Mathematics Concepts: Pythagoras, Factorization, Probability
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Mathematics Concepts: Pythagoras, Factorization, Probability

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Questions and Answers

What is the duration of the examination?

  • 1 hour
  • 1 hour 30 minutes (correct)
  • 2 hours
  • 1 hour 15 minutes

    • Which materials are NOT required for the examination?

  • Graphing paper (correct)
  • Calculator
  • Protractor
  • Ruler graduated in centimetres and millimetres

    • What is the maximum total mark for this paper?

  • 90
  • 80 (correct)
  • 100
  • 70

    • Which statement about pencil usage in the exam is correct?

    <p>Pencils must be dark (HB or B) for diagrams.</p> Signup and view all the answers

    What should a candidate do if they forget to fill in their name and candidate number?

    <p>Ask the invigilator for guidance.</p> Signup and view all the answers

    In the case that a calculator does not have a π button, what value should be used for π?

    <p>3.142</p> Signup and view all the answers

    What is advised to do if a candidate completes all questions and has extra time?

    <p>Check answers if there is time.</p> Signup and view all the answers

    What type of tier is this exam categorized under?

    <p>Foundation Tier</p> Signup and view all the answers

    What is the total number of sections on Majid's spinner?

    <p>3</p> Signup and view all the answers

    What is the probability that the arrow will land on any one of the sections?

    <p>$ rac{1}{3}$</p> Signup and view all the answers

    If Majid says the probability of landing on section 2 is correct, which value must it represent?

    <p>$ rac{1}{3}$</p> Signup and view all the answers

    Is Majid's statement about the probability of landing on 2 accurate?

    <p>Yes, it is correct because the spinner has three sections.</p> Signup and view all the answers

    What would be the probability of not landing on section 2?

    <p>$ rac{2}{3}$</p> Signup and view all the answers

    What is the combined probability of landing on either section 1 or section 3?

    <p>$ rac{2}{3}$</p> Signup and view all the answers

    If Majid spins the spinner 9 times, how many times would he expect to land on section 2?

    <p>3 times</p> Signup and view all the answers

    Which of the following statements is true about the spinner?

    <p>Each section has an equal probability of being landed on.</p> Signup and view all the answers

    What is the length of side CB in triangle ABC, given side AB is 19 cm and side AC is 10 cm?

    <p>16.4 cm</p> Signup and view all the answers

    What is the product of the prime factors of the number 90?

    <p>2 x 3 x 5</p> Signup and view all the answers

    What type of triangle is triangle ABC?

    <p>Right-angled triangle</p> Signup and view all the answers

    If side AB of triangle ABC measures 19 cm, which of the following must be true regarding the sides of the triangle?

    <p>AB must be the longest side of the triangle.</p> Signup and view all the answers

    To what three significant figures should the length of CB be rounded?

    <p>16.4 cm</p> Signup and view all the answers

    Which of the following equations represents the relationship between the sides of triangle ABC given its right angle?

    <p>AB² + AC² = CB²</p> Signup and view all the answers

    What is the approximate area of triangle ABC if it has a base of 19 cm and height of 10 cm?

    <p>95 cm²</p> Signup and view all the answers

    Which of the following could be the length of side AC in triangle ABC if CB is calculated using the Pythagorean theorem?

    <p>12 cm</p> Signup and view all the answers

    How many bars of chocolate does Saira buy in total?

    <p>24 bars</p> Signup and view all the answers

    How many of the chocolate bars are white chocolate?

    <p>2 bars</p> Signup and view all the answers

    If there are 24 bars of chocolate and 2 are white, how many are milk chocolate?

    <p>22 bars</p> Signup and view all the answers

    What fraction of the chocolate bars are white chocolate?

    <p>$\frac{1}{12}$</p> Signup and view all the answers

    What percentage of the total bars are milk chocolate?

    <p>75%</p> Signup and view all the answers

    If Saira wanted to maintain the same ratio of white to milk chocolate but had only 12 bars, how many would be white chocolate?

    <p>2 bars</p> Signup and view all the answers

    If Saira decides to give away all the white chocolate bars, how many bars does she have left?

    <p>22 bars</p> Signup and view all the answers

    If Saira decides to buy 12 more bars, maintaining the same quantities of white and milk chocolate, how many total bars will she have?

    <p>36 bars</p> Signup and view all the answers

    What is the value of y when x = 1 for the function y = x² - x?

    <p>1</p> Signup and view all the answers

    Which of the following values for x yields the maximum value of y = x² - x?

    <p>0.5</p> Signup and view all the answers

    What is the quadratic equation representation of the function y = x² - x?

    <p>ax² + bx + c = 0</p> Signup and view all the answers

    Using the values in the table, what is the value of y when x = -2?

    <p>6</p> Signup and view all the answers

    If the equation x² - x = 4 is solved graphically, where will the solutions be found?

    <p>At points where y = 4 on the graph</p> Signup and view all the answers

    What is the nature of the graph of the function y = x² - x?

    <p>Quadratic</p> Signup and view all the answers

    Which x-value results in the lowest output value for y = x² - x within the given range?

    <p>0</p> Signup and view all the answers

    What is the y-intercept of the function y = x² - x?

    <p>0</p> Signup and view all the answers

    Study Notes

    Pythagoras

    • A right-angled triangle has a hypotenuse that is the longest side
    • The other two sides are shorter, and are called the legs or the "adjacent" and "opposite" sides relative to an angle
    • Pythagoras' Theorem states: a² + b² = c² where c is the hypotenuse
    • Use the theorem to calculate the length of any side of a right-angled triangle when you know two side lengths

    Prime Factorization

    • Prime factorization is when you break down a positive integer into its prime number factors.
    • A prime number is a whole number greater than 1 that has only two divisors (factors): unity (1) and itself.
    • When 90 is broken down into prime factors you get: 2 x 3 x 3 x 5

    Probability

    • Probability is the chance of a specific event happening out of all the possible outcomes that could occur.
    • The probability that a specific outcome will happen from a set of events is the number of times that specific outcome can occur divided by the total number of possible outcomes.
    • Probability is represented as a decimal or a fraction.

    Fractions in Real World Problems

    • You can use fractions to calculate the proportion of a whole item or set of items.
    • The whole number must be multiplied by the numerator of the fraction, then divided by the denominator of the fraction.

    Quadratic Graphs

    • Quadratic equations are of the form y = ax² + bx + c, where a, b and c are constants.
    • When plotted on a graph, the equation results in a parabola
    • The parabola intersects the y-axis at the point with the same coordinates as the constant "c" in the equation

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    Pearson Edexcel Level 1/Level 2 GCSE (9-1) Mathematics June 2024 PDF

    Description

    This quiz covers important mathematical concepts including Pythagoras' theorem, prime factorization, and basic probability. Each section provides foundational knowledge and examples to help you understand how to apply these principles in problem-solving. Test your understanding and boost your mathematical skills!

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