Maths, explained clearly.
Step-by-step worked examples, common mistakes, and unlimited free practice worksheets — aligned with the UK National Curriculum and GCSE.
- 01Algebra3 min read
Exponential Growth & Decay
Exponential growth and decay models appear throughout GCSE mathematics, from population dynamics to compound interest calculations. Students often struggle with the distinction between linear and exponential change, particularly when applying the formula y = a · bˣ to real-world scenarios.
- 02Algebra3 min read
Exponents & Powers
Exponents and powers form the backbone of algebraic manipulation, yet students consistently struggle with the fundamental rules. When Year 9 pupils encounter 3² × 3⁴ = 3⁸ instead of 3⁶, they're missing crucial index laws that underpin GCSE success.
- 03Algebra3 min read
Inequalities
Inequalities form the backbone of algebraic thinking in Years 8-11, bridging the gap between simple equations and complex mathematical modelling. When Charlotte spends less than £15 at the tuck shop or Harry needs more than 60% to pass his GCSE, they're using inequality concepts without realising it.
- 04Algebra3 min read
Linear Equations
Linear equations form the backbone of GCSE algebra, yet many Year 11 students still struggle with the systematic approach needed to isolate variables. Whether solving x + 6 = 7 or tackling 8x - 32 = 4x, the key lies in performing identical operations to both sides of the equation.
- 05Algebra3 min read
Logarithms
Logarithms bridge the gap between GCSE algebra and A-level mathematics, appearing in Year 12 curricula across England. These inverse operations to exponentiation unlock exponential equations that standard algebraic methods cannot solve.
- 06Algebra3 min read
Polynomials
Polynomials form the backbone of GCSE algebra, from simple linear expressions like 3x + 2 to complex quadratics such as x² + 5x + 6. Year 9 students first encounter polynomial addition, whilst Year 10 pupils tackle multiplication and factorisation.
- 07Algebra3 min read
Quadratic Equations
Quadratic equations form the cornerstone of GCSE mathematics, appearing in over 15% of exam questions across Foundation and Higher tiers. These polynomial equations, where the highest power of x is 2, challenge Year 10 and 11 students to master factorisation, completing the square, and the quadratic formula.
- 08Algebra3 min read
Scientific Notation
Scientific notation transforms unwieldy numbers like 93,000,000 miles (Earth to Sun) into the elegant 9.3 × 10⁷. Year 8 students often struggle with this GCSE foundation skill, particularly when moving decimal points and determining positive versus negative exponents.
- 09Algebra3 min read
Systems of Equations
Systems of equations appear in Year 9 GCSE preparation when students must find where two lines intersect on a coordinate plane. These simultaneous equations require methodical substitution or elimination techniques to determine the unique solution pair (x, y).
- 010Algebra4 min read
Two-Step Equations
Two-step equations form the foundation of algebraic problem-solving in Year 8, requiring students to perform inverse operations in the correct sequence. These equations, typically in the form ax + b = c, appear frequently in GCSE Foundation papers and real-world applications from calculating mobile phone bills to determining ticket prices.
- 011Arithmetic4 min read
Addition Properties
Addition properties form the foundation of mental maths strategies that Year 2 pupils need to master before tackling more complex calculations. Understanding why 7 + 3 equals 3 + 7, and how to group numbers like (6 + 4) + 2 versus 6 + (4 + 2), builds number sense that supports algebraic thinking in later key stages.
- 012Arithmetic3 min read
Addition
Addition forms the bedrock of every maths lesson from Reception through GCSE, yet many pupils struggle with place value alignment and carrying. Year 1 pupils must confidently add numbers to 20, whilst Year 2 students tackle two-digit addition with regrouping.
- 013Arithmetic3 min read
Decimal Arithmetic
Decimal arithmetic forms the foundation of financial literacy and measurement skills that Year 4 and 5 pupils need to master. When students struggle with adding 12.5 + 3.75 or calculating the cost of 2.3kg of apples at £1.45 per kg, they're missing crucial life skills that extend far beyond the classroom.
- 014Arithmetic3 min read
Decimal Word Problems
Decimal word problems appear in Year 4 SATs and continue through GCSE Foundation, challenging students to apply decimal operations to real-world scenarios. These problems require students to interpret context, select appropriate operations, and handle money calculations with precision.
- 015Arithmetic3 min read
Factors, GCF & LCM
Year 7 students frequently struggle with prime factorisation when finding HCF and LCM, often confusing the two concepts entirely. The National Curriculum requires mastery of these skills by Year 7, building on Year 5 foundations of identifying multiples and factors.
- 016Arithmetic3 min read
Intro to Multiplication
Multiplication transforms Year 2 and Year 3 classrooms when pupils grasp that 4 × 3 means three groups of 4, not just memorised facts. This fundamental concept bridges counting and abstract number work, forming the foundation for all future mathematical operations.
- 017Arithmetic3 min read
Long Division
Long division transforms Year 5 and 6 pupils from relying on calculators to confidently tackling multi-digit problems with pencil and paper. This essential skill bridges the gap between basic times tables knowledge and complex mathematical reasoning required for GCSE success.
- 018Arithmetic3 min read
Modular Arithmetic
Modular arithmetic forms the backbone of digital security systems and computer programming, yet many Year 10 students struggle with the concept of remainders in mathematical contexts. Understanding how numbers 'wrap around' after reaching a certain value proves essential for GCSE Further Mathematics and A-level preparation.
- 019Arithmetic3 min read
Multiplication & Division in Daily Life
Children encounter multiplication and division hundreds of times each day, from sharing sweets equally amongst friends to calculating the total cost of school dinner tickets. These fundamental operations form the backbone of mathematical reasoning in Year 2 through GCSE, appearing in everything from basic times tables to complex problem-solving scenarios.
- 020Arithmetic3 min read
Multiplication Properties
Year 4 pupils often struggle when Oliver calculates 7 × 8 = 56 but Amelia writes 8 × 7 and gets confused about whether the answer changes. Understanding multiplication properties helps students recognise patterns that make mental maths faster and builds confidence for algebraic thinking in Key Stage 3.