Brevet mathematics paper 2026 with full solutions (DNB)

Duration: 20 minutes — no calculator allowed. For each question, copy out its number and the matching answer. No justification is required. For the multiple-choice questions, only one answer is correct.

1. Write the number 0.75 as a fraction.
2. Work out the sum -4.7 + 3.5.
3. In the proportionality table in the paper, 6 corresponds to 18 and 12 corresponds to a. What is the value of a?
4. A bag contains 10 red balls, 4 blue balls and 6 green balls. One ball is drawn at random, every ball being equally likely to be chosen. What is the probability of getting a blue ball?
   • A. 1/4
   • B. 4/20
   • C. 4/16
   • D. 1/3
5. What is the solution of the equation 10x + 16 = -64?
   • A. 8
   • B. -4.8
   • C. -8
   • D. -14
6. What is the scientific notation of the number 0.00458?
   • A. 458 × 10⁻³
   • B. 4.58 × 10³
   • C. 4.58 × 10⁻³
   • D. 458 × 10⁻⁵
7. The pie chart in the paper shows how 24 students answered a multiple-choice question. How many students chose answer B?
8. What is the perimeter of the rectangle in the paper, which measures 10 mm by 5 mm?
   • A. 30 mm
   • B. 30 mm²
   • C. 50 mm
   • D. 50 mm²
9. Triangle DEF has a right angle at E, with DE = 6 cm, EF = 8 cm and DF = 10 cm. Which expression gives the cosine of angle EDF?
   • A. 4/5
   • B. 3/5
   • C. 5/3
   • D. 4/3

The table in the paper shows the number of medals won by 9 countries at the Paris 2024 Paralympic Games.

1. How many gold medals did the Netherlands win?
2. Work out the number of gold medals won by Australia.
3. Show that the statement “More than 20% of the medals won by Great Britain are bronze” is true.
4. a. Find the median of the set of medal totals won by these 9 countries. Show your working.
   b. Interpret this result in the context of the exercise.
5. Brazil won 20 silver medals in Tokyo in 2021 and 26 in Paris in 2024. What is the percentage increase?

On the figure in the paper:

• the lines (BD) and (CE) meet at A;
• the lines (BC) and (DE) are parallel;
• AB = 6.4 cm, AC = 4.8 cm, AD = 4.8 cm and BC = 8 cm.

1. Show that triangle ABC has a right angle at A.
2. Show that DE = 6 cm and AE = 3.6 cm.
3. Show that angles ABC and ADE are equal. Show your working.
4. Show that triangles ABC and ADE are similar.
5. Find the area of the quadrilateral BCDE.

Parts A and B are independent.

Part A — Reading from a graph

The curve in the paper shows the volume of a sphere, in cm³, as a function of its radius, in cm.

1. Use the graph to find the image of 3.6 under this function.
2. The volume of a sphere is 660 cm³. Read its radius from the graph.

Part B — 3D printing

We want to make solid plastic spheres of radius 2.5 cm with a 3D printer. Recall that V = 4/3 × π × R³.

1. Show that the volume of a sphere, rounded to the nearest whole number, is 65 cm³.
2. We have a spool of 1,000 cm³ of plastic. What is the greatest number of spheres that can be made?
3. The density of the plastic is 0.9 g/cm³. Work out the mass of one sphere.

We have 112 strawberry sweets and 140 caramel sweets to make up identical bags. Every sweet must be used.

1. Can we make up 16 bags?
2. The prime factorisation of 112 is 2⁴ × 7. What is the prime factorisation of 140?
3. What is the greatest number of bags that can be made? What will each bag then contain?