18 exam-style Edexcel GCSE Higher (1MA1) congruence questions with full worked solutions and B1/M1/C1 mark schemes. Every diagram is drawn accurately to match its labels. What’s inside: Easy: spotting congruent shapes and triangles, naming SSS, SAS, ASA/AAS and RHS, and why AAA and SSA are not enough. Medium: missing sides and angles in congruent shapes, congruence from transformations, and a scaffolded first proof. Hard: unscaffolded formal proofs (parallelograms, isosceles triangles, squares, kites, midpoints, alternate angles, RHS) and grade 7 to 9 questions combining congruence with angle facts and trigonometry. Includes a How to write a congruence proof box and model proofs with the reason for every step. Typeset in LaTeX, print-friendly. Ideal for: students sitting Edexcel GCSE Higher Mathematics (1MA1), plus tutors and teachers building targeted practice.

27 Edexcel-style GCSE Higher (1MA1) quadratics revision questions worth 104 marks, with full mark-scheme worked solutions (M1, A1, B1 marks shown line by line). What’s inside: Easy: factorising (including a not equal to 1 and the difference of two squares) and solving by factorising. Medium: the quadratic formula (2 decimal places and surd form), completing the square for turning points and maximum or minimum values, and sketching or reading quadratic graphs. Hard: quadratic inequalities, forming and solving quadratics from area and Pythagoras contexts, and grade 8 to 9 multi-mark questions including simultaneous equations with a circle. Worded like real Edexcel papers, with a Watch out box on the common slips: signs, the plus or minus step, dividing out a, and simplifying surds. Typeset in LaTeX, print-friendly. Ideal for: Year 10 and 11 students sitting Edexcel GCSE Higher Mathematics (1MA1), plus tutors and teachers building targeted practice.

30 fully worked questions on indices and surds for OCR B (MEI) A-Level Maths (H640), built for Year 12 students who want exact algebra they can trust under exam conditions. Questions are written in the style of the H640 Section A and Section B papers, with command words such as Find, Show that and Determine, and eight questions carry the instruction “In this question you must show detailed reasoning”. The pack covers the laws of indices for negative, zero and fractional powers, evaluating expressions like 27 to the power of minus two thirds, writing expressions in the form ax^n ready for differentiation and integration, solving index equations by matching bases without logarithms, simplifying surds, expanding brackets with surds, rationalising denominators including conjugate pairs, and surds in context such as exact lengths, areas, triangles, and equations with answers in the form a + b root c. Every solution is broken into single steps with a plain English reason, an arrow note on every line and OCR style M1, A1 and B1 marks placed exactly where a mark scheme rewards them, so students see how marks are earned and where they are lost. The total is 152 marks. Ideal for homework, revision, tutoring or self study, and a complete answer for every question is included. What’s inside: Easy: 10 questions on evaluating indices, simplifying surds, expanding surd brackets, writing powers as ax^n, simple index equations and a first rationalisation Medium: 13 questions on negative and fractional indices, harder index equations, rationalising with conjugates, surds in right-angled triangles, rectangles and the cosine rule, surd equations and an index proof Hard: 7 questions on telescoping surd sums, the exact distance between two intersection points, a cuboid with surd edges, a hidden quadratic in 2^x, a chain of fractional index identities and an equation with a rejected root

30 fully worked questions on quadratic functions and equations for OCR B (MEI) A-Level Maths (H640), built for Year 12 students who want to solve, sketch and reason about quadratics with confidence. Questions are written in the style of the H640 papers, with command words such as Find, Show that, Determine and Hence, two questions carry the detailed reasoning instruction, and several come with a labelled diagram of a parabola, a line and a tangent, or two intersecting curves. The pack covers solving by factorising, completing the square and the quadratic formula, quadratics hidden inside a function of the unknown such as x to the fourth or the square root of x, completing the square to find the turning point and line of symmetry and sketch the curve, the discriminant for distinct, repeated and no real roots including finding a range for a parameter, a line meeting a curve and tangency, simultaneous equations with one linear and one quadratic, quadratic inequalities in set notation and with and or or, and modelling with area, profit and ball height including the limits of the model. Every solution is broken into single steps with a plain English reason, an arrow note on every line and OCR style M1, A1 and B1 marks placed exactly where a mark scheme rewards them, so students see how marks are earned and where they are lost. The total is 170 marks. Ideal for homework, revision, tutoring or self study, and a complete answer for every question is included. What’s inside: Easy: 10 questions on factorising, completing the square, the formula, the discriminant, a first inequality, reading roots from a graph and one linear and one quadratic simultaneous equation Medium: 13 questions on hidden quadratics, sketching with the turning point and intercepts, parameters in the discriminant, tangents, ranges of k, double inequalities and profit and ball height models Hard: 7 questions on tangents from a point, counting the real roots of a quartic, a parameter with a trap, a fence optimisation with a restriction, two intersecting parabolas, a vertex on a line and lattice points in a region

