‹ Back to Mathematics

This is not another list of guides — it is the order to fix things in. Every guide named here is also in the syllabus list; what this page adds is which one matters most, and why.

Your arithmetic is not the problem

You scored 61 out of 77 on the Foundations Check in August, and the score is the least interesting part. Number sense and the four operations came back solid on all seven steps — right up to Extended level, with no gap anywhere. That is a real asset, and it rules out the thing people usually assume.

What the check actually found is two loose bricks sitting above that solid arithmetic. Fix those two and a good deal of what currently feels hard gets easier on its own.

Where it broke, lowest first
Indices & standard formbroke at step 2 (age 11–12) · E1.3, E1.7, E1.8, E1.9 — all four high non-calculator risk
Algebraic manipulationbroke at step 3 (age 13–14) · E2.1, E2.2, E2.4
Ratio and proportionbroke at step 5 · E1.11, E1.12
Coordinates and gradientbroke at step 5 · E3.3, E3.5, E3.6

Everything else broke at step 6 or 7, which is Extended level and exactly where it should be. Also worth knowing: 5 answers you were sure about were wrong, and sign errors turned up in more than one topic. Both are dealt with in the guides below.

Fix them in this order
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1 · Indices, Roots and Standard Form
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Your lowest break, and the one costing most. Rebuilt from what a power actually means, up through the index laws, negative and fractional indices, standard form and estimation. Non-calculator throughout.
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2 · Algebraic Manipulation
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Starts with the sign rules built from the number line, because sign errors were your one recurring mistake. Then like terms, substitution, brackets, factorising and indices in algebra.
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3 · Ratio and Proportion
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Sharing in a ratio, the unitary method, inverse proportion and rates — all worked by hand.
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4 · Coordinates, Straight Lines and Gradient
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Gradient built from a picture rather than a formula, then y = mx + c, parallel and perpendicular lines. Three of these are high non-calculator risk.
Where these findings came from
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Foundations Check DONE · 9 AUG
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Sat 9 August 2026 — 61 out of 77. 77 questions across 11 strands, each climbing from primary level to Extended, hunting the lowest broken rung rather than a score. You do not need to sit it again; it is here so you can see the working behind the plan above.