding undoes subtraction, multiplying undoes division, squaring undoes square-rooting, and so on.
Question 34 of 44

34. Question
Topic: Practical Applications

Please have pen and paper handy to show workings out. 📝

🚜 The following formula is used to calculate the amount of fuel ( $F$ ) in litres required to plough $H$ hectares of land:

$F = 3 H + 5$

a) 🚜 How much fuel is required to plough 10 hectares?

b) ⛽ How many hectares can be ploughed using 29 litres of fuel?
- a)
  
  f =
  
  litres of fuel
  
  b)
  
  h =
  
  hectares
  
  ⌨️ Type your answer in the fields provided.
Correct

Incorrect

Hint

Hint: A formula works like a number-machine—run the steps forward for an output, or reverse them to recover the input.

Example – Formula: M = 3x + 5

If x = 4, find M

Forwards Number Machine (symbols):

x → × 3 → + 5 → M

Forwards Number Machine (values):

4 → × 3 → 12 → + 5 → 17

So, M = 17.

If M = 17, find x

Backwards Number Machine (symbols):

x ← ÷ 3 ← − 5 ← M

Backwards Number Machine (values):

4 ← ÷ 3 ← 12 ← − 5 ← 17

So, x = 4.

💡 To reverse a number-machine, undo each operation in the opposite order: adding undoes subtraction, multiplying undoes division, squaring undoes square-rooting, and so on.
Question 35 of 44

35. Question
Topic: Practical Applications

Please have pen and paper handy to show workings out. 📝

🚜 The following formula is used to calculate the horsepower ( $H$ ) of a tractor, where $P$ is the power in kilowatts:

$H = 2 \sqrt{P} + 8$

a) 🚜 What is the horsepower if the power is 25kW?

b) 💪 What is the power if the horsepower is 22hp?
- a)
  
  h =
  
  hp
  
  b)
  
  p =
  
  kW
  
  ⌨️ Type your answer in the fields provided.
Correct

Incorrect

Hint

Hint: A formula works like a number-machine—run the steps forward for an output, or reverse them to recover the input.

Example – Formula: M = 3x + 5

If x = 4, find M

Forwards Number Machine (symbols):

x → × 3 → + 5 → M

Forwards Number Machine (values):

4 → × 3 → 12 → + 5 → 17

So, M = 17.

If M = 17, find x

Backwards Number Machine (symbols):

x ← ÷ 3 ← − 5 ← M

Backwards Number Machine (values):

4 ← ÷ 3 ← 12 ← − 5 ← 17

So, x = 4.

💡 To reverse a number-machine, undo each operation in the opposite order: adding undoes subtraction, multiplying undoes division, squaring undoes square-rooting, and so on.
Question 36 of 44

36. Question
Topic: Practical Applications

Please have pen and paper handy to show workings out. 📝

🍢 The following formula is used to calculate the time ( $T$ ) in minutes it takes to prepare and cook kebabs:

$T = 2.5 \cdot k + 16$

a) 🕒 How long does it take to prepare and cook 10 kebabs?

b) 🍢 How many kebabs can be prepared and cooked in 26 minutes?
- a)
  
  T =
  
  mins
  
  b)
  
  k =
  
  kebabs
  
  ⌨️ Type your answer in the fields provided.
Correct

Incorrect

Hint

Hint: A formula works like a number-machine—run the steps forward for an output, or reverse them to recover the input.

Example – Formula: M = 3x + 5

If x = 4, find M

Forwards Number Machine (symbols):

x → × 3 → + 5 → M

Forwards Number Machine (values):

4 → × 3 → 12 → + 5 → 17

So, M = 17.

If M = 17, find x

Backwards Number Machine (symbols):

x ← ÷ 3 ← − 5 ← M

Backwards Number Machine (values):

4 ← ÷ 3 ← 12 ← − 5 ← 17

So, x = 4.