30 fully worked questions on polynomials and the factor theorem for OCR B (MEI) A-Level Maths (H640), built for Year 12 students who want to expand, divide, factorise and sketch polynomials with confidence. The questions follow the style of the H640 papers, with command words such as Find, Show that, Determine and Hence, and seven questions carry the detailed reasoning instruction. The pack covers expanding and simplifying products of brackets, algebraic division by a linear factor such as (x - a) or (ax + b), using the factor theorem to show a linear expression is a factor, finding unknown coefficients from one or two given factors, fully factorising cubics and quartics, solving polynomial equations, showing that a cubic has exactly one real root, sketching cubics and quartics with repeated roots and negative leading coefficients, and finding where a line meets a cubic curve. Every solution is broken into single steps with a plain English reason, an arrow note on every line and OCR style M1, A1 and B1 marks placed exactly where a mark scheme rewards them, so students see how marks are earned and where they are lost. Several solutions include a clearly labelled sketch. The total is 168 marks. Ideal for homework, revision, tutoring or self study, and a complete answer for every question is included. What’s inside: Easy: 10 questions on expanding brackets, dividing by a linear factor, the factor theorem, factorising simple cubics and a first sketch Medium: 13 questions on unknown coefficients, solving cubics and quartics, one real root, repeated roots, sketching and a line meeting a cubic Hard: 7 questions on multi-part quartics, tangent lines, a cuboid volume, reading a cubic from its graph, surd answers and a family of cubics with a parameter

30 fully worked questions on differentiation for OCR B (MEI) A-Level Mathematics (H640), built for Year 12 students (and Year 13 revision) who want to differentiate powers of x with confidence and then use the derivative to solve exam-style problems. Questions follow the H640/01 and H640/02 Section A and Section B style, with command words such as Find, Show that and Determine, and three questions carry the instruction to show detailed reasoning. The pack covers the gradient of a chord tending to the tangent gradient, differentiation from first principles for x squared, x cubed and quadratics, differentiating kx to the power n for rational n (including roots and reciprocals rewritten as powers), gradient at a point, second derivatives, stationary points and their nature, increasing and decreasing functions, tangents and normals, rates of change with units, optimisation (open box, fencing, cylinder tin) and sketching the gradient function from a curve. Six questions come with a clear TikZ diagram. Every solution is broken into single steps with a plain English reason, an arrow note on every line and OCR style M1, A1 and B1 marks placed exactly where a mark scheme rewards them, so students see how marks are earned and where they are lost. The total is 174 marks. Only powers of x are used, so no chain, product or quotient rule is needed. Ideal for homework, revision, tutoring or self study, and a complete answer for every question is included. What’s inside: Easy: 10 questions on chord gradients, differentiating powers and brackets, gradient at a point, a tangent, first principles for x squared, a simple increasing function and rate of change with units Medium: 13 questions on first principles for quadratics and cubics, roots and reciprocals as powers, finding unknown constants, stationary points and their nature, increasing and decreasing functions, tangents and normals, no stationary points and sketching the gradient function Hard: 7 questions on optimisation (box, fencing, cylinder), a tangent and area of a triangle with a normal meeting the curve again, sketching f’ for a quartic, constants from stationary points and a tangent that meets a cubic again

