Daily Practice - 11+ Entrance

Shape 1: an arrow pointing North. Shape 2: an arrow pointing East. Shape 3: an arrow pointing South. What does Shape 4 look like?

A solid is built on a 3 by 3 grid. The centre stack has height 3, and all eight surrounding stacks have height 2. A unit cube counts as completely hidden if it has no visible left, right, front, back or top face (the underside does not count). How many unit cubes in this solid are completely hidden?

A solid stands on a 3 by 2 grid (columns A, B, C; rows 1, 2). Heights: A1 = 1, B1 = 2, C1 = 1, A2 = 2, B2 = 1, C2 = 1. What is the front elevation, reading columns A, B, C?

A square sheet is folded in half vertically, then folded in half again horizontally, so the final folded shape is a quarter of the original size. A single hole is punched through all the layers, well away from both crease lines. How many holes will there be once fully unfolded, and why?

Shape 1 is an L-shaped hexagon: a 4cm by 4cm square with a 2cm by 2cm notch cut from its top-right corner. Shape 2 is a 2cm by 2cm square. Shape 2's marked edge is joined exactly into the notch, filling it completely. What shape is formed?