Problem Solving Unit

Year 9 Interactive Maths - Second Edition

Problem 3.1 Cube Using a graphics calculator or otherwise, find the smallest natural N whose cube ends in the digits 99.
Problem 3.2 Ratio The sides of a right-angled triangle have lengths a – b, a and a + b where a > b > 0. a. Show that a = 4b b. Find the ratio of a to b.
Problem 3.3 Space Diagonal The diagonal of a cube is the line joining the vertices that are not on the same face. The diagonal of the cube shown is 9 cm. What is the total surface area of the cube?
Problem 3.4 Small Square The 8 cm sides of a large square are divided into 4 equal parts. The square PQRS is then drawn. a. What is the area of the large square? b. What is the area of the small square? c. What is the ratio of the area of the small square to the area of the large square?
Problem 3.5 Area
Problem 3.6 The Square The diameter of the circle shown in the diagram is 14 cm. What is the area of the square PQRS?
Problem 3.7 What Part?

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