30 fully worked questions on the binomial expansion for OCR B (MEI) A-Level Maths (H640), built for Year 12 students who want to expand (a + bx)^n for a positive integer n with confidence and then use the result to solve problems. The questions follow the style of the H640 Section A and Section B papers, with command words such as Find, Show that and Determine, and three questions carry the detailed reasoning instruction. The pack covers factorials and nCr notation, Pascal’s triangle, full expansions up to the sixth power, the first few terms in ascending powers, a single term or coefficient (including a negative b and two variables), finding an unknown constant or the power n from a coefficient or a ratio of coefficients, products such as (1 + 2x)(1 - x)^6, the term independent of x in expansions such as (x - 2/x)^6 and (2x^2 + 1/x)^9, estimating values such as 1.02^8 and 0.99^10 with a comment on accuracy, and exact surd expansions such as (2 + root 3)^4. Every solution is broken into single steps with a plain English reason, an arrow note on every line and OCR style M1, A1 and B1 marks placed exactly where a mark scheme rewards them, so students see how marks are earned and where they are lost. The total is 147 marks. Ideal for homework, revision, tutoring or self study, and a complete answer for every question is included. What’s inside: Easy: 10 questions on factorials, nCr, Pascal’s triangle, full expansions, a single coefficient and finding n from nC2 Medium: 13 questions on unknown constants, products of brackets, ratios of coefficients, the term independent of x in (x - 2/x)^6 and a proof with nCr, estimating 1.02^8 and 0.99^10, exact surds, sums of binomial coefficients and two variables Hard: 7 questions on finding a and n together, terms independent of x, a missing x squared term, accuracy of an estimate, surd conjugates, a proof with factorials and a combined estimate

30 fully worked questions on integration for OCR B (MEI) A-Level Maths (H640), built for Year 12 students who want to master the reverse of differentiation and the area under a curve with confidence. Questions follow the style of the H640 papers, with command words such as Find, Evaluate, Determine and Show that, a number of questions carrying the instruction “In this question you must show detailed reasoning”, and clearly drawn shaded diagrams for the area questions. The pack covers integrating powers of x including roots, reciprocals, expanded brackets and simple fractions, finding the constant of integration from a point on the curve or a tangent condition, definite integrals with exact answers, area between a curve and the x-axis including regions partly below the axis, areas bounded by a curve and a line found by subtracting a triangle or trapezium, areas between two curves as one area under a graph minus another, finding an unknown limit or coefficient from a given area, and the limit of a sum of rectangles. Every solution is broken into single steps with a plain English reason, an arrow note on every line and OCR style M1, A1 and B1 marks placed exactly where a mark scheme rewards them, so students see how marks are earned and where they are lost. The total is 165 marks. Ideal for homework, revision, tutoring or self study, and a complete answer for every question is included. What’s inside: Easy: 10 questions on integrating powers, roots, reciprocals and expanded brackets, finding a curve from its gradient and a point, definite integrals and simple areas under a curve Medium: 13 questions on tangent conditions, exact definite integrals, unknown limits and coefficients, areas below and across the x-axis, areas bounded by a curve and a line, and the rectangle approximation Hard: 7 questions on areas between a line and a curve, two-curve regions, a three-root cubic, a tangent condition with an area, a tunnel modelling problem and an area-matching problem with a surd answer

30 fully worked questions on forces and Newton’s laws for OCR B (MEI) A-Level Maths (H640), built for Year 12 students who want to model forces and apply F = ma with confidence. Almost every question has a clear force diagram, in the style of the H640/01 Mechanics papers, with command words such as Find, Show that and Determine, and one question carries the detailed reasoning instruction. The pack covers the language of forces and modelling assumptions (light, smooth, inextensible, particle), weight, resultants of perpendicular and vector forces, equilibrium, Newton’s three laws, motion in a straight line under F = ma, lifts and cranes, cars towing trailers, trains with couplings, two particles over a smooth pulley, a particle on a smooth table joined to a hanging particle, what happens when a string breaks or a particle lands, and multi-stage problems that combine Newton’s second law with suvat. Every solution is broken into single steps with a plain English reason, an arrow note on every line and OCR style M1, A1 and B1 marks placed exactly where a mark scheme rewards them, so students see how marks are earned and where they are lost. The total is 191 marks. Ideal for homework, revision, tutoring or self study, and a complete answer for every question is included. What’s inside: Easy: 10 questions on weight and normal reaction, modelling words, resultants of two forces, F = ma on a straight line, Newton’s first and third laws, and forces given as vectors Medium: 13 questions on a car and trailer, a train, lifts, a crane, a parachutist, smooth pulleys, blocks in contact, vector forces and equilibrium Hard: 7 questions on pulley systems with a landing or a breaking string, a lift in stages, a trailer after the tow-bar breaks, vector forces over time and a three particle system

