TARA Problem Solving: Practice Questions and Worked Answers

Quick answer

Work through the three TARA Problem Solving question types with original examples and step-by-step answers. Practise selecting useful data, finding a method and spotting the same relationship in a different form.

The module contains 22 multiple-choice questions and lasts 40 minutes, within the three-part TARA test format. The examples below are original TaraPrep teaching questions, not official questions or a prediction of test difficulty. Try each before reading its answer, then move to a timed free mock.

The module assumes only a defined set of basic mathematical skills, but students must apply them flexibly and without a calculator.

What does the Problem Solving module test?

Problem Solving is about finding a route through a new problem when there is no ready-made method already provided. Students may need to:

• Decide which information is relevant
• Build a method from the information given
• Compare data shown in different forms
• Work accurately with simple arithmetic, percentages, measures and graphs

The difficulty usually comes from the reasoning process, not from advanced maths.

TARA Problem Solving format

There is only one correct answer to each question. Students should attempt every question because wrong answers are not penalised. The TARA scoring guide explains how correct-answer patterns become separate scaled results for Problem Solving and Critical Thinking.

The three official Problem Solving question types

The official TARA Question Guide names three main kinds of Problem Solving question.

Some questions may involve more than one of these skills at once.

1. Relevant Selection

Relevant Selection questions include extra information, just as real-world problems often do. The task is to ignore distractions and use only what helps solve the problem.

Students should ask:

• What is the question really asking for?
• Which numbers or facts affect that answer?
• Which details are present but unnecessary?

This skill is easy to underestimate because the arithmetic may be simple after the right information has been chosen.

Practice question: museum tickets

A school takes 28 pupils and 4 teachers to a museum. Pupil tickets cost £7 and adult tickets cost £11. One adult enters free for every complete group of 10 pupils. The museum's teaching room holds 60 people. How much does the school pay for admission?

Worked answer: C, £218. There are two complete groups of 10 pupils, so two teachers enter free. The pupils cost 28 × £7 = £196. The two paying teachers cost £22. Total: £196 + £22 = £218.

The room capacity does not affect ticket prices. £240 ignores the free places; £207 incorrectly allows a third free adult for the remaining eight pupils. Identify the eligibility rule before doing the arithmetic.

2. Finding Procedures

Finding Procedures questions ask students to invent the route to the answer. The required maths may be basic, but the method is not handed to them.

For example, a question might require a student to:

• Remove one component from a total
• Split the remainder in a ratio
• Apply different percentage changes
• Add the revised values back together

The challenge is seeing the sequence of steps clearly.

Practice question: buying enough notebooks

Notebooks come in packs of 8 for £11 or packs of 12 for £15. A club needs at least 50 notebooks and can buy any combination of whole packs. What is the lowest possible cost?

Worked answer: C, £67. Three large packs and two small packs give 36 + 16 = 52 notebooks for £45 + £22 = £67. To check that this is the cheapest combination, list the minimum number of small packs needed for each possible number of large packs:

Six or more large packs already cost at least £90, so they cannot improve the answer. Although large packs have a lower cost per notebook, buying only large packs is not the cheapest way to meet this particular minimum. Round up to whole packs and compare feasible combinations.

3. Identifying Similarity

Identifying Similarity questions ask students to compare patterns, relationships or representations. This can include:

• Matching a chart to another chart
• Comparing data shown in different forms
• Recognising rotations or reflections
• Understanding relationships in two-dimensional or three-dimensional shapes

These questions reward attention to structure rather than surface appearance.

Practice question: matching proportions

A survey records 6 votes for red, 9 for blue and 15 for green. Which set of percentages represents the same results?

Worked answer: C. There are 30 votes. Red has 6/30 = 20%, blue has 9/30 = 30%, and green has 15/30 = 50%. Equivalently, the original ratio 6:9:15 simplifies to 2:3:5.

Every option totals 100%, so checking the total alone cannot identify the answer. Option B uses the right percentages with two labels swapped. Match each category's share, not just the overall shape or the largest value.

What maths does the TARA expect?

The official content specification gives a clear list of the mathematical knowledge required. The companion guide on maths for TARA Problem Solving separates the required topics from advanced material that candidates do not need to revise.

Number concepts

• Simple fractions
• Place value
• Percentages

Numerical operations

• Addition, subtraction, multiplication and division
• Percentage calculations
• Everyday calculations with decimals and fractions
• Mean averages

Quantities

• Time and calendars
• Money
• Measures

Space and spatial reasoning

• Area
• Perimeter
• Volume

Tables and graphs

• Extracting information from graphs and charts
• Extracting information from tables

Students are also expected to know common metric relationships such as:

What does "no calculator" mean in practice?

Students do not need advanced calculations, but they do need confidence with arithmetic under time pressure. The best preparation is not only to practise the right topics, but to practise doing them neatly and efficiently by hand.

Useful habits include:

• Estimating before calculating
• Writing units beside values
• Keeping ratio working organised
• Checking whether the answer size is sensible

What makes this section difficult?

The most common problem is not the maths syllabus itself. It is that students may:

• Use irrelevant information
• Miss an intermediate step
• Misread a chart or table
• Calculate accurately from the wrong starting point
• Spend too long trying to force one method

How should students approach the module?

1. Read the final question carefully before processing all the data
2. Mark the information that matters
3. Decide on a method before starting long calculations
4. Keep rough work structured
5. Use estimation to catch unreasonable answers
6. Move on if a question is taking too long

What should students practise?

The best preparation combines:

• Timed mixed practice
• Focused work on the three question types
• Short daily arithmetic drills
• Review of the official maths list
• Reflection on method, not just the final answer

The TARA preparation study plan shows when to move from these focused skills into timed modules and full mock papers.

TaraPrep separates focused Problem Solving questions from the mental-maths trainer. Use the trainer for slow arithmetic and the question bank for selection, procedure and representation errors; they solve different problems.

Official sources

• UAT-UK TARA content specification
• UAT-UK TARA preparation materials

If a student gets a question wrong, they should ask whether the issue was:

• Understanding the task
• Choosing the information
• Choosing the method
• Carrying out the arithmetic
• Checking the answer

Last reviewed against official sources 16 July 2026.