Maths paper 1

• What is the focus of the video discussed in the study material?

  The video focuses on the advanced information released for the 2022 maths GCSE higher paper one.
• What resource is provided for students in the video?

  A checklist of topics for the advanced information for papers one, two, and three is provided.
• How can students access the checklist mentioned in the video?

  Students can download and print the checklist from the description of the video.
• What should students do if they want to focus on specific topics in the video?

  Students can click on the chapters at the bottom left of the video to navigate to specific topics.
• What is the first step in solving the problem "three-fifths of a number is 48"?

  Identify that three-fifths of a number means that three parts out of five equal 48.
• How do you find the value of one part when three-fifths of a number is 48?

  You divide 48 by 3 to find the value of one part.
• What is the total number when three-fifths equals 48?

  The total number is 80, calculated as \(16 \times 5\).
• What is the first step in adding mixed numbers like "three and four-fifths" and "three-sevenths"?

  The first step is to convert mixed numbers into improper fractions.
• How do you convert "three and four-fifths" into an improper fraction?

  You multiply 3 by 5 and add 4 to get \( \frac{19}{5} \).
• What is the lowest common multiple of 5 and 7?

  The lowest common multiple of 5 and 7 is 35.
• How do you create equivalent fractions with a common denominator of 35 for \( \frac{19}{5} \) and \( \frac{3}{7} \)?

  You multiply \( \frac{19}{5} \) by \( \frac{7}{7} \) and \( \frac{3}{7} \) by \( \frac{5}{5} \).
• What is the process to add the fractions \( \frac{133}{35} \) and \( \frac{15}{35} \)?

  You add the numerators to get \( \frac{148}{35} \) while keeping the denominator the same.
• How do you convert \( \frac{148}{35} \) into a mixed number?

  You divide 148 by 35 to find how many times it fits, which is 4, with a remainder of 8.
• What is the final answer for the mixed number from \( \frac{148}{35} \)?

  The final answer is \( 4 \frac{8}{35} \).
• What is the first step in dividing mixed numbers like "one and one-fifth" by "three-quarters"?

  Convert the mixed numbers into improper fractions first.
• What is the reciprocal of \( \frac{3}{4} \)?

  The reciprocal of \( \frac{3}{4} \) is \( \frac{4}{3} \).
• How do you multiply the fractions \( \frac{6}{5} \) and \( \frac{4}{3} \)?

  You multiply the numerators to get 24 and the denominators to get 15, resulting in \( \frac{24}{15} \).
• How do you convert \( \frac{24}{15} \) into a mixed number?

  You divide 24 by 15 to get 1 with a remainder of 9, resulting in \( 1 \frac{9}{15} \).
• What is the simplified form of \( 1 \frac{9}{15} \)?

  The simplified form is \( 1 \frac{3}{5} \).
• What is the first step in converting a recurring decimal like 0.47 with a recurring 7 into a fraction?

  Set \( x = 0.47 \) and identify the recurring part.
• What happens when you multiply the recurring decimal \( x = 0.47 \) by 10?

  You get \( 4.7 \) with the recurring 7 still present.
• How do you eliminate the recurring part when subtracting \( 4.7 \) and \( 0.47 \)?

  You subtract to get \( 4.3 \) and \( 9x = 4.3 \).
• What is the final step to express \( x \) as a fraction after finding \( 9x = 4.3 \)?

  You divide both sides by 9 to find \( x \).
• What is the value of \( x \) when \( 9x = 4.3 \)?

  The value of \( x \) is \( \frac{4.3}{9} \).
• Why is it important to express the final answer as a fraction in simplest form?

  It ensures clarity and accuracy in mathematical communication.
• What is the significance of understanding the process of converting decimals to fractions?

  It helps in solving various mathematical problems involving recurring decimals.
• What is the result of $4.77 - 0.47$?


  $4.3$
• When subtracting $10x - 1x$, what is the result?


  $9x$
• Why is it unnecessary to write a zero after $4.3$?


  Because $4.3$ is already in its simplest decimal form
• What should you do before converting a decimal to a fraction?

  Multiply both sides by 10 to eliminate the decimal
• What is the fraction representation of $x$ after multiplying by 10?


  $x =$$\frac{43}{90}$
• How do you determine if a fraction is in its simplest form?

  Check if the numerator and denominator have any common factors
• What are the prime factors of $525$?


  $3, 5^2, 7$
• What does a negative exponent indicate?

  It indicates the reciprocal of the base
• What does the denominator in a power indicate?

  It indicates the root to be taken
• What is the result of $25^{-\frac{1}{2}}$?


  $\frac{1}{5}$
• How do you calculate $\left(\frac{8}{27}\right)^{\frac{2}{3}}$?


  $\frac{4}{9}$
• What is the square root of $80$ expressed in the form $k\sqrt{5}$?


  $4\sqrt{5}$
• Why is $\sqrt{20}$ not in its simplest form?


  Because it can be simplified further to $2\sqrt{5}$
• How can you combine $\sqrt{40} +$$\sqrt{90}$?


  By simplifying both to have a common radical term