Problems from Oct 14, 2026

All 12 problems from Oct 14, 2026, across Physics, Math, Chemistry, Electrical engineering. Try each one first, then check the answer and the main steps below.

Physics

Problem 1: In front of a mirror

A person stands 1.5 metres in front of a flat mirror.

How far is the person from their own image in the mirror, in metres?

Answer: 3 m

How it is solved

  1. The image is as far behind as the object is in front: The image is $1.5$ m behind the mirror.
  2. Add both distances: $1.5 + 1.5$. ($3.0\ \text{m}$)

Problem 2: Out and back

A bus drives $60$ km to a town at $30$ km/h, then returns along the same road at $60$ km/h.

What is the average speed for the whole round trip, in kilometres per hour?

Answer: 40 km/h

How it is solved

  1. Time for each leg: $2\ \text{h}$ and $1\ \text{h}$
  2. Total distance and time: $120\ \text{km}$ in $3\ \text{h}$
  3. Average speed = total distance ÷ total time: $40\ \text{km/h}$

Problem 3: Pushing up a ramp

A box of mass $20\ \text{kg}$ is pushed up a smooth (frictionless) ramp that is $5\ \text{m}$ long and rises $3\ \text{m}$. Use $g = 10\ \text{N/kg}$.

What steady push along the ramp is needed, in newtons?

Answer: 120 N

How it is solved

  1. Weight: $200\ \text{N}$
  2. The ramp does the same work with a longer path: $120\ \text{N}$

Math

Problem 1: A hiking trail

A trail of 60 km is split into three parts. The first part is 18 km and the second part is 25 km.

How long is the third part, in km?

Answer: 17

How it is solved

  1. Add the known parts: $18 + 25$. ($43$)
  2. Subtract from the whole: $60 - 43$. ($17$)

Problem 2: Coin jar

A box holds $40$ items. Each is either a nickel (worth 5¢) or a dime (worth 10¢). Together they are worth 335¢.

How many dimes are in the box?

Answer: 27

How it is solved

  1. Pretend every one is a nickel: $200$ cents
  2. See how far off that is: $135$ cents short
  3. Swap one at a time: $27$ dimes

Problem 3: Area of a trapezium

A garden bed is a trapezium. The two parallel sides are $14$ cm and $8$ cm long, and the height between them is $6$ cm.

What is the area of the shape, in square centimetres?

Answer: 66

How it is solved

  1. Add the parallel sides: $22$
  2. Use half of that times the height: $66$

Chemistry

Problem 1: Reading a burette

A student reads a burette during a titration. The picture shows the scale and where the liquid surface is. Read it to two decimal places.

The reading then goes up by 2. What is the new reading?

Answer: 25.47

How it is solved

  1. Read the scale: The liquid surface is at $23.47$. ($23.47$)
  2. Add the change: $23.47 + 2$. ($25.47$)

Problem 2: Water from hydrogen

The reaction is $\ce{2H2 + O2 -> 2H2O}$. Atomic masses: H $=1$, O $=16$.

How many grams of $\ce{H2O}$ are made from $8\ \text{g}$ of $\ce{H2}$?

Answer: 72 g

How it is solved

  1. Moles of $\ce{H2}$: $4\ \text{mol}$
  2. Use the ratio in the equation: $4\ \text{mol}$ of $\ce{H2O}$
  3. Back to grams: $72\ \text{g}$

Problem 3: Adding a catalyst

The energy diagram is for a reaction with and without a catalyst. The reactants start at $40$ kJ. The peak is $110$ kJ without a catalyst and $75$ kJ with one.

By how many kilojoules does the catalyst lower the energy that must be put in to start the reaction (the activation energy)?

Answer: 35 kJ

How it is solved

  1. Activation energy = peak - reactants
  2. Subtract: $35\ \text{kJ}$

Electrical engineering

Problem 1: Counting a high output

The timing diagram shows inputs A and B of an AND gate over 8 time slots. A is 01101100 and B is 00111010.

In how many time slots is the output high (1)?

Answer: 2

How it is solved

  1. Work out the output in every slot: Output: 00101000.
  2. Count the ones: There are $2$ ones. ($2$)

Problem 2: Two side by side

Two resistors, $30$ ohms and $60$ ohms, are connected in parallel.

What is the combined resistance, in ohms?

Answer: 20 ohm

How it is solved

  1. Use the product over the sum
  2. Put in the numbers: $20\ \Omega$

Problem 3: Three parallel branches

A 12 V battery is connected across resistors of 30, 60, 20 ohms in parallel.

What total current does the battery supply, in amps?

Answer: 1.2 A

How it is solved

  1. Current in each branch
  2. Add the branch currents: $1.2\ \text{A}$