💡 To reverse a number-machine, undo each operation in the opposite order: adding undoes subtraction, multiplying undoes division, squaring undoes square-rooting, and so on.
Question 37 of 44

37. Question
Topic: Practical Applications

Please have pen and paper handy to show workings out. 📝

✂️ The following formula is used to calculate the total cost ( $C$ ) in pounds for $n$ haircuts:

$C = 15 n + 10$

a) ✂️ What is the cost for 3 haircuts?

b) 💷 How many haircuts can be done for £85?
- a)
  
  c =
  
  £
  
  b)
  
  n =
  
  haircuts
  
  ⌨️ Type your answer in the fields provided.
Correct

Incorrect

Hint

Hint: A formula works like a number-machine—run the steps forward for an output, or reverse them to recover the input.

Example – Formula: M = 3x + 5

If x = 4, find M

Forwards Number Machine (symbols):

x → × 3 → + 5 → M

Forwards Number Machine (values):

4 → × 3 → 12 → + 5 → 17

So, M = 17.

If M = 17, find x

Backwards Number Machine (symbols):

x ← ÷ 3 ← − 5 ← M

Backwards Number Machine (values):

4 ← ÷ 3 ← 12 ← − 5 ← 17

So, x = 4.

💡 To reverse a number-machine, undo each operation in the opposite order: adding undoes subtraction, multiplying undoes division, squaring undoes square-rooting, and so on.
Question 38 of 44

38. Question
Topic: Practical Applications

Please have pen and paper handy to show workings out. 📝

🍞 The following formula is used to calculate the weight ( $W$ ) of flour needed in kilograms, where $n$ is the number of loaves being baked:

$W = 3 n^{2} - 7$

a) 🍞 What is the weight of flour for 4 loaves?

b) 🥖 How many loaves can be made if 68kg of flour is used?
- a)
  
  w =
  
  kg
  
  b)
  
  n =
  
  loaves
  
  ⌨️ Type your answer in the fields provided.
Correct

Incorrect

Hint

Hint: A formula works like a number-machine—run the steps forward for an output, or reverse them to recover the input.

Example – Formula: M = 3x + 5

If x = 4, find M

Forwards Number Machine (symbols):

x → × 3 → + 5 → M

Forwards Number Machine (values):

4 → × 3 → 12 → + 5 → 17

So, M = 17.

If M = 17, find x

Backwards Number Machine (symbols):

x ← ÷ 3 ← − 5 ← M

Backwards Number Machine (values):

4 ← ÷ 3 ← 12 ← − 5 ← 17

So, x = 4.

💡 To reverse a number-machine, undo each operation in the opposite order: adding undoes subtraction, multiplying undoes division, squaring undoes square-rooting, and so on.
Question 39 of 44

39. Question
Topic: Practical Applications

Please have pen and paper handy to show workings out. 📝

🚗 The following formula is used to calculate the distance ( $d$ ) in kilometres, covered by a car:

$d = 60 \cdot t - 10$

a) 🕒 How far does the car travel in 2 hours?

b) 🚗 How many hours does it take to travel 170 kilometres?
- a)
  
  d =
  
  hours
  
  b)
  
  t =
  
  km
  
  ⌨️ Type your answer in the fields provided.
Correct

Incorrect

Hint

Hint: A formula works like a number-machine—run the steps forward for an output, or reverse them to recover the input.

Example – Formula: M = 3x + 5

If x = 4, find M

Forwards Number Machine (symbols):

x → × 3 → + 5 → M

Forwards Number Machine (values):

4 → × 3 → 12 → + 5 → 17

So, M = 17.

If M = 17, find x

Backwards Number Machine (symbols):

x ← ÷ 3 ← − 5 ← M

Backwards Number Machine (values):

4 ← ÷ 3 ← 12 ← − 5 ← 17

So, x = 4.

