Maths — Pure Mathematics 1

Maths YMA01 — specification explorer

All 22 specification statements from the official Pearson Edexcel specification, as printed — filter by paper, unit or tier exactly as Pearson Edexcel assesses them.

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22 spec points

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Every statement · P1

Assessment homes come from the parsed Pearson specification (content summaries & assessment overviews). Hover a chip for the printed rule. Filters appear only where the qualification has that structure — a linear IGCSE has no unit scope, and only Maths A splits Foundation / Higher tiers.

1. Algebra and functions

1.1Laws of indices for all rational a m × a n = a m + n , a m ÷ a n = a m − n , ( a m ) n = a mn exponents. m n m The equivalence of a n and a should be known.P1
1.2Use and manipulation of surds. Students should be able to rationalise denominators.P1
1.3Quadratic functions and their graphs.P1
1.4
The discriminant of a quadratic function.:
- Need to know and to use b² − 4ac > 0, b² − 4ac = 0 and b² − 4ac < 0
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1.5Completing the square. Solution of Solution of quadratic equations by factorisation, use of the quadratic equations. formula, use of a calculator and completing the square. b 2 ( b 2 ) ax 2 + bx + c = a ( x + )+ ( c − ( 2 a ) 4 a ) ( ) ( )P1
1.6Solve simultaneous equations; analytical solution by substitution.P1
1.7Interpret linear and quadratic For example, inequalities graphically. ax + b > cx + d , px 2 + qx + r ≥ 0, px 2 + qx + r < ax + b. Interpreting the third inequality as the range of x for which the curve y = px 2 + qx + r is below the line with equation y = ax + b. Including inequalities with brackets and fractions. These would be reducible to linear or quadratic inequalities, e.g. a < b becomes ax < bx 2 , x ≠ 0.P1
1.8
Represent linear and quadratic inequalities graphically.:
- Represent linear and quadratic inequalities such as y > x + r and y > ax² + bx + c graphically. Shading and use of dotted and solid line convention is required.
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1.9
Solutions of linear and quadratic inequalities.:
- For example, solving ax + b > cx + d, px² + qx + r 0, px² + qx + r < ax + b.
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1.10
Algebraic manipulation of polynomials, including expanding brackets and collecting like terms, factorisation.:
- Students should be able to use brackets. Factorisation of polynomials of degree n, n 3, e.g. x³ + 4x² + 3x.The notation f(x) may be used.
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1.11
Graphs of functions; sketching curves defined by simple equations. Geometrical interpretation of algebraic solution of equations. Use of intersection points of graphs of functions to solve equations.:
- Functions to include simple cubic functions and the reciprocal functions y = k⁄x and y = k⁄x² with x ≠ 0. Knowledge of the term asymptote is expected. Also, trigonometric graphs.
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1.12
Knowledge of the effect of simple transformations on the graph of y = f(x) as represented by y = af(x), y = f(x) + a, y = f(x + a), y = f(ax). rdinate geometry in the (x, y) plane:
- Students should be able to apply one of these transformations to any of the above functions (quadratics, cubics, reciprocals, sine, cosine, and tangent) and sketch the resulting graphs. Given the graph of any function y = f(x), students should be able to sketch the graph resulting from one of these transformations.
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2. Coordinate geometry in the ( x , y ) plane

1. Coordinate geometry in the ( x , y ) plane

2.1
Equation of a straight line, including the forms y − y₁ = m(x − x₁) and ax + by + c = 0.:
- To include:(i) the equation of a line through two given points(ii) the equation of a line parallel (or perpendicular) to a given line through a given point. For example, the line perpendicular to the line 3x + 4y = 18 through the point (2, 3) has equation y − 3 = 4⁄3(x − 2).
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2.2Conditions for two straight lines to be parallel or perpendicular to each other.P1

3. Trigonometry

1. Trigonometry

3.1
The sine and cosine rules, and the area of a triangle in the form 1⁄2 ab sin C.:
- Including the ambiguous case of the sine rule.
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3.2
Radian measure, including use for arc length and area of sector.:
- Use of the formulae s = rθ and A = 1 r²θ. 2
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3.3
Sine, cosine and tangent functions. Their graphs, symmetries and periodicity.:
- Knowledge of graphs of curves with equations such as y = 3 sin x, y = sin x+π⁄6, y = sin 2x is expected.
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4. Differentiation

1. Differentiation

4.1
The derivative of f(x) as the gradient of the tangent to the graph of y = f(x) at a point; the gradient of the tangent as a limit; interpretation as a rate of change; second order derivatives.:
- For example, knowledge that dy⁄dx is the rate of change of y with respect to x. Knowledge of the chain rule is not required. The notation f ′(x) and f ′′(x) may be used.
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4.2
Differentiation of xⁿ, and related sums, differences and constant multiples.:
- The ability to differentiate expressions such as (2x + 5)(x − 1) and (x² + 5x − 3)⁄3x is expected.
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4.3Applications of differentiation to gradients, tangents and normals. Use of differentiation to find equations of tangents and normals at specific points on a curve.P1

5. Integration

1. Integration

5.1
Indefinite integration as the reverse of differentiation.:
- Students should know that a constant of integration is required.
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5.2
Integration of xⁿ and related sums, differences and constant multiples.:
- (Excluding n = −1 and related sums, differences and multiples). For example, the ability to integrate expressions such as 1⁄2x² − 3x⁻¹ and (x + 2)²⁄x is expected. Given f ′(x) and a point on the curve, students should be able to find an equation of the curve in the form y = f(x).
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