Problems from Oct 17, 2026
All 12 problems from Oct 17, 2026, across Physics, Math, Chemistry, Electrical engineering. Try each one first, then check the answer and the main steps below.
Physics
Problem 1: A short sprint
A sprinter covers $150\ \text{m}$ in $12\ \text{s}$ at a steady pace.
What is the average speed, in metres per second?
Answer: 12.5 m/s
How it is solved
- Use speed = distance ÷ time: $150 \div 12$. ($12.5\ \text{m/s}$)
Problem 2: A load on a beam
A load of $40\ \text{N}$ hangs $3\ \text{m}$ from the pivot of a beam, on the left.
What is the turning effect (moment) of the load about the pivot, in newton-metres?
Answer: 120
How it is solved
- Moment = force × distance from the pivot: $120\ \text{N m}$
Problem 3: A pair of gears
A small gear of $10$ teeth is turned at $90$ turns per minute and meshes with a gear of $30$ teeth.
How many turns per minute does the large gear make?
Answer: 30
How it is solved
- Teeth passing a point: $900$ teeth
- The big gear must move the same number of teeth: $900 \div 30 = 30$ turns
Math
Problem 1: Tickets for the school play
The box office starts the day with $360$ tickets. By closing time, $25\%$ of them have been sold.
How many tickets are left?
Answer: 270
How it is solved
- Find how many were sold: $25\%$ of $360$ is $360 \times 25 \div 100$. ($90$ sold)
- Take that away from the start: $360 - 90$. ($270$)
Problem 2: Spread of a class
Test marks of eight students. The box plot summarises the results.
What is the interquartile range?
Answer: 9.5
How it is solved
- Read the quartiles
- Subtract: $9.5$
Problem 3: A coaster in a box
A round coaster of radius $6$ cm fits exactly in a square box, touching all four sides. The box has side $12$ cm.
What is the area of the square that is not covered by the circle? Use a calculator value for $\pi$ and give the answer to the nearest whole number.
Answer: 31
How it is solved
- Area of the square: $144$
- Area of the circle: $113.1$
- Subtract: $30.9$, about $31$
Chemistry
Problem 1: Counting in calcium hydroxide
One unit of a compound has the formula $\ce{Ca(OH)2}$.
How many atoms are there in $7$ units?
Answer: 35
How it is solved
- Count the atoms in one unit: A number after a symbol multiplies that atom. A number after a bracket multiplies everything inside it. One unit has 1 Ca + 2 O + 2 H. ($5$ atoms)
- Multiply by the number of units: $5 \times 7$. ($35$)
Problem 2: Lemon and milk
Each pH step down makes a liquid ten times more acidic. The picture shows lemon juice and milk.
How many times more acidic is lemon juice than milk?
Answer: 10000
How it is solved
- Read both markers
- The gap is the number of tens: $10000$
Problem 3: Hydrogen from magnesium
The reaction is $\ce{Mg + 2HCl -> MgCl2 + H2}$. Magnesium reacts with plenty of acid. Assume one mole of any gas takes up $22.4\ \text{L}$. Atomic masses: Mg $=24$.
What volume of $\ce{H2}$ is made from $48\ \text{g}$ of $\ce{Mg}$?
Answer: 44.8 L
How it is solved
- Moles of the starting material: $2\ \text{mol}$
- Moles of gas made: $2\ \text{mol}$
- Volume: $44.8\ \text{L}$
Electrical engineering
Problem 1: Current in a resistor
A $9\ \text{V}$ supply is connected across a resistor of $300\ \Omega$.
What current flows, in milliamps?
Answer: 30 mA
How it is solved
- Use I = V ÷ R: $9 \div 300$ amps. ($0.03\ \text{A}$)
- Change to milliamps: Multiply by $1000$. ($30\ \text{mA}$)
Problem 2: Finding tau
A resistor of 2000 ohms charges a capacitor of 100 microfarads. The time constant is the resistance in ohms times the capacitance in farads.
What is the time constant, in seconds?
Answer: 0.2 s
How it is solved
- Use the units in ohms and farads: $0.0001\ \text{F}$
- Multiply: $0.2\ \text{s}$
Problem 3: The missing resistance
A $9$ V supply drives $30$ mA through two resistors in series, one of $100$ ohms.
What is the resistance of the second resistor, in ohms?
Answer: 200 ohm
How it is solved
- Total resistance: $300\ \Omega$
- Take away the known one: $200\ \Omega$