Problems from Oct 16, 2026

All 12 problems from Oct 16, 2026, across Physics, Math, Chemistry, Electrical engineering. Try each one first, then check the answer and the main steps below.

Physics

Problem 1: Appliance power

The bar chart shows the power, in watts, of 3 appliances (from left to right: lamp, fan, radio). They run for 5, 10, 4 hours, in that order.

How much energy do they use in total, in kilowatt-hours?

Answer: 0.78

How it is solved

  1. Energy for each = power × time: $60 \times 5 = 300$ Wh; $40 \times 10 = 400$ Wh; $20 \times 4 = 80$ Wh.
  2. Add and change to kilowatt-hours: $780 \div 1000$. ($0.78\ \text{kWh}$)

Problem 2: Mixing hot and cool water

$200\ \text{g}$ of water at $80\ ^\circ\text{C}$ is mixed with $300\ \text{g}$ of the same water at $20\ ^\circ\text{C}$. No heat is lost.

What is the final temperature, in $^\circ\text{C}$?

Answer: 44

How it is solved

  1. Heat lost equals heat gained
  2. Write the equation
  3. Solve for T: $T = 44\ ^\circ\text{C}$

Problem 3: Speeding up from rest

A train starts from rest and speeds up steadily to $12\ \text{m/s}$ in $6\ \text{s}$.

How far does it travel in those $6$ seconds, in metres?

Answer: 36 m

How it is solved

  1. The area under the graph is a triangle: $36\ \text{m}$

Math

Problem 1: The middle value

Seven students' scores in a quiz are shown. The bar chart shows each value.

What is the median?

Answer: 7

How it is solved

  1. Read the bars and put them in order: $3, 4, 5, 7, 8, 9, 12$.
  2. Take the middle one: There are $7$ values, so the middle is number $4$. ($7$)

Problem 2: Filling the tank

A tank can be filled by one pipe alone in $6$ hours, or by a second pipe alone in $3$ hours.

How many hours does it take to fill the tank when both work together at the same time?

Answer: 2

How it is solved

  1. Rate of each
  2. Add the rates: $\frac{9}{18}$ of the job each hour
  3. Flip it: $2$ hours

Problem 3: Extending a line

A straight line is drawn on a graph. The line passes through the points (1, 3) and (3, 7).

What is the value of $y$ when $x = 6$?

Answer: 13

How it is solved

  1. Find the gradient: $2$
  2. Find where it crosses the y-axis: $c = 1$
  3. Put in the x value: $13$

Chemistry

Problem 1: Counting carbons in butane

The picture shows the structure of butane. Each corner or end of a line without a label is a carbon atom.

How many carbon atoms does a molecule of butane have?

Answer: 4

How it is solved

  1. Count the unlabelled corners and ends: Each one is a carbon atom. ($4$)

Problem 2: How many particles?

A sample contains $0.5$ mol of molecules. One mole contains $6.0 \times 10^{23}$ particles.

How many particles are there? Give your answer as a number times $10^{23}$.

Answer: 3

How it is solved

  1. Multiply by the number in one mole: $3 \times 10^{23}$

Problem 3: Decay of a sample

The graph shows a radioactive sample decaying. Half of it is left after every $5$ days.

What fraction is left after $15$ days? Give a reduced fraction.

Answer: 1/8

How it is solved

  1. Count the half-lives: $3$ half-lives
  2. Halve it that many times: $\frac{1}{8}$

Electrical engineering

Problem 1: Walking the machine

The state machine starts in S0. Each input moves it along the arrow with that label. The inputs arrive in this order: 1, 1, 0, 1.

How many of the moves end in state S2?

Answer: 1

How it is solved

  1. Follow each input: States after each move: S1, S2, S0, S1.
  2. Count the S2s: $1$. ($1$)

Problem 2: Current in two branches

A $9$ V battery is connected across two resistors in parallel: $18$ ohms and $36$ ohms.

What total current does the battery supply?

Answer: 0.75 A

How it is solved

  1. Each branch has the full voltage
  2. Current in each
  3. Add them: $0.75\ \text{A}$

Problem 3: A and not B

The output Y is high only when A is 1 and B is 0 (a NOT gate turns B round before the AND gate). Over 8 time slots, A is 01101101 and B is 00110110.

In how many slots is Y high?

Answer: 3

How it is solved

  1. Turn B round
  2. AND it with A: $3$