GED and HiSET mathematics — geometry and measurement

Geometry on these tests is measurement with a purpose: how much fencing, how much film, how many tiles, how long the ramp. There is no diagram anywhere in this set — every figure is described in words, which is harder and also closer to how the question arrives in life.

The first thing it tests is whether the right quantity is being calculated at all. A dog run eighteen feet by twelve needs sixty feet of fencing, not two hundred and sixteen: the perimeter runs along the edge and the area covers the ground inside, and the units say which is which. A fountain is given by its diameter rather than its radius, which is where the commonest circle mistake lives — halve it before squaring, or the answer comes out four times too big. And a countertop needs nine boxes of protective film rather than eight, because thirty-five square feet divided by four is 8.75 and eight boxes leave three square feet bare. Rounding down is always wrong when the material is what you are buying.

The rest is the standard toolkit, each in a situation: the area of a triangular flowerbed; a countertop with a square notched out of one corner, which is one area minus another; the circumference of a circular patio; the volume of a shipping crate and of a cylindrical water barrel, both with 3.14 for pi; the length of a wheelchair ramp from its base and its height; a missing side in a pair of similar triangles, found by scale; two angles given as x and 2x with a right angle beside them; and ninety square feet of floor turned into square yards — divided by nine, not by three, which is the trap that catches people who convert the length and forget that the area has two dimensions.

Everything is written in plain words and digits, with no notation to decode. Each answer was worked out twice before it was used, and an independent solver reproduced all twelve.

Zestly is an independent study tool. It is not affiliated with GED Testing Service, which owns the GED test, or with the HiSET program, and it is not a test centre.

• Decide whether a situation calls for perimeter, area or volume, and use the matching units
• Find the area of a triangle and of a shape made by removing one rectangle from another
• Work out the circumference and the area of a circle, halving a diameter before squaring it
• Find the volume of a rectangular box and of a cylinder
• Round a quantity of material up to whole units, and say why rounding down is never right
• Find the third side of a right triangle from the other two
• Use scale to find a missing side in similar triangles, and solve for an unknown angle in a triangle
• Convert an area from square feet to square yards by dividing by nine

Written for this exercise; no diagrams, every figure described in words. From the bank: "A countertop measures 7 feet by 5 feet. Protective film is sold in boxes, each covering 4 square feet, and a box cannot be split. How many boxes are needed?" Thirty-five divided by four is 8.75, and eight boxes leave three square feet of the counter bare — so nine.