| Average changes when members join or leave the group | 6 | 2017–2025 |
| Maximise or minimise one value given an average and distinct/bounded others | 8 | 2018–2022 |
| Repeated replacement of a mixture: concentration × (1 − f) each time | 6 | 2018–2025 |
| Discriminant conditions for real, distinct or no real roots | 6 | 2017–2022 |
| Exponential equation turned into a quadratic in a^x | 6 | 2017–2025 |
| Integer equations solved by listing factor pairs | 5 | 2017–2025 |
| Infinite geometric series: a/(1 − r) | 5 | 2017–2025 |
| Marked price, discount and profit: MP × (1 − d) = CP × (1 + p) | 6 | 2017–2025 |
| Mixing solutions in a given ratio to find an unknown strength | 5 | 2017–2021 |
| Work completed in phases as workers join, leave or slow down | 5 | 2018–2025 |
| Person-days or person-hours are proportional to work done | 5 | 2020–2025 |
| Count divisors of a special form using prime-factor exponents | 5 | 2019–2025 |
| Counting numbers with distinct digits under conditions | 5 | 2020–2024 |
| Symmetric functions of roots via sum and product (Vieta) | 5 | 2017–2024 |
| Area of a region bounded by modulus graphs | 5 | 2017–2023 |
| Logs with bases that are powers of one base: convert to a common base | 5 | 2017–2025 |
| AP problems: write terms as a + (n − 1)d and solve | 5 | 2017–2025 |
| Regular hexagon as six equilateral triangles | 5 | 2017–2025 |
| Selling parts at different prices, rest as a mixture, to hit an overall profit | 4 | 2018–2022 |
| Comparing simple and compound interest on the same principal | 4 | 2019–2025 |
| Successive resales: multiply the profit and loss factors along the chain | 4 | 2017–2024 |
| Adding the same amount to each changes the ratio; difference stays fixed | 4 | 2017–2024 |
| Minimum or maximum of a quadratic at its vertex | 4 | 2020–2025 |
| Polynomial or rational inequalities by the sign of factors | 4 | 2017–2024 |
| Set equal powers or logs to a common k and take logs | 4 | 2017–2020 |
| Compare powers by summing exponents or taking logs | 4 | 2018–2025 |
| Three-set Venn diagrams: maximise or minimise a region | 4 | 2020–2025 |
| Rectangle or box in a circle or sphere: diagonal = diameter | 4 | 2018–2024 |
| Medians and centroid: 2:1 split and equal-area pieces | 4 | 2017–2024 |
| Parallelogram diagonals bisect each other: share a midpoint | 4 | 2017–2025 |
| Capital split across different interest rates: total interest | 6 | 2019–2025 |
| Integer solutions of a linear equation with count and range constraints | 5 | 2020–2025 |
| AM–GM bound on a sum of reciprocal-type terms | 5 | 2020–2023 |
| Sums of |x − a|: distance on the number line | 5 | 2017–2022 |
| Change of base: log_a b = 1 / log_b a | 5 | 2018–2021 |
| Integer solutions of x + y + z = n with lower or upper bounds | 5 | 2017–2022 |
| Chord and centre: r^2 = d^2 + (half chord)^2 | 5 | 2018–2025 |
| Transferring between two vessels and back: track each liquid | 4 | 2019–2025 |
| Work done in a repeating daily roster of workers | 4 | 2021–2024 |
| After meeting, speed ratio = √(ratio of remaining times) | 4 | 2020–2023 |
| Delay or stoppage on the way: new speed needed to arrive on time | 4 | 2020–2025 |
| Two items at different profit/loss rates: overall profit equation | 4 | 2019–2023 |
| Rearrange into a sum of squares equal to zero, so each square is zero | 4 | 2018–2024 |
| Equations with |x|: split into sign cases and count roots | 4 | 2019–2023 |
| Triangles with a common height: areas proportional to bases | 4 | 2021–2023 |
| Adding a pure component to shift a mixture's concentration | 3 | 2020–2024 |
| Pipes and cisterns with a draining pipe: net rate = fill − drain | 3 | 2017–2023 |
| Meeting time moving towards each other vs. in the same direction | 3 | 2018–2022 |
| Late at one speed, early at another: solve for distance | 3 | 2017–2024 |
| Boats and streams: upstream = b − s, downstream = b + s | 3 | 2017–2025 |
| Races: 'A beats B by x' as distance ratios over the course | 3 | 2017–2020 |
| One starts later from the other end: cover the head start, then meet | 3 | 2017–2020 |
| Loan repaid in instalments under compound interest | 3 | 2018–2025 |
| Two successive percentage changes with related rates | 3 | 2021–2024 |
| Total change from parts growing at different percentages | 3 | 2019–2021 |
| Pass mark from two scores relative to it | 3 | 2018–2020 |
| Combined average of two groups from group sizes and averages | 3 | 2017–2025 |
| Writing a number as m^n: n must divide every prime exponent | 3 | 2018–2024 |
| Equate exponents of each prime on both sides | 3 | 2019–2025 |
| Unique, none or infinitely many solutions of a 2×2 linear system | 3 | 2020–2024 |
| Multiplicative functional equations: evaluate at prime powers | 3 | 2017–2024 |
| nth term = S_n − S_(n−1) | 3 | 2018–2022 |
| Circular segment area = sector − triangle | 3 | 2017–2024 |
| Chords in a circle: similar triangles and power of a point | 3 | 2019–2025 |
| Regular polygons: exterior angle = 360°/n | 3 | 2019–2023 |
| Two kinds of workers or pipes in two combinations: solve for unit rates | 4 | 2018–2019 |
| Two mixing ratios give two equations for the components' values | 3 | 2018–2025 |
| Wages split in proportion to the work each person did | 3 | 2017–2021 |
| Trains crossing: relative speed covers the sum of lengths | 3 | 2020–2021 |
| Transfer between two holders changes the ratio; total stays fixed | 3 | 2018–2025 |
| Common terms of two APs form an AP with difference = LCM | 3 | 2019–2023 |
| Chained logs telescope via change of base | 3 | 2020–2024 |
| Rhombus: side and area give the diagonals via (d1 ± d2)^2 | 3 | 2021–2025 |
| Incircle of a right triangle: r = (a + b − c)/2 | 3 | 2021–2024 |
| Remainder of a large power: find the cycle of remainders | 3 | 2024 |
Ninetynine