A charitable foundation receives a grant of . The grant is distributed in three stages. First, of the total grant is allocated to a research project. Express as a decimal. Express as a percentage. Calculate the amount of money allocated to the research project. The remaining money after the research allocation is then used for a development program. 40% of this remaining money is allocated to the development program. Express 40% as a fraction in its simplest form. Express 40% as a decimal. Calculate the amount of money allocated to the development program. The money remaining after the development program allocation is used for administrative costs. Calculate the amount of money allocated to administrative costs. Express the amount allocated to administrative costs as a percentage of the original total grant. Give your answer correct to one decimal place.

To express as a decimal: [1 mark - Scoring note: Award for the correct decimal value.] To express as a percentage: [1 mark - Scoring note: Award for the correct percentage value.] To calculate the amount of money allocated to the research project: 45\,000" data-type="block-math"> [1 mark - Scoring note: Award for the correct calculation and final amount.] To express 40% as a fraction in its simplest form: [1 mark - Scoring note: Award for the correct fraction in simplest form.] To express 40% as a decimal: [1 mark - Scoring note: Award for the correct decimal value.] First, find the money remaining after the research allocation: 75\,000" data-type="block-math"> Then, calculate 40% of this remaining amount: 30\,000" data-type="block-math"> [1 mark - Scoring note: Award M1 for calculating the remaining amount after research, and A1 for the correct amount for the development program.] To calculate the amount of money allocated to administrative costs: 30\,000 = $45\,000" data-type="block-math"> [1 mark - Scoring note: Award for the correct calculation of administrative costs.] To express the amount allocated to administrative costs as a percentage of the original total grant: 120\,000} \times 100\%" data-type="block-math"> [1 mark - Scoring note: Award M1 for setting up the correct fraction and multiplying by 100, and A1 for the correct percentage rounded to one decimal place.]

In 2023, The Global Academy had 1200 students. The student population was divided into day students and boarding students.75% of the students in 2023 were day students. Express 75% as a fraction in its simplest form and as a decimal.Calculate the number of day students and the number of boarding students in 2023.In 2024, the number of day students increased by of the number of day students in 2023. Express as a decimal and as a percentage.Calculate the new number of day students in 2024.The number of boarding students decreased by 10% from 2023 to 2024. Calculate the new number of boarding students in 2024.Calculate the total number of students in 2024. Then, calculate the percentage increase in the total number of students from 2023 to 2024. Give your answer correct to 1 decimal place.

Fraction: [1 mark - Scoring note: Accept or equivalent simplified fraction.]Decimal: [1 mark - Scoring note: Accept 0.75.]Number of day students in 2023: [1 mark - Scoring note: Method for calculating day students.]Number of boarding students in 2023: [1 mark - Scoring note: Correct number of boarding students, or correctly following through from their day students.]Decimal: [1 mark - Scoring note: Accept 0.2.]Percentage: [1 mark - Scoring note: Accept 20% or equivalent.]Increase in day students: [1 mark - Scoring note: Method for calculating the increase in day students.]New number of day students in 2024: [1 mark - Scoring note: Correct new number of day students.]Decrease in boarding students: [1 mark - Scoring note: Method for calculating the decrease in boarding students.]New number of boarding students in 2024: [1 mark - Scoring note: Correct new number of boarding students.]Total students in 2024: [1 mark - Scoring note: Correct total number of students in 2024, or correctly following through from their part (d) and (e).]Percentage increase: [1 mark - Scoring note: Correct method for percentage increase.][1 mark - Scoring note: Correct final answer for percentage increase, correct to 1 decimal place.]

A company's annual profit changed over three years.In 2023, the profit increased by 15% compared to 2022.In 2024, the profit decreased by of the 2023 profit.The profit in 2024 was million.Express 15% as a fraction in its simplest form and as a decimal.Express as a percentage and as a decimal.Calculate the company's profit in 2023.Calculate the company's profit in 2022. Give your answer in dollars, correct to the nearest thousand.

Fraction: [1 mark - Scoring note: For or equivalent fraction in simplest form.]Decimal: [1 mark - Scoring note: For .]Percentage: [1 mark - Scoring note: For .]Decimal: [1 mark - Scoring note: For .]Convert million to dollars: [1 mark - Scoring note: For correctly converting million to .]Profit in 2024 is of the 2023 profit.So, 1\,350\,000 \div \frac{7}{8}$[1 mark - Scoring note: For setting up the division by or multiplication by .]1\,350\,000 \times \frac{8}{7} = 1\,542\,857.141\,542\,8571\,542\,857.11\,542\,857.141\,542\,860 to 3 s.f.)[1 mark - Scoring note: For the correct profit in 2023, rounded to at least 3 significant figures or 2 decimal places for currency.]Profit in 2023 is or times the profit in 2022.[1 mark - Scoring note: For correctly identifying the multiplier or and setting up the division.]Using the unrounded value for : [1 mark - Scoring note: For substituting the unrounded or sufficiently accurate value of into the calculation.][1 mark - Scoring note: For calculating the unrounded or sufficiently accurate value of .]Rounding to the nearest thousand dollars: 1\,342\,000[1 mark - Scoring note: For the final answer rounded correctly to the nearest thousand dollars.]

A charity organised a fundraising gala. The total money raised was $15 000.Of the total money raised, came from direct donations.Express as a decimal.Express as a percentage.Ticket sales accounted for 45% of the total money raised.Calculate the amount of money raised from ticket sales.Express 45% as a fraction in its simplest form.The remaining money was raised through merchandise sales. The charity spent $1800 on organising the event.Calculate the amount of money raised from merchandise sales.Calculate the profit made by the charity.Express the profit as a percentage of the total money raised, correct to 1 decimal place.The charity decided to distribute the profit such that of the profit goes to a local animal shelter and the rest goes to a community development project. Express the amount given to the community development project as a fraction of the total money raised. Give your answer in its simplest form.

[1 mark - Scoring note: Accept or equivalent fraction/percentage if not explicitly asked for decimal.][1 mark - Scoring note: Accept or equivalent decimal/fraction.][1 mark - Scoring note: M1 for or equivalent. A1 for correct answer.][1 mark - Scoring note: Accept or equivalent simplest form.]Percentage for merchandise: Amount from merchandise: [1 mark - Scoring note: M1 for correct method to find merchandise amount (e.g., or ). A1 for correct answer.]Profit = [1 mark - Scoring note: Accept .]Percentage profit = Rounded to 1 decimal place: [1 mark - Scoring note: M1 for . A1 for (must include the zero for 1 d.p. accuracy).]Fraction of profit for community development project = Amount for community development project = Fraction of total money raised = [1 mark - Scoring note: M1 for finding the amount for the community project, e.g., .][1 mark - Scoring note: M1 for setting up the fraction , e.g., .][1 mark - Scoring note: A1 for the correct answer in its simplest form, .]

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IGCSE (CAMBRIDGE)|9th and 10th|Extended Maths (0580)

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