Sample 11+ Maths Problem-Solving Questions (With Solutions)

Sample 11+ Maths Problem-Solving Questions (With Solutions)

Is your child preparing for the 11+ maths exam? This guide aims to provide parents and pupils with a variety of sample problem-solving for 11 Plus maths exam papers, complete with detailed solutions. They are designed to help students improve their skills and be confident about these challenging exams.

Sample Questions and Answers to 11+ Maths Problem-Solving

Sample 11+ Maths Problem-Solving Questions (With Solutions)

These sample questions cover topics typically found in schools’ 11+ maths exam papers, providing students with helpful test practice and explanations in different areas of mathematics. 

Sample 1: Number Sequences

Question: What is the next number in the sequence: 2, 5, 10, 17, 26, …?

Solution: Identify the pattern by looking at the differences between consecutive numbers: 5−2=3; 10−5=5; 17−10=7; 26−17=9 

The differences are increasing by two each time. So, the next difference should be 9+2=11. Add 11 to the last number in the sequence: 26+11=37. The next number is 37.

Sample 2: Decimals and Fraction Conversion

Question: Convert 0.75 to fractions. 

Solution: To convert decimals to fractions, write the decimal as fractions with one as the denominator and then multiply the numerator and denominator by ten until the numerator is an integer: 0.75=75/100​ 

Simplify by dividing both the numerator and the denominator by their greatest common divisor (25): 75/100 = 3/4​

Sample 3: Percentages Problem-solving

Question: What is 20% of 150?

Solution: To find percentages – 20% of 150: 0.20×150 = 30.

Sample 4: Algebra Problem-solving

Question: Solve for the algebra expression x: 3x+5=20

Solution: First, isolate the variable x: 3x+5=20. Subtract 5 from both sides: 3x=15. Divide by 3: x=5

Sample 5: Geometry Word Problems

Question: A rectangle has a length of 10 cm and a width of 4 cm. What is the area and perimeter of the rectangle?

Solution: Area: Area=length×width=10×4=40 cm2

Perimeter: Perimeter=2(length+width)=2(10+4)=2×14=28 cm

Sample 6: Ratio Word Problems

Question: The ratio of the number of apples to oranges in a basket is 3:2. If there are 15 apples, how many oranges are there?

Solution: Let the number of oranges be x. The ratio of apples to oranges is given by: 15/x=3/2.​ Solve for x: 3x=30 x=10. So, there are 10 oranges.

Sample 7: Measurement and Units

Question: How many millilitres are there in 2.5 litres? 

Solution: Since 1 litre is equal to 1000 millilitres, multiply the number of litres by 1000: 2.5×1000=2500. So, there are 2500 millilitres in 2.5 litres.

Sample 8: Probability Test 

Question: A bag contains 3 red balls, 2 green balls, and 5 blue balls. What is the probability of drawing a green ball?

Solution: First, find the total number of balls: 3+2+5=10. The number of green balls is 2. The probability is the ratio of the number of favourable outcomes to the total number of outcomes: Probability = 2/10=1/5​.

Sample 9: Money and Cost

Question: Jenny buys 3 notebooks for £2.50 each and a pack of pencils for £1.75. She pays with a £10 note. How much change does she get?

Solution: Calculate the total cost of the notebooks: 3×2.50=7.50 GBP. Add the cost of the pencils: 7.50+1.75=9.25 GBP. Subtract the total cost from the amount Jenny paid: 10−9.25=0.75 GBP. So, Jenny gets £0.75 in change.

Sample 10: Time and Speed

Question: A car travels at 60 km/h. How far will it travel in 2 hours and 30 minutes?

Solution: Convert the time to hours: 2 hours 30 minutes=2.5 hours. Calculate the distance using the speed formula (distance = speed × time): 60×2.5=150 km. So, the car will travel 150 km.

Sample 11: Form and Angle

Question: A triangle has angles measuring 50° and 60°. What is the measure of the third angle?

Solution: The sum of the angles in a triangle is always 180°. Calculate the third angle: 180−(50+60)=180−110=70°. So, the measure of the third angle is 70°.

Sample 12: Addition and Subtraction 

Question: Calculate the result of 5432−276+198.

Solution: First, subtract 276 from 5432: 5432−276=5156. Then, add 198 to the result: 5156+198=5354. So, the result is 5354.

Problem-Solving Strategies for 11 Plus Maths Questions

Understand the Maths Problem 

The first step in solving any 11+ maths problem is to understand what is being asked. Read the test problem carefully and identify the key information.

Break down the problem into smaller parts if necessary. Look for keywords and phrases that indicate mathematical operations, such as “total,” “difference,” or “product.” 

Draw a Shape or Diagram 

Visualising the problem can often make it easier for children to understand and solve the maths tests instead of word comprehension or vocabulary. Drawing a diagram, such as a straight line, a geometric shape, or a chart, can help clarify the relationships between different elements of the problem.

For example, if the problem involves distance or shape, a simple sketch on paper can show the answers to how different distances or shapes relate to each other. 

Choose a Strategy

Different mathematical problems may require students to use different approaches to answers. Some common strategies during the tests include: 

  • Working Backwards: Start from the desired result, reverse the solution operations to find the starting point, and then proceed to the answers.
  • Trial and Error: Make an educated guess, check if it satisfies the conditions, and adjust the answers if necessary.
  • Simplifying the Problem: Break down a complex problem into simpler parts that are easier to solve and pinpoint answers.
  • Looking for Patterns: Identify patterns or sequences that can lead to an answer. 

Practice Regularly

Consistent practice is key to becoming proficient in problem-solving for maths questions. A student needs to prepare and work on a variety of problems to build confidence and improve skills.

Use resources, practice papers, and timed tests to simulate exam conditions. We highly encourage you to review mistakes with parents or tutors for complete support and to understand where you went wrong with the tasks and how to avoid similar errors in the future.

Master the 11 Plus

A unique, confidence-boosting way to study for the 11 Plus


Mastering 11 Plus maths problem-solving paper is all about preparation, practice, and understanding the strategies behind each answer.

By working through these sample maths questions and answers, students can better understand mathematical concepts, enhance their problem-solving abilities, and be confident in answering these challenging exams.