## Exam-Style Questions.## Problems adapted from questions set for previous Mathematics exams. |

## 1. | GCSE Higher |

An isosceles triangle shaped frame is made from four pieces of metal. The frame has a height of 8 metres and a base of length 12 metres.

The weight of the metal is 2.5kg per metre. Calculate the total weight of the metal in the frame.

## 2. | GCSE Higher |

ABC is a right-angled triangle as shown in the diagram below. Calculate the length of AB giving your answer correct to three significant figures.

## 3. | GCSE Higher |

An arborist sights the top of a tree using a clinometer and reads the angle of elevation to be 29^{o}. Her clinometer is 28 metres from the base of the tree and is on a tripod making it 1.5 metres above ground level.

This diagram is not drawn to scale.

Calculate the full height of the tree.

## 4. | GCSE Higher |

The diagram shows a trapezium where the sides AC and BD are parallel.

Calculate the length of side CD

## 5. | GCSE Higher |

Four copies of a green right-angled triangle are used to enclose a yellow square.

Find the area of the yellow square if the longest side of the green triangle is of length \(a\) cm and the shortest side is \(b\) cm.

## 6. | GCSE Higher |

The diagram shows a rectangular-based pyramid, TABCD (not drawn to scale).

The horizontal base ABCD has sides of lengths 11m and 15m. The centre of the base of the pyramid is M.

Angle TMC is 90° and angle TCM is 70°

The volume of a pyramid is \( \frac13 \) × area of base × perpendicular height. Calculate the volume of this pyramid.

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