30 fully worked questions on exponentials and logarithms for OCR B (MEI) A-Level Maths (H640), built for Year 12 students who want exam-style practice on the whole Year 1 exponentials and logarithms topic. Questions follow the style of the H640/01 and H640/02 papers, with command words such as Find, Show that, Determine and Sketch, three questions carrying the detailed reasoning instruction, and several with a labelled graph. The pack covers the graph of y = a^x and its asymptote, converting between index and log form, the laws of logs, solving a^x = b by taking logs including hidden quadratics and inequalities, solving log equations and rejecting invalid roots, e^x and ln x, the gradient of e^kx, growth and decay models with their limitations, and reducing y = ax^n and y = ab^x to linear form. Every solution is broken into single steps with a plain English reason, an arrow note on every line and OCR style M1, A1 and B1 marks placed exactly where a mark scheme rewards them. The total is 175 marks. Ideal for homework, revision, tutoring or self study, and a complete answer for every question is included. What’s inside: Easy: 10 questions on y = a^x, index and log form, evaluating and combining logs, solving a^x = b, e^x and ln x, the gradient of e^kx and a simple growth model Medium: 13 questions on log laws, equations with unequal bases, hidden quadratics, inequalities, log equations, sketching e^x and ln x, linear form from graphs and data, cooling and half-life Hard: 7 questions on stationary points of exponential curves, competing drug models, compound interest in e^kt form, estimating constants from data, and bounded growth

30 fully worked questions on motion graphs for OCR B (MEI) A-Level Maths (H640), built for Year 12 and Year 13 students who want to read and use displacement time, velocity time and acceleration time graphs with confidence. Most questions come with a clearly labelled graph, in the style of the H640/01 Mechanics papers, with command words such as Find, Show that and Determine, and three questions carry the detailed reasoning instruction. The pack covers gradient as velocity and acceleration, area as displacement, the difference between distance and displacement, speed against velocity, average speed and average velocity, sketching a velocity time graph from a description, journeys that reverse direction, two vehicles on one graph and when one catches the other, and finding an unknown speed or time from a total distance. No calculus is needed. Every solution is broken into single steps with a plain English reason, an arrow note on every line and OCR style M1, A1 and B1 marks placed exactly where a mark scheme rewards them, so students see how marks are earned and where they are lost. The total is 205 marks. Ideal for homework, revision, tutoring or self study, and a complete answer for every question is included. What’s inside: Easy: 10 questions on reading gradients and areas from graphs, distance against displacement, average speed and sketching a journey Medium: 14 questions on acceleration time graphs, reversing motion, a bouncing ball, two cyclists and deriving the suvat equations from a graph Hard: 6 questions on unknown speeds from total distance, sprinters level at a point, a car catching a lorry, stopping distance and overtaking

30 fully worked questions on constant acceleration for OCR B (MEI) A-Level Maths (H640), built for Year 12 and Year 13 students who want to master the suvat equations and know exactly which one to use. Every question is written in the style of the H640/01 Mechanics papers, with command words such as Find, Show that and Determine, and three questions carry the detailed reasoning instruction. The pack covers all five suvat equations, choosing the right equation from what is given and what is wanted, converting kilometres per hour to metres per second, deceleration to rest and stopping distances, multi stage journeys, vertical motion under gravity with g = 9.8, balls thrown from a height, two times at the same height from a quadratic, two particles meeting, and interpreting negative roots. You also practise stating the positive direction before you start, which is where many marks are lost. Every solution is broken into single steps with a plain English reason, an arrow note on every line and OCR style M1, A1 and B1 marks placed exactly where a mark scheme rewards them. The total is 165 marks. Ideal for homework, revision, tutoring or self study, and a complete answer for every question is included. What’s inside: Easy: 9 questions using each suvat equation, unit conversion, deceleration to rest and simple vertical motion Medium: 14 questions on quadratics in t, stopping distances, two particles meeting and multi stage journeys Hard: 7 questions on times at a given distance, rockets, symmetric flight, last second problems and bouncing balls

