Your sentences are correct and natural. Both “in a bid to” and “bridge a gap” are commonly used by native speakers, especially in formal writing, news articles, and academic contexts. Let me break them down so you can use them naturally. 1. “In a bid to” Meaning: “in an attempt to”, “with the goal of”. It sounds slightly formal and is typical in journalism and official reports. Examples: The government cut taxes in a bid to boost spending. She changed her study routine in a bid to improve her exam results. The company reduced prices in a bid to attract more customers. Your original example is perfect: The examiners set the pass mark lower in a bid to bridge a gap… 2. “Bridge a gap” Meaning: to reduce a difference, to bring two groups or results closer together, to fix a discrepancy. Used both literally and figuratively. Examples: We need to bridge the gap between theory and practice. The program aims to bridge the gap between rural and urban healthcare. The new course was created to bridge a gap in students’ understanding. Your second sentence is also natural: Some people argue that it is necessary to bridge a gap between the poor and the rich… If you want a slightly smoother wording: …in order to ensure equal access to education and healthcare. Wrap-up suggestion Both expressions are natural, especially in formal or academic English. Your usage is correct. The only thing to keep in mind is that “in a bid to” often appears in news-style writing, and “bridge a gap” is very flexible and common in many contexts.