20 page Perimeter, Areas, Volumes, Algebra Booklet Primary-Higher Problem Solving + Solutions

20 page pdf booklet.
There are examples of how to carry out unit conversions for areas followed by 16 questions on unit conversions.
There are then 14 questions asking students to find missing areas, heights and widths (for shapes including squares, rectangles, trapezia, kites and rhombuses) using number values required for substitution into area formulae.
Three example algebraic problems are then reviewed and full workings (with reminders about BODMAS) provided:
1) Substitution of an x value into length and width expressions to find a missing area of a rectangle;
2) Finding the value of x given an area value for a rectangle, and length and width in terms of x;
3) Finding the value of x and a width given expressions in x for opposite lengths in a rectangle as well as its value of area.
These examples are followed by 10 questions which require substitution of algebraic terms into such area formulae as per the 3 examples provided.
A further 4 more difficult questions (aimed at GCSE/National 5 level - with worked solutions) is included relating to: finding ratios of areas e.g. areas of regular shapes in a tessellation, inlaid parallelograms/trapezia and comparing lengths, areas and volumes of shapes with various sections removed (including spheres, segments, arc lengths, and a tetrahedron).
Finally, 3 questions (with worked solutions) on optimisation (relating to perimeter, areas and volumes of various shapes) for Higher/A level students are then reviewed.
There is an emphasis on using exact values throughout.