💡 To reverse a number-machine, undo each operation in the opposite order: adding undoes subtraction, multiplying undoes division, squaring undoes square-rooting, and so on.
Question 40 of 44

40. Question
Topic: Practical Applications

Please have pen and paper handy to show workings out. 📝

🛠️ The following formula is used to calculate the time ( $T$ ) in hours needed to repair $M$ machines:

$T = 3.5 M + 2$

a) 🛠️ How long does it take to repair 5 machines?

b) ⏳ How many machines can be repaired in 24 hours?
- a)
  
  t =
  
  hours
  
  b)
  
  m =
  
  machines
  
  ⌨️ Type your answer in the fields provided.
Correct

Incorrect

Hint

Hint: A formula works like a number-machine—run the steps forward for an output, or reverse them to recover the input.

Example – Formula: M = 3x + 5

If x = 4, find M

Forwards Number Machine (symbols):

x → × 3 → + 5 → M

Forwards Number Machine (values):

4 → × 3 → 12 → + 5 → 17

So, M = 17.

If M = 17, find x

Backwards Number Machine (symbols):

x ← ÷ 3 ← − 5 ← M

Backwards Number Machine (values):

4 ← ÷ 3 ← 12 ← − 5 ← 17

So, x = 4.

💡 To reverse a number-machine, undo each operation in the opposite order: adding undoes subtraction, multiplying undoes division, squaring undoes square-rooting, and so on.
Question 41 of 44

41. Question
Topic: Practical Applications

Please have pen and paper handy to show workings out. 📝

🚛 The following formula is used to calculate the fuel consumption ( $F$ ) in litres for a journey, where $d$ is the distance travelled in kilometres:

$F = 4 d + 15$

a) 🚛 How much fuel is consumed for a journey of 10km?

b) ⛽ What distance can be travelled if 75 litres of fuel are used?
- a)
  
  f =
  
  litres
  
  b)
  
  d =
  
  km
  
  ⌨️ Type your answer in the fields provided.
Correct

Incorrect

Hint

Hint: A formula works like a number-machine—run the steps forward for an output, or reverse them to recover the input.

Example – Formula: M = 3x + 5

If x = 4, find M

Forwards Number Machine (symbols):

x → × 3 → + 5 → M

Forwards Number Machine (values):

4 → × 3 → 12 → + 5 → 17

So, M = 17.

If M = 17, find x

Backwards Number Machine (symbols):

x ← ÷ 3 ← − 5 ← M

Backwards Number Machine (values):

4 ← ÷ 3 ← 12 ← − 5 ← 17

So, x = 4.

💡 To reverse a number-machine, undo each operation in the opposite order: adding undoes subtraction, multiplying undoes division, squaring undoes square-rooting, and so on.
Question 42 of 44

42. Question
Topic: Practical Applications

Please have pen and paper handy to show workings out. 📝

📚 The following formula is used to calculate the total cost ( $C$ ) in pounds, for buying books:

$C = 5 \cdot n + 3$

a) 📖 What is the total cost of buying 8 books?

b) 💷 How many books can be bought for £28?
- a)
  
  c =
  
  £
  
  b)
  
  n =
  
  Books
  
  ⌨️ Type your answer in the fields provided.
Correct

Incorrect

Hint

Hint: A formula works like a number-machine—run the steps forward for an output, or reverse them to recover the input.

Example – Formula: M = 3x + 5

If x = 4, find M

Forwards Number Machine (symbols):

x → × 3 → + 5 → M

Forwards Number Machine (values):

4 → × 3 → 12 → + 5 → 17

So, M = 17.

If M = 17, find x

Backwards Number Machine (symbols):

x ← ÷ 3 ← − 5 ← M

Backwards Number Machine (values):

4 ← ÷ 3 ← 12 ← − 5 ← 17

So, x = 4.

💡 To reverse a number-machine, undo each operation in the opposite order: adding undoes subtraction, multiplying undoes division, squaring undoes square-rooting, and so on.
Question 43 of 44

43. Question
Topic: Practical Applications

Please have pen and paper handy to show workings out. 📝

📦 The following formula is used to calculate the volume ( $V$ ) of a shipment in cubic metres containing $B$ boxes:

$V = 0.8 B + 2$

a) 📦 What is the volume of a shipment containing 10 boxes?

b) 🚚 How many boxes can fit in a shipment with a volume of 18 cubic metres?
- a)
  
  v =
  
  cubic metres
  
  b)
  
  b =
  
  boxes
  
  ⌨️ Type your answer in the fields provided.
Correct

Incorrect

Hint

Hint: A formula works like a number-machine—run the steps forward for an output, or reverse them to recover the input.

