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National 5 Mathematics

This page contains free Dynamic Worksheets relating to the National 5 Mathematics course. If you want resources for other levels of course, go to our Free Resources homepage.

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Free Dynamic Worksheets covering entire course:

Free Solver Spreadsheets (easy ways for teachers to check answers to questions):

Free Dynamic Worksheets covering specific topics at this level:

Outcome Topic(s) Worksheet(s)
Non-calculator skills All non-calculator skills
  • Nat5-noncalc: mixed non-calculator practice questions for National 5 Mathematics
  • Fractions-10: mixed add, take away, multiply and divide (option to vary size of denominator)
  • Integers-03: mixed: all four operations with integers (option to vary size of numbers allowed in questions)
Numeracy Unit - all Assessment Standards   No content yet
All Units - reasoning skills (#2.1, #2.2) Choosing a strategy; explaining a solution No content yet
Expressions and Formula Unit: Assessment Standard 1.1 Surds, Indices, Standard Form
  • Indices-01a: change numbers from standard form into normal form (option to decide whether indices are positive, negative or both; and to vary length of number)
  • Indices-01b: change numbers from normal form into standard form (option to decide whether indices are positive, negative or both; and to vary length of number)
  • Surds-01: Simplifying surd expressions
Expressions and Formula Unit: Assessment Standard 1.2 Brackets, Factorising, Completing the Square
  • Quadratics-01: Factorising trinomials with prime coefficient of x² (option to specify constraints on coefficients and whether negatives are involved)
  • Quadratics-04: Substitute into quadratic expressions of the form ax² + bx + c (options to vary size of coefficients and to allow negatives)
  • Quadratics-05: Substitute into quadratic expressions of the form ax² + bx + c, a(x + b)² + c or (ax + b)(cx + d) (options to choose which expressions to allow, and to vary size of coefficients and to allow negatives
  • Quadratics-07: Factorising trinomials (option to specify whether negatives are involved)
Expressions and Formula Unit: Assessment Standard 1.3 Algebraic Fractions No content yet
Expressions and Formula Unit: Assessment Standard 1.4 Gradients, Volumes of Solids, Arcs and Sectors
  • Rounding-03: rounding whole numbers and decimals to a given number of significant figures (option to vary length of original number, and how many significant figures may be required)
  • StraightLine-01: find the gradient between two coordinate points (option to choose whether gradients are allowed to be whole number, fractional, positive, integer etc)
Relationships Unit: Assessment Standard 1.1 Straight lines, Linear equations/inequations, Simultaneous Equations, Changing the Subject
  • Equations-10: simultaneous equations in two variables (option to vary level of mathematical demand, in particular as to whether coefficients and answers are allowed to be negative)
Relationships Unit: Assessment Standard 1.2 Parabolas No content yet
Relationships Unit: Assessment Standard 1.3 Quadratic Equations
  • Quadratics-02: Solving a quadratic equation by factorising (option to specify constraints on coefficients)
  • Quadratics-03: Solving a quadratic equation using the quadratic formula (option to specify constraints on coefficients)
Relationships Unit: Assessment Standard 1.4 Angles, Similar Volumes, Converse of Pythagoras No content yet
Relationships Unit: Assessment Standard 1.5 Trigonometric Graphs and Equations
  • Equations-09: equations involving sin/cos/tan, CAST (option to vary level of mathematical demand, in particular to decide whether equations require rearranging, and whether or not negative values of sin/cos/tan are allowed)
Applications Unit: Assessment Standard 1.1 Sine rule, cosine rule No content yet
Applications Unit: Assessment Standard 1.2 Vectors, 3d-coordinates No content yet
Applications Unit: Assessment Standard 1.3 Appreciation, Depreciation, Fractions, Mixed numbers
  • Percentages-06: compound interest (options to vary difficulty of percentage, number of years, size of initial amount, whether to allow months as well as years, and whether question is asking for bank balance or interest)
Applications Unit: Assessment Standard 1.4 Scatter Graphs, Standard Deviation, Semi Interquartile Range
  • Statistics-01: Median, quartiles and five-figure summary (option to decide whether or not data is already ordered)
  • Quartile solver: you input a data set, and the spreadsheet works out the median, quartiles and the semi-interquartile range
  • Statistics-02: Standard deviation
  • Statistics-07: Median, quartiles and semi-interquartile range (option to decide whether or not data is already ordered) Be sure to ensure that InterQuartile range option is selected rather than Semi-InterQuartile range (from 2021-22, the National 5 syllabus includes IQR and no longer includes SIQR)
  • Standard Deviation solver: you input a data set, and the spreadsheet works out the standard deviation, and all associated quantities - helps with checking working