Unit 1: Significant Figures and Accuracy Exam

A mathematics student decides to use an approximation to π of 355/115. What is his percentage error in using this value, giving your answer in standard form?

• 1.74 × 10⁰ %

• 2.7 × 10⁻¹ %

• 1.5 × 10 %

• 3.1 × 10¹ %

• 8.3 minutes

• 2.5 minutes

• 12.4 minutes

• 0.5 minutes

Vertical posts are to be placed around the outer edge of a children’s park. Each post is formed from a cuboid with a right square-based pyramid on top. The cuboid part of the post is machine-made such that its width, and hence the width of the pyramid, is exactly 20 cm. The length from the apex of the pyramid, A, to any corner of the base of the pyramid is 14.6 cm, but this is only accurate to the nearest tenth of a centimetre. Write down the upper bound and lower bound for the possible lengths of edge AC.

• None of these

Vertical posts are to be placed around the outer edge of a children’s park. Each post is formed from a cuboid with a right square-based pyramid on top. The cuboid part of the post is machine-made such that its width, and hence the width of the pyramid, is exactly 20 cm. The length from the apex of the pyramid, A, to any corner of the base of the pyramid is 14.6 cm, but this is only accurate to the nearest tenth of a centimetre. Point H is the midpoint of BC. What are the upper and lower bounds for AH, the slant height of the pyramid?

• None of these

Zaha is designing a bridge to cross a river. She believes that the weight of the steel needed for this bridge is approximately 53 632 000 kg. The exact weight of the steel needed for the bridge is 55 625 000 kg. Find the percentage error in Zaha’s approximation.

• 3.58%

• 1.25%

• 7.90%

• 0.85%

Zaha is designing a bridge to cross a river. She believes that the weight of the steel needed for this bridge is approximately 53 632 000 kg. The exact weight of the steel needed for the bridge is 55 625 000 kg. Zaha’s design is used to build five identical bridges. Find the weight of the steel needed for these five bridges, to three significant figures.

• 268,000,000 kg.

• 278,000,000 kg.

• 256,000,000 kg.

• 286,000,000 kg.

• 2.78 × 10^8 kg

• 2.68 × 10^8 kg

• 2.68 × 10^7 kg

• 2.87× 10^8 kg

In an electric circuit, the resistance (R ohms) of a component may be calculated using the formula R = V/I where V is the potential difference across the component and I is the current through the component. The potential difference is measured as 6 V to the nearest Volt, and the current is measured as 0.2 A to the nearest tenth of an ampere. Calculate the lower and upper bounds for the resistance.

• Upper: 43.3 Ohms

  Lower: 22 Ohms

• Upper: 36.7 Ohms

  Lower: 30 Ohms

• Upper: 26 Ohms

  Lower: 22 Ohms

• Upper: 43.3 Ohms

  Lower: 36.7 Ohms

In an electric circuit, the resistance (R ohms) of a component may be calculated using the formula R = V/I where V is the potential difference across the component and I is the current through the component. The potential difference is measured as 6 V to the nearest Volt, and the current is measured as 0.2 A to the nearest tenth of an ampere. b. The actual value of the resistor is 30 Ohms. Calculate the maximum possible percentage error that could be obtained.

• 26.7%

• 63.6%

• 44.4%

• None of the these

A pendant is made in the shape of a circular sector OAB, with angle ∠AÔB = 40° and a radius of 12 cm. Find the perimeter of the pendant.

• 36 cm

• 32.4 cm

• 24 cm

• 8.38 cm