Abacus Beta programme

Build speed, confidence & number sense.

Beta Group is designed for learners from Grade 2 onwards, progressing from strong abacus foundations to advanced calculations.

5 progressive levels Grade 2 onwards Abacus-based learning
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Beta Group

Olympiad Syllabus

Choose a level to view its assessment pattern, formulas and sample paper.

View Beta Group sample paper →
1
For Grade 2 onwards

Basic abacus & the Big Friend formula

The first 20 sums are direct sums with no formula at all. The remaining 50 bring in the Big Friend (complements of 10) formula.

Set A — Grade 2 to 4

70 questions5 min70 marks
20 Q Direct sum, single/double digit, 3 rows
20 Q Big Friend addition & subtraction, double digit, 3 rows
30 Q Mixed zigzag sums, double & single digit, 4 rows
All sums calculated on the abacus.Sample paper ↗

Set B — Grade 5 to 8

70 questions5 min70 marks
20 Q Direct sum, single/double digit, 3 rows
20 Q Big Friend addition & subtraction, double digit, 4 rows
30 Q Mixed zigzag sums, double & single digit, 4 rows
All sums calculated on the abacus.Sample paper ↗

Big Friend — addition / subtraction formula

Big Friend of 9 is 1 +9 = +10 −1 −9 = −10 +1
Big Friend of 8 is 2 +8 = +10 −2 −8 = −10 +2
Big Friend of 7 is 3 +7 = +10 −3 −7 = −10 +3
Big Friend of 6 is 4 +6 = +10 −4 −6 = −10 +4
Big Friend of 5 is 5 +5 = +10 −5 −5 = −10 +5
Big Friend of 4 is 6 +4 = +10 −6 −4 = −10 +6
Big Friend of 3 is 7 +3 = +10 −7 −3 = −10 +7
Big Friend of 2 is 8 +2 = +10 −8 −2 = −10 +8
Big Friend of 1 is 9 +1 = +10 −9 −1 = −10 +9
2
For Grade 3 onwards

Small Friend & Combination formulas

Introduces the Small Friend formula (base 5) alongside the Combination, or "family," formulas for +/− 6, 7, 8 and 9.

Level 2 syllabus

70 questions5 min70 marks
20 Q Big Friend addition & subtraction, single/double digit, 4 rows
20 Q Small Friend addition & subtraction, single/double digit, 3–4 rows
20 Q Mixed zigzag sums, double & single digit, 3–4 rows
10 Q Mixed questions across all formulas, 6 rows
All sums calculated on the abacus.Sample paper ↗

Small Friend formula

Small Friend of 4 is 1 +4 = −1 +5 −4 = +1 −5
Small Friend of 3 is 2 +3 = −2 +5 −3 = +2 −5
Small Friend of 2 is 3 +2 = −3 +5 −2 = +3 −5
Small Friend of 1 is 4 +1 = −4 +5 −1 = +4 −5

Combination formula

Combination of 6 is 1 +6 = +10 −5 +1 −6 = −10 +5 −1
Combination of 7 is 2 +7 = +10 −5 +2 −7 = −10 +5 −2
Combination of 8 is 3 +8 = +10 −5 +3 −8 = −10 +5 −3
Combination of 9 is 4 +9 = +10 −5 +4 −9 = −10 +5 −4
3
For Grade 3 onwards

All formulas together

Direct, Small Friend, Big Friend and Combination formulas are now used together. Suited to students at abacus Level 3, with Level 4 students also eligible to sit this paper.

Level 3 syllabus

70 questions5 min70 marks
20 Q Addition & subtraction, single digit, 8 rows
20 Q Addition & subtraction, double digit, 4 rows
20 Q Addition & subtraction, three digit, 2 rows
10 Q Mixed zigzag questions, single/double digit, 5 rows
All sums calculated on the abacus.Sample paper ↗
4
For Grade 4 onwards

Multiplication & division enter

Direct, Small Friend, Big Friend and Combination formulas, now joined by multiplication and division. Suited to students at abacus Level 4, with Level 5 students also eligible.

Level 4 syllabus

70 questions5 min70 marks
20 Q Addition & subtraction, double digit, 6 rows
20 Q Addition & subtraction, three digit, 2 rows
10 Q Multiplication, double digit by single digit (11×1)
10 Q Division, three digit by single digit (111÷1)
10 Q Mixed zigzag questions, single/double digit, 6 rows
All sums calculated on the abacus.Sample paper ↗
5
For Grade 4 onwards

The advanced level

Every formula — Direct, Small Friend, Big Friend, Combination — plus multiplication and division, at full pace. For students who have completed abacus Level 5.

Level 5 syllabus

70 questions5 min70 marks
20 Q Addition & subtraction, double digit, 6 rows
20 Q Addition & subtraction, three digit, 3 rows
10 Q Multiplication, three digit by single digit (111×1)
10 Q Division, four digit by single digit (1111÷1)
10 Q Multiplication, two digit by two digit (11×11)
All sums calculated on the abacus.Sample paper ↗