Example – Formula: M = 3x + 5

If x = 4, find M

Forwards Number Machine (symbols):

x → × 3 → + 5 → M

Forwards Number Machine (values):

4 → × 3 → 12 → + 5 → 17

So, M = 17.

If M = 17, find x

Backwards Number Machine (symbols):

x ← ÷ 3 ← − 5 ← M

Backwards Number Machine (values):

4 ← ÷ 3 ← 12 ← − 5 ← 17

So, x = 4.

💡 To reverse a number-machine, undo each operation in the opposite order: adding undoes subtraction, multiplying undoes division, squaring undoes square-rooting, and so on.
Question 44 of 44

44. Question
Topic: Practical Applications

Please have pen and paper handy to show workings out. 📝

🏠 The following formula is used to calculate the heating cost ( $C$ ) in pounds, where $t$ is the number of hours the heating is on:

$C = 2 t^{2} - 5$

a) 🏠 What is the heating cost if the heating is on for 3 hours?

b) 💷 How many hours is the heating on if the cost is 45 pounds?
- a)
  
  c =
  
  pounds
  
  b)
  
  t =
  
  hours
  
  ⌨️ Type your answer in the fields provided.
Correct

Incorrect

Hint

Hint: A formula works like a number-machine—run the steps forward for an output, or reverse them to recover the input.

Example – Formula: M = 3x + 5

If x = 4, find M

Forwards Number Machine (symbols):

x → × 3 → + 5 → M

Forwards Number Machine (values):

4 → × 3 → 12 → + 5 → 17

So, M = 17.

If M = 17, find x

Backwards Number Machine (symbols):

x ← ÷ 3 ← − 5 ← M

Backwards Number Machine (values):

4 ← ÷ 3 ← 12 ← − 5 ← 17

So, x = 4.

💡 To reverse a number-machine, undo each operation in the opposite order: adding undoes subtraction, multiplying undoes division, squaring undoes square-rooting, and so on.

PA.3B, SEC 3, Practical Applications (44)

PA.3B, SEC 3, Practical Applications (44)

Quiz Summary

Information

Results

Results

Categories

1. Question

Topic: Practical Applications

Please have pen and paper handy to show workings out. 📝

🛠️ The following formula is used to calculate the time (T) in hours to assemble a machine:

T=4⋅m+2

a) 🕒 How long does it take to assemble 3 machines?

b) ⚙️ How many machines can be assembled in 18 hours?

a) t = hours b) m = Machines

⌨️ Type your answer in the fields provided.

Hint

2. Question

Topic: Practical Applications

Please have pen and paper handy to show workings out. 📝

🚧 The following formula is used to calculate the total cost (C) in pounds for renting equipment for d days:

C=50d+20

a) 🚧 What is the cost for renting equipment for 5 days?

b) 💷 How many days can the equipment be rented for £320?

a) c = £ b) d = days

⌨️ Type your answer in the fields provided.

Hint

3. Question

Topic: Practical Applications

Please have pen and paper handy to show workings out. 📝

💊 The following formula is used to calculate the dosage (D) in milligrams of a medication, where W is the weight of the patient in kilograms:

D=5W+15

a) 💊 What is the dosage for a patient weighing 36kg?

b) ⚕️ What is the weight of a patient if the dosage is 55mg?

a) d = mg b) w = kg

⌨️ Type your answer in the fields provided.

Hint

4. Question

Topic: Practical Applications

Please have pen and paper handy to show workings out. 📝

💧 The following formula is used to calculate the amount of water (W) in litres filled in a tank:

W=50⋅h+100

a) 💦 How much water is in the tank after 4 hours?

b) 🛁 How many hours does it take to fill 450 litres of water?

a) w = Liters b) h = Hours

⌨️ Type your answer in the fields provided.

