The load capacity C C\,C kN of a support is modelled by C=kd3/2C=kd^{3/2}C=kd3/2, where d d\,d cm is its depth and k k\,k is a positive constant.
A support of depth 4 cm has a load capacity of 40 kN.
Determine the value of kkk.
Determine the depth of a support with a modelled load capacity of 135 kN.
According to the model, state the factor by which the load capacity changes when the depth is doubled. Give the factor in exact form.
303 exam-style questions on OCR (MEI) A Level Maths 1.2 Algebra, covering 1.2.1 Algebraic vocabulary and notation, 1.2.2 Solve linear equations, 1.2.3 Change the subject of a formula, 1.2.4 Solve quadratic equations, 1.2.5 Discriminant of a quadratic, 1.2.6 Linear simultaneous equations, 1.2.7 One linear one quadratic simultaneous equations, 1.2.8 Points of intersection and solutions, 1.2.9 Linear inequalities, 1.2.10 Quadratic inequalities, 1.2.11 Expressing solutions of inequalities, 1.2.12 Use and manipulate surds, 1.2.13 Rationalise the denominator, 1.2.14 Laws of indices, 1.2.15 Negative, fractional and zero indices, 1.2.16 Proportional relationships, 1.2.17 Partial fractions (A-level only), and 1.2.18 Simplify rational expressions (A-level only). Each one has a worked solution and a mark scheme showing where the marks go.