30 fully worked questions on the sine rule, the cosine rule and the area of a triangle for OCR B (MEI) A-Level Maths (H640), built for Year 12 and Year 13 students who want to choose the right rule quickly and apply it accurately. Nearly every question has a labelled triangle or bearings diagram, in the style of the H640/01 papers, with command words such as Find, Show that and Determine, and three questions carry the detailed reasoning instruction. The pack covers finding sides and angles, deciding which rule to use, the ambiguous case where the sine rule gives two triangles (and when only one is valid), three figure bearings and back bearings, angles of elevation, finding an angle from an area, exact answers using sin 30, cos 120 and surds, quadrilaterals split into triangles and an interception problem that leads to a quadratic. Every solution is broken into single steps with a plain English reason, an arrow note on every line and OCR style M1, A1 and B1 marks placed exactly where a mark scheme rewards them, so students see how marks are earned and where they are lost. The total is 163 marks. Ideal for homework, revision, tutoring or self study, and a complete answer for every question is included. What’s inside: Easy: 10 questions on the sine rule, the cosine rule, area, choosing the rule and a simple bearings problem Medium: 13 questions on the ambiguous case, bearings, exact areas, angles of elevation and cosine rule quadratics Hard: 7 questions on two leg bearings, counting triangles, a quadrilateral, a median, an angle double another and an interception

Thirty fully worked trigonometric identities and equations questions written for OCR B (MEI) A-Level Mathematics (H640), Year 12, with every line of every solution explained and annotated with the MEI mark codes (M, A and B marks) so you can see exactly where the marks are won. The pack follows the specification (Mt5, Mt6 and Mt7): tan x = sin x / cos x, sin squared x + cos squared x = 1, proving identities, and solving equations in degrees over stated intervals, including multiple and shifted angles such as sin 2x, cos(x + 30) and tan 3x. It also covers equations that are quadratic in sin, cos or tan, rejecting impossible roots, and the classic trap of dividing by a factor that could be zero. Questions are set in MEI exam style with command words such as Find, Show that and Determine, and “In this question you must show detailed reasoning” questions, plus a harbour-tide modelling problem. What’s inside: Easy: 10 questions to get started, covering sin x = k, cos x = k and tan x = k with symmetry, exact values, simple multiple and shifted angles, and finding cos and tan from sin. Medium: 13 questions on quadratics in sin, cos and tan, the quadratic formula, multiple angles over longer intervals, equations using tan x = sin x / cos x, a student-error question and proving identities. Hard: 7 multi-step exam-style questions on identity proofs with fractions, detailed-reasoning quadratics in shifted and multiple angles, a show-that-then-solve question and a modelling question. Each worked solution is broken down one operation per line with a short note beside it, which makes the pack ideal for self-study, homework, revision and tutor use.

30 fully worked questions on variable acceleration for OCR B (MEI) A-Level Maths (H640), built for Year 12 and Year 13 students who want to master calculus in kinematics. Every question is written in the style of the H640/01 Mechanics papers, with command words such as Find, Determine and Show that, and one question carries the detailed reasoning instruction. The pack covers v = dx/dt and a = dv/dt, integrating with initial conditions, instantaneous rest, greatest and least velocity, displacement and average velocity, two particles meeting, and the signature hard skill: distance travelled across a change of direction. You also practise spotting when suvat is valid, which is only when acceleration is constant. Every solution is broken into single steps with a plain-English reason, an arrow note on every line and OCR style M1, A1 and B1 marks placed exactly where a mark scheme rewards them, so students see how marks are earned and where they are lost. Questions run from entry level to multi-step exam style and the total is 172 marks. Ideal for homework, revision, tutoring or self study, and a complete answer for every question is included. What’s inside: Easy: 10 questions on differentiating and integrating polynomial motion, rest, displacement and average velocity Medium: 13 questions on distance travelled, meeting particles, unknown constants and modelling Hard: 7 questions on multi-stage distance, two-particle problems and exam-style reasoning

