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SAMPLE — not a real child. Jayden is a public demo.
Standard Hub · Maths

Jayden's Maths Hub

A private revision website for one child.

Current → target
4→6
ExamJune 2027
Board / tierAQA · Higher · Y11
Vectors Circle theorems Quadratic equations

Paper map

AQA GCSE Maths Higher

Red · live Amber · live Green · hold

Number

Integers, decimals, fractions
Factors, primes, bounds
Index laws, standard form, surds

Algebra

Expressions, formulae, sequences
Linear equations & graphs
Quadratic equationsAmber · priority 3
Simultaneous & algebraic fractions

Ratio

Ratio & reverse percentages
Direct / inverse proportion
Compound measures, similarity

Geometry

Angles, Pythagoras, trig
VectorsRed · priority 1 Circle theoremsAmber · priority 2
Area, volume, transformations

Probability

Trees & Venn diagrams
Averages & diagrams
Sampling, box plots, histograms

Tracker

R / A / G

Vectors

Column → resultant → midpoint → magnitude

Circle theorems

Name the theorem, then the angle

Quadratic equations

Factorise, then formula

Workspaces

Three live topics

RED · START HERE

Vectors

Next: column → resultant → midpoint → magnitude

Vector AB on a coordinate grid x y 123 456 789 123 456 7 4 3 A B AB 4 3
1 · Column vector2 marks

Point C is (−2, 5). Vector CD = (7, −3). Write the coordinates of D.

2 · Resultant2 marks

Vector m = (4, −1) and vector n = (−6, 5). Write the resultant m + n as a column vector.

3 · Midpoint2 marks

E is (3, −8) and F is (−5, 2). Find the midpoint of EF.

4 · Mixed4 marks

Vector u = (3, −4) and vector v = (5, 12). Find u + v as a column vector, then find the magnitude of u + v. Leave the magnitude in exact form if it is not an integer.

Write the column, then the working. Leave √ exact unless told otherwise.

Worked example · Vectors

Stem: Point A is (1, 2). Vector AB = (5, −12). Write the coordinates of B, then find the magnitude of AB.

  1. B is found by adding the column to the start point: 1 + 5 = 6 and 2 + (−12) = −10, so B is (6, −10). Method Accuracy
  2. Magnitude uses √(x² + y²): √(5² + (−12)²) = √(25 + 144) = √169. Method
  3. √169 = 13, so |AB| = 13. Accuracy
AMBER

Circle theorems

Next: name the theorem, then the angle

Angle in a semicircle 41° 90° P Q R diameter Angle in a semicircle = 90°
1 · Angle in a semicircle4 marks

PQ is a diameter of a circle. R lies on the circumference. Angle QPR = 41°. Name the theorem that gives the size of angle PRQ, find that angle, and hence find angle PQR.

2 · Cyclic quadrilateral3 marks

ABCD is a cyclic quadrilateral. Angle ABC = 3x + 15 and angle ADC = 2x + 25. Find x, naming the theorem you use.

3 · Tangent–radius3 marks

A circle has centre O. PT is a tangent at P. OP is a radius. Angle TOP = 48°. Find angle OPT, with a reason, then find angle OTP.

4 · Mixed4 marks

A circle has centre O. Tangents from an external point T touch the circle at A and B. Angle ATB = 72°. Write the size of angle OAT with a reason, then find angle AOB.

Theorem name first (often a mark), then the calculation.

Worked example · Circle theorems

Stem: AB is a diameter of a circle. C is a point on the circumference. Angle BAC = 34°. Name the theorem that gives angle ACB, find that angle, then find angle ABC.

  1. The angle in a semicircle is a right angle, so angle ACB = 90°. Method · name the theorem Accuracy
  2. Angles in a triangle sum to 180°, so angle ABC = 180° − 90° − 34° = 56°. Method Accuracy
AMBER

Quadratic equations

Next: factorise, then formula

y = x² + 5x + 6 x y −3 −2 (0, 6) y = x² + 5x + 6 x-intercepts (−3, 0) and (−2, 0)
1 · Factorise3 marks

Solve x² − x − 12 = 0 by factorising.

2 · Formula · surd form4 marks

Solve x² + 6x + 2 = 0 using the quadratic formula. Leave your answers in surd form.

3 · Completing the square4 marks

Write x² − 10x + 21 in the form (x − p)² + q. Hence write the coordinates of the turning point of y = x² − 10x + 21.

4 · Mixed5 marks

A patio is a rectangle. The length is 4 m more than the width. The area is 45 m². Let the width be w metres. Show that w² + 4w − 45 = 0, then solve the equation and give the width of the patio.

Set = 0. Show substitution. Simplify the surd.

Worked example · Quadratic equations

Stem: Solve x² + 4x − 2 = 0 by completing the square. Leave the answers in surd form.

  1. Rearrange: x² + 4x = 2. Method
  2. Complete the square: (x + 2)² − 4 = 2, so (x + 2)² = 6. Method
  3. Take square roots: x + 2 = ±√6, hence x = −2 ± √6. Method Accuracy · surd form

Plan

Four weeks to June 2027

Week 1

Vectors rebuild

Columns, resultant, midpoint.

Week 2

Circle theorems

Name it, then the angle.

Week 3

Quadratics + mix

Factorise, formula, one vector.

Week 4

Mixed paper-style

All three, notes closed.

Tonight

Three checks

Buy

Sample vs paid

This SAMPLE

  • Public demo · “Jayden” is not a real child
  • AQA GCSE Maths Higher · Year 11 · 4 → 6 · June 2027
  • Full-paper board · deep work on three live topics
  • Four original questions + one worked example per topic