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Mathematics

Integers, Decimals & Place Value is a key part of GCSE Mathematics. Build fluency with the method, then apply it to unfamiliar and multi-step problems. A whole number that can be positive, negative, or zero (e.g. -3, 0, 7). The value of a digit determined by its position in a number. For example, in 345 the 3 represents 300. The order of operations: Brackets, Indices (or Orders), Division, Multiplication, Addition, Subtraction.

Mathematics

Fractions, Decimals & Percentages is a key part of GCSE Mathematics. Build fluency with the method, then apply it to unfamiliar and multi-step problems. Fractions that represent the same value, e.g. 1/2 = 2/4 = 3/6. A fraction where the numerator is greater than or equal to the denominator, e.g. 7/4. A number consisting of a whole number and a proper fraction, e.g. 1¾.

Mathematics

Indices & Standard Form is a key part of GCSE Mathematics. Build fluency with the method, then apply it to unfamiliar and multi-step problems. A small number written above and to the right of a base number indicating how many times to multiply it by itself. E.g. 2³ = 2 × 2 × 2 = 8. aᵐ × aⁿ = aᵐ⁺ⁿ. When multiplying with the same base, add the powers. aᵐ ÷ aⁿ = aᵐ⁻ⁿ. When dividing with the same base, subtract the powers.

Mathematics

Surds is a key part of GCSE Mathematics. Build fluency with the method, then apply it to unfamiliar and multi-step problems. An irrational root that cannot be simplified to a whole number, e.g. √2, √3, √5. Express the number under the root as a product involving a perfect square. E.g. √12 = √(4×3) = 2√3. √a × √b = √(ab). Multiply the numbers under the roots. E.g. √3 × √5 = √15.

Mathematics

Algebraic Expressions is a key part of GCSE Mathematics. Build fluency with the method, then apply it to unfamiliar and multi-step problems. A letter or symbol used to represent an unknown value in an expression or equation, e.g. x, y. A single number, variable, or number multiplied by a variable, e.g. 3x, −5, 2y². The number in front of a variable. In 5x, the coefficient is 5.

Mathematics

Solving Linear Equations is a key part of GCSE Mathematics. Build fluency with the method, then apply it to unfamiliar and multi-step problems. An equation where the highest power of the variable is 1. It produces a straight line when graphed. E.g. 2x + 3 = 11. Undo operations in reverse order to isolate the variable. E.g. to solve 2x + 3 = 11, subtract 3 then divide by 2. Collect variable terms on one side and constants on the other. E.g. 5x − 2 = 3x + 8 → 2x = 10 → x = 5.

Mathematics

Solving Quadratic Equations is a key part of GCSE Mathematics. Build fluency with the method, then apply it to unfamiliar and multi-step problems. An equation of the form ax² + bx + c = 0 where a ≠ 0. The highest power of x is 2. Write ax² + bx + c = 0 as (x + p)(x + q) = 0, then set each bracket equal to zero. x = (−b ± √(b² − 4ac)) / 2a. Used to solve any quadratic equation ax² + bx + c = 0.

Mathematics

Simultaneous Equations is a key part of GCSE Mathematics. Build fluency with the method, then apply it to unfamiliar and multi-step problems. Two or more equations with the same unknowns that are solved together to find values satisfying all equations. Add or subtract the equations to eliminate one variable, then solve for the other. May need to multiply first. Rearrange one equation to express a variable in terms of the other, then substitute into the second equation.

Mathematics

Sequences is a key part of GCSE Mathematics. Build fluency with the method, then apply it to unfamiliar and multi-step problems. A sequence where the difference between consecutive terms is constant. E.g. 3, 7, 11, 15 (common difference = 4). The fixed amount added to each term to get the next in an arithmetic sequence. Found by subtracting consecutive terms. The formula for the nth term of an arithmetic sequence: a + (n−1)d, or equivalently dn + (a−d).

Mathematics

Straight Line Graphs is a key part of GCSE Mathematics. Build fluency with the method, then apply it to unfamiliar and multi-step problems. A measure of how steep a line is. Calculated as rise ÷ run, or (y₂ − y₁) ÷ (x₂ − x₁). The equation of a straight line where m is the gradient and c is the y-intercept. The point where a line crosses the y-axis. In y = mx + c, the y-intercept is (0, c).

Mathematics

Quadratic & Other Graphs is a key part of GCSE Mathematics. Build fluency with the method, then apply it to unfamiliar and multi-step problems. The U-shaped (or inverted U-shaped) curve of a quadratic function y = ax² + bx + c. The maximum or minimum point of a parabola. Found by completing the square or using x = −b/(2a). A quadratic graph is symmetric about the vertical line x = −b/(2a), passing through the vertex.

Mathematics

Inequalities is a key part of GCSE Mathematics. Build fluency with the method, then apply it to unfamiliar and multi-step problems. A mathematical statement showing that one expression is greater than, less than, or not equal to another. Uses <, >, ≤, ≥. Solve like an equation but reverse the inequality sign when multiplying or dividing by a negative number. Show solutions on a number line: open circle (○) for < or >, filled circle (●) for ≤ or ≥.