Worked solutions for OCR B (MEI) A-Level Maths (H640): trigonometric graphs and exact values, all in degrees. 30 exam-style questions with every line of working explained, each step annotated with MEI mark codes (M1, A1, B1) so you can see exactly where the marks come from. Covers the graphs of sin x, cos x and tan x (period, amplitude, asymptotes, turning points), symmetry and periodicity, CAST, exact values for 30, 45 and 60 degrees derived from the equilateral and right-isosceles triangles, transformations such as y = a sin x + d, y = sin(bx) and y = cos(x + c), counting and locating solutions from a graph, and finding a, b, c and d from a sketch. Clear TikZ graphs are included wherever the question needs one. Questions run from entry level to genuine exam style, including “show that” and “in this question you must show detailed reasoning” problems. Ideal for Year 12 students, tutors and independent revision, with a key facts page including a full exact values table. What’s inside: Easy: 11 questions on exact values, the equilateral and right-isosceles triangles, symmetry, CAST signs and basic sketches of sin, cos and tan Medium: 13 questions on transformed graphs, reading a, b, c and d from a sketch, counting solutions, exact value arithmetic and a Ferris wheel model Hard: 6 questions with multi-part sketches, tan x = 2 sin x, a harbour tide model and detailed reasoning with exact trig values Total 140 marks. Full worked solutions included for every question.

20 original Junior Maths Challenge-style multiple-choice questions on number, every one written fresh in the style, format and difficulty of the UKMT Junior Mathematical Challenge (Year 8 and below), with full worked solutions. This drill targets the number skills that decide JMC scores: comparing huge powers without a calculator (2^50 against 3^30, 2^100 against 10^30 using the 2^10 = 1024 benchmark), last-digit cycles, prime factorisation and index laws, divisibility tests for 3, 6 and 9, counting factors, trailing zeros, consecutive-integer sums, HCF and LCM, inclusion-exclusion counting and digit-product puzzles. What’s inside: 6 Easy, 8 Standard and 6 Challenging questions, each with five options A to E and exactly one correct answer, plausible distractors built from the slips students actually make, a JMC-style mark allocation (5 marks for Q1-14, 6 marks for Q15-20) and an answer grid. Every worked solution breaks the method into short, annotated steps, names the key insight in a ‘Why this works’ note, and shows a ‘Fast route’ elimination trick where one exists, so students learn the competition reasoning rather than just the answer. Ideal for able Year 7 and Year 8 students preparing for the Junior Maths Challenge, Junior Kangaroo and Junior Olympiad, for maths clubs and enrichment sessions, and for tutors stretching strong KS3 students beyond the curriculum. No calculator needed. Original UKMT-style practice material written by Locus Tutors; not produced by, affiliated with or endorsed by the UK Mathematics Trust.

A complete, original Junior Maths Challenge-style mock paper for Year 7 and Year 8 students, built in exactly the same format as the real JMC: 25 multiple-choice questions (A to E), 60 minutes, no calculator, Questions 1 to 15 worth 5 marks and 16 to 25 worth 6 marks, 135 marks in total, no negative marking. Every question is freshly written for this paper and ramps from quick warm-ups to genuinely tricky final problems, across a fresh spread of contexts: time and calendar puzzles, place value and digit problems, shape dissection and area, sequences that fall into loops, ratio, reflective symmetry on grids, and logic puzzles including knights and knaves. Diagrams are drawn in crisp vector graphics. The second half of the pack is what makes it stand out: a full worked solution for every question, broken into clear steps with a note on every line, plus a ‘Key insight’ explaining the idea behind the hard questions and a ‘Fast route in the exam’ showing how strong candidates eliminate options quickly. An answer grid, a marking guide and a blank student answer sheet are included, so it works as a timed mock, homework or a one-to-one tuition session. Ideal preparation for the Junior Mathematical Challenge and a natural stepping stone towards the Junior Kangaroo and Junior Olympiad. Original practice material written in the style of UKMT challenges by a Locus Tutors tutor; not produced, affiliated with or endorsed by the UK Mathematics Trust.

