Problems from Oct 12, 2026

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

Physics

Problem 1: Pushing a box

A heavy box is pushed along the floor. The forces on it are shown. Up and down balance out.

What is the net force, in newtons, to the right?

Answer: 30 N

How it is solved

  1. Forces in the same line: Right: $50\ \text{N}$. Left: $20\ \text{N}$.
  2. Subtract the smaller from the larger: $50 - 20$. ($30\ \text{N}$)

Problem 2: An efficient machine

A machine takes in $800$ J of energy and is $65\%$ efficient.

How much useful energy does it give out, in joules?

Answer: 520 J

How it is solved

  1. Efficiency means the useful share: $520\ \text{J}$

Problem 3: Lifting a block

A crane gives 600 J of energy to a 3 kg block. Use $g = 10\ \text{N/kg}$.

How high is it lifted, in metres?

Answer: 20 m

How it is solved

  1. Energy = mass × g × height
  2. Divide: $20\ \text{m}$

Math

Problem 1: Muffins at the stand

The bar chart shows the number of muffins sold on each of five days.

How many muffins were sold in total over the five days?

Answer: 80

How it is solved

  1. Add the bars: $12 + 18 + 15 + 22 + 13$. ($80$)

Problem 2: Adding two dice

Two fair six-sided dice are rolled.

What is the probability that the two numbers add to $7$? Give a reduced fraction.

Answer: 1/6

How it is solved

  1. All the outcomes: $36$ outcomes
  2. Outcomes that add to $7$: $6$ outcomes
  3. Make a fraction: $\frac{1}{6}$

Problem 3: A round table

A round table has a radius of 5 cm. Use $\pi = 3.14$.

What is its area, in square centimetres?

Answer: 78.5

How it is solved

  1. Use area = pi times radius squared: $78.5\ \text{cm}^2$

Chemistry

Problem 1: Neutrons in sodium

The picture shows an atom of sodium with mass number $23$.

How many neutrons does it have?

Answer: 12

How it is solved

  1. Count the protons: The atom has $11$ protons. ($11$)
  2. Mass number = protons + neutrons: $23 - 11$. ($12$)

Problem 2: Oxygen to burn methane

The fuel burns as $\ce{CH4 + 2O2 -> CO2 + 2H2O}$. Atomic masses: C $=12$, H $=1$, O $=16$.

How many grams of oxygen ($\ce{O2}$) are needed to burn $16\ \text{g}$ of $\ce{CH4}$?

Answer: 64 g

How it is solved

  1. Moles of fuel: $1\ \text{mol}$
  2. Moles of oxygen from the ratio: $2\ \text{mol}$
  3. Back to grams: $64\ \text{g}$

Problem 3: Blending two salt solutions

100 g of a 10% salt solution is mixed with 300 g of a 20% salt solution.

What is the percent by mass of the mixture?

Answer: 17.5

How it is solved

  1. Solute in each
  2. Add the solute and the totals
  3. Divide: $17.5\%$

Electrical engineering

Problem 1: Frequency from a scope

The scope screen shows one full wave. Each horizontal division is $1\ \text{ms}$ and one full wave is $4$ divisions wide.

What is the frequency of the wave, in hertz?

Answer: 250 Hz

How it is solved

  1. Time for one wave: $4 \times 1\ \text{ms} = 4\ \text{ms}$. ($4\ \text{ms}$)
  2. Frequency = 1 ÷ period: $1 \div 0.004$. ($250\ \text{Hz}$)

Problem 2: Adding in binary

Two binary numbers are added: $1011$ and $0110$.

What is the sum, written in ordinary (decimal) numbers?

Answer: 17

How it is solved

  1. Change each to decimal: $11$ and $6$
  2. Add: $17$

Problem 3: How long a battery lasts

A battery holds 2400 mAh and a device draws 300 mA.

For how many hours can it run?

Answer: 8 h

How it is solved

  1. Hours = capacity ÷ current: $8\ \text{h}$