Hint

5. Question

Topic: Practical Applications

Please have pen and paper handy to show workings out. 📝

⚡ The following formula is used to calculate the electrical power (P) in watts of a circuit:

P=IV+5

a) ⚡ What is the power if the current is 3A and the voltage is 12V?

b) 💡 What is the current if the power is 53W and the voltage is 10V?

a) p = W b) i = voltage

⌨️ Type your answer in the fields provided.

Hint

6. Question

Topic: Practical Applications

Please have pen and paper handy to show workings out. 📝

🔥 The following formula is used to calculate the water pressure (P) needed to extinguish a fire, where h is the height of the fire in metres:

P=4h2–20

a) 🚒 What is the pressure needed for a fire 5m high?

b) 💦 What is the height of the fire if the required pressure is 124 units?

a) p = units b) h = m

⌨️ Type your answer in the fields provided.

Hint

7. Question

Topic: Practical Applications

Please have pen and paper handy to show workings out. 📝

🍰 The following formula is used to calculate the total cost (C) of ordering n cakes:

C=12n+5

a) 🎂 How much does it cost to order 6 cakes?

b) 🍰 How many cakes can be ordered for £101?

a) c = £ b) n = cakes

⌨️ Type your answer in the fields provided.

Hint

8. Question

Topic: Practical Applications

Please have pen and paper handy to show workings out. 📝

🛠️ The following formula is used to calculate the time ( $T$ ) in hours to assemble a machine:

$T = 4 \cdot m + 2$

a)

t =

hours

b)

m =

Machines

🚧 The following formula is used to calculate the total cost ( $C$ ) in pounds for renting equipment for $d$ days:

$C = 50 d + 20$

a)

c =

£

b)

d =

days

💊 The following formula is used to calculate the dosage ( $D$ ) in milligrams of a medication, where $W$ is the weight of the patient in kilograms:

$D = 5 \sqrt{W} + 15$

a)

d =

mg

b)

w =

kg

💧 The following formula is used to calculate the amount of water ( $W$ ) in litres filled in a tank:

$W = 50 \cdot h + 100$

a)

w =

Liters

b)

h =

Hours

⚡ The following formula is used to calculate the electrical power ( $P$ ) in watts of a circuit:

$P = I V + 5$

a)

p =

W

b)

i =

voltage

🔥 The following formula is used to calculate the water pressure ( $P$ ) needed to extinguish a fire, where $h$ is the height of the fire in metres:

$P = 4 h^{2} - 20$

a)

p =

units

b)

h =

m

🍰 The following formula is used to calculate the total cost ( $C$ ) of ordering $n$ cakes:

$C = 12 n + 5$

a)

c =

£

b)

n =

cakes

🛠️ The following formula is used to calculate the torque ( $τ$ ) in newton-metres:

$τ = F r + 2$

a)

t =

Nm

b)

f =

N

🛫 The following formula is used to calculate the lift force ( $F$ ) in newtons generated by an aircraft, where $v$ is the speed in metres per second:

$F = 2 v^{2} + 50$

a)

f =

N

b)

v =

m/s

🚌 The following formula is used to calculate the total number of passengers ( $P$ ) on a bus route after $t$ stops:

$P = 15 t - 10$

a)

p =

passengers

b)

t =

stops

💊 The following formula is used to calculate the total dosage ( $D$ ) of medicine in milligrams:

$D = 2 W + 10$

a)

d =

mg

b)

w =

kg

✈️ The following formula is used to calculate the distance ( $D$ ) travelled by a plane in kilometres, where $t$ is the time in hours:

$D = 300 t - 100$

a)

d =

km

b)

t =

hours

☕ The following formula is used to calculate the cost ( $C$ ) in pounds for serving $n$ coffees:

$C = 1.5 n + 10$

a)

c =

£

b)

n =

coffees

🚀 The following formula is used to calculate the final velocity ( $v$ ) of an object:

$v = u + a t$

a)

t =

4m/s²

b)

v =

seconds