A complete Junior Maths Challenge-style mock paper with fully worked solutions, built to the exact format of the real UKMT Junior Mathematical Challenge: 25 multiple-choice questions (A to E), 60 minutes, no calculator, Questions 1 to 15 worth 5 marks and Questions 16 to 25 worth 6 marks, 135 marks in total with no negative marking. Every question is original, written fresh in the style and difficulty of the JMC for Year 8 and below, and the paper ramps from quick warm-ups to genuine stretch problems. Inside: arithmetic shortcuts, fractions and percentages, telescoping products, divisibility tests, comparing large powers, last-digit cycles, angle chasing in a regular hexagon, area puzzles, tilted-square counting, truth-teller and liar logic, and a case-by-case counting finale. The worked solutions are the real value. Each question gets a step-by-step solution with every line annotated, the key insight that unlocks it, and a Challenge tip explaining the trap behind the most tempting wrong option and the fastest elimination route. Includes an exam-style instructions page, a student answer grid, a full answer key and marking guide. Ideal for JMC preparation, maths clubs, enrichment lessons, gifted and talented groups, and confident Year 6 to Year 8 students who want a timed practice paper. Original UKMT-style practice material; not produced by or affiliated with the UK Mathematics Trust.

A full Hamilton Mathematical Olympiad-style mock for Year 10: 6 original problems, 2 hours, 10 marks each (60 in total), written in the style, format and difficulty of the UKMT Hamilton Olympiad, the follow-on round for top Year 10 scorers in the Intermediate Maths Challenge. Every problem comes with a complete model write-up that shows a student exactly how an olympiad answer should be presented: letters defined, every step justified, one idea per line, with right-margin notes and mark allocations showing where the marks are won. Each solution closes with a ‘What a marker wants to see’ box covering the ways strong students drop marks: testing examples instead of proving, skipping the converse in a ‘find all’ question, stating SAS without the included angle, or assuming what they want to prove in an inequality. Inside: a Diophantine tiling problem cracked by factorising (m-6)(n-6)=24; a proof about sums of consecutive integers using remainders, extended to perfect squares and cubes; a two-squares geometry proof by congruence with full angle-chase to show perpendicularity (TikZ diagrams); a parity and counting problem on a 3x3 grid; an AM-GM style inequality chain finishing with a cuboid optimisation; and a hard exponential Diophantine equation, 2^a + 9 = b^2, solved by splitting on parity with modular arithmetic and difference of two squares. Also includes an instructions page, a key-facts box and an answers-at-a-glance grid. Ideal for able Year 10 students preparing for the IMC follow-on rounds, maths clubs, enrichment sets and anyone aiming for the top grades who wants to learn how to write proofs properly. Original UKMT-style practice material written by Locus Tutors. Not official UKMT material and not affiliated with or endorsed by the UK Mathematics Trust.

A second full-length Intermediate Maths Challenge-style mock paper with complete worked solutions, built to the exact format of the real UKMT Intermediate Challenge: 25 multiple-choice questions (A to E), 60 minutes, no calculator, 135 marks, with Questions 1 to 15 worth 5 marks and Questions 16 to 25 worth 6 marks, plus the real negative marking (minus 1 on Questions 16 to 20, minus 2 on Questions 21 to 25). Every question is original, written fresh in the style and at the genuine difficulty of the Intermediate Challenge, with all-new contexts so it pairs perfectly with Mock Paper 1. What’s inside: a cover with instructions, the scoring table and a key-facts panel, 25 questions ramping from quick warm-ups to genuine Gold-level problems, a printable answer sheet and a one-glance answer key. The paper is built around six high-yield themes: surds and indices (comparing huge powers, a surd value that collapses a cubic), circle geometry (angle in a semicircle, chords, a circle inscribed in a quarter-circle), sequences (cycling recurrences, Fibonacci-style puzzles), rates and speed (filling with a leak, the average-speed trap), 3D shapes (the painted cuboid, a drilled cylinder, the octahedron inside a cube) and probability (complements, inclusion-exclusion, remainder classes), finishing with a completing-the-square number theory problem. The worked solutions are the real value: every question gets a step-by-step solution that explains the key insight, names the trap behind each tempting wrong option, and shows a fast elimination route, so students learn exactly when to guess and when to leave a box blank under negative marking. Ideal for Year 9 to 11 students preparing for the Intermediate Mathematical Challenge (and the Kangaroo and Olympiad follow-on rounds), for maths club practice, and for tutors and teachers setting a timed mock. Original UKMT-style practice material; not official UKMT papers.