Problems from Oct 18, 2026

All 12 problems from Oct 18, 2026, across Physics, Math, Chemistry, Electrical engineering. Try each one first, then check the answer and the main steps below.

Physics

Problem 1: Time for one wave

A wave has a frequency of 4 Hz.

How long does one cycle take, in seconds?

Answer: 0.25 s

How it is solved

  1. Period = 1 ÷ frequency: $1 \div 4$. ($0.25\ \text{s}$)

Problem 2: A thrown stone

A $0.5$ kg stone is thrown at $20$ m/s.

What is its kinetic energy, in joules?

Answer: 100 J

How it is solved

  1. Use kinetic energy = ½ × mass × speed²: $100\ \text{J}$

Problem 3: Sonar depth

A ship sends a pulse of sound straight down. The echo from the sea floor comes back after 0.4 s. Sound travels at 1500 m/s in water.

How deep is the water, in metres?

Answer: 300 m

How it is solved

  1. Distance there and back: $600\ \text{m}$
  2. Depth is half of that: $300\ \text{m}$

Math

Problem 1: One unknown

A taxi charges a fixed 7 dollars plus 3 dollars for every kilometre, so a trip costs 22 dollars in total. Let $x$ be the number of kilometres.

Solve for $x$.

Answer: 5

How it is solved

  1. Take away the constant: $3x = 22 - 7 = 15$. ($3x = 15$)
  2. Divide by the number in front of x: $x = 15 \div 3$. ($x = 5$)

Problem 2: A twelve-sided coin

A coin is a regular shape with $12$ equal sides and equal angles.

What is the size of one inside angle of the shape, in degrees?

Answer: 150

How it is solved

  1. Angle sum of the whole shape: $10 \times 180 = 1800^\circ$
  2. Share it equally: $1800 \div 12 = 150^\circ$

Problem 3: Growing bacteria

A culture starts with 5 bacteria. Every hour the number is multiplied by 3. This goes on for 3 hours. The chart shows the count at the start and after each step except the last.

How many are there at the end?

Answer: 135

How it is solved

  1. Each step multiplies by the same number: $45$
  2. One more step: $135$

Chemistry

Problem 1: A salt solution

15 g of salt is stirred into 185 g of water until it dissolves.

What is the total mass of the mixture, in grams?

Answer: 200 g

How it is solved

  1. Add the masses: $15 + 185$. ($200\ \text{g}$)

Problem 2: Making sodium hydroxide solution

Atomic masses: Na $=23$, O $=16$, H $=1$.

How many grams of $\ce{NaOH}$ are needed to make $250\ \text{mL}$ of a $0.1\ \text{M}$ solution?

Answer: 1 g

How it is solved

  1. Moles needed: $0.025\ \text{mol}$
  2. Mass of that many moles: $1\ \text{g}$

Problem 3: Average mass of chlorine

The table shows the isotopes of chlorine and how common each one is.

What is the average atomic mass of chlorine?

IsotopeMass numberMass (u)Abundance (%)
Cl-35353575
Cl-37373725
Average atomic mass35.5100

Answer: 35.5

How it is solved

  1. Multiply each mass by its share
  2. Add them: $35.5$

Electrical engineering

Problem 1: Currents in parallel

A battery is connected to three parallel branches. The branch currents are 3, 2, 1.5 amps.

What total current flows from the battery, in amps?

Answer: 6.5 A

How it is solved

  1. Currents in parallel branches add: $3 + 2 + 1.5$. ($6.5\ \text{A}$)

Problem 2: A gate that needs A

A logic circuit has three inputs A, B and C, and an output $Z$ where $Z = A \text{ AND } (B \text{ OR } C)$.

Three inputs can be set in $8$ different ways. For how many of those $8$ settings is $Z$ equal to $1$?

Answer: 3

How it is solved

  1. Work out what makes Z equal 1
  2. Count the settings: $3$

Problem 3: Energy for a pump

A 12 V pump draws 5 A for 10 minutes.

How much energy does it use, in kilojoules?

Answer: 36 kJ

How it is solved

  1. Power: $60\ \text{W}$
  2. Energy = power × time in seconds: $36000\ \text{J}$
  3. Change to kilojoules: $36\ \text{kJ}$