Ratio and proportion

Evaluate — 2 marks

A student is investigating the relationship between the force applied to a spring and the extension it produces. She applies forces of 2 N, 4 N, 6 N and 8 N to an identical spring and measures the extensions as 4 cm, 8 cm, 12 cm and 16 cm respectively.

What is the ratio of force to extension for this spring? Express your answer in simplest form. [1 mark]
Evaluate whether the spring obeys Hooke's Law based on the data provided. Explain your reasoning. [1 mark]

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Explain — 5 marks

A physics teacher is preparing two solutions for a class experiment. Solution A contains 3 grams of salt dissolved in 150 cm³ of water. Solution B contains 5 grams of salt dissolved in 250 cm³ of water. The teacher wants to understand which solution is more concentrated.

Calculate the ratio of salt to water in Solution A. Express your answer in the form 1:n. [2 marks]
Calculate the ratio of salt to water in Solution B. Express your answer in the form 1:n. [2 marks]
Explain which solution is more concentrated and how the ratios you calculated support your answer. [1 mark]

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Show — 4 marks

A physics teacher is preparing a practical experiment comparing the extension of two different springs. Spring A extends by 8 cm when a 2 N force is applied. Spring B extends by 12 cm when a 3 N force is applied.

Show that the ratio of extension to force for Spring A is 4:1. [1 mark]
Calculate the ratio of extension to force for Spring B. Express your answer in the form n:1. [2 marks]
Using your answers from parts (a) and (b), show which spring is stiffer by comparing the ratios. [1 mark]

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Divides 12 cm by 3 N to give 4 cm/N (1 mark)
Expresses answer as 4:1 (1 mark)
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Describe — 4 marks

A student investigates the relationship between the extension of a spring and the force applied to it. She hangs different masses from a spring and measures the extension produced. Her results show that when a 100 g mass is added, the spring extends by 4 cm. When a 250 g mass is added, the spring extends by 10 cm.

Describe the relationship between the mass and the extension of the spring shown by these results. [2 marks]
A 500 g mass is now added to the spring. Describe how you would use the ratio and proportion method to predict the extension produced. [2 marks]

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State — 4 marks

A recipe for granola uses oats, nuts, and dried fruit in the ratio 3 : 2 : 1 by weight. A café uses 450 grams of oats when making a large batch.

(01.1) State the total weight of nuts and dried fruit used in this batch. [2 marks]
(01.2) The café wants to make a smaller batch using 300 grams of ingredients in total. State the weight of oats required. [2 marks]

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(01.1) M1 for method: 450 ÷ 3 (= 150) or sight of 3 parts for nuts and fruit combined
(01.1) A1 for 450 grams
(01.2) M1 for method: 300 ÷ 6 × 3 or 300 × 3/6 or equivalent
(01.2) A1 for 150 grams

Evaluate — 2 marks

Explain — 5 marks

Show — 4 marks

Describe — 4 marks

State — 4 marks

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