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. (D)</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. (B)</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 (A)</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. (C)</p> Signup and view all the answers

What type of tier is this exam categorized under?

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

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

<p>3 (A)</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}$ (B)</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}$ (B)</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. (B)</p> Signup and view all the answers

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

<p>$ rac{2}{3}$ (B)</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}$ (C)</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 (B)</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. (B)</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 (B)</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 (B)</p> Signup and view all the answers

What type of triangle is triangle ABC?

<p>Right-angled triangle (B)</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. (A)</p> Signup and view all the answers

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

<p>16.4 cm (D)</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 (A)</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 (D)</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 (D)</p> Signup and view all the answers

How many bars of chocolate does Saira buy in total?

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

How many of the chocolate bars are white chocolate?

<p>2 bars (B)</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 (A)</p> Signup and view all the answers

What fraction of the chocolate bars are white chocolate?

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

What percentage of the total bars are milk chocolate?

<p>75% (D)</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 (C)</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 (A)</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 (B)</p> Signup and view all the answers

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

<p>1 (D)</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 (A)</p> Signup and view all the answers

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

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

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

<p>6 (A)</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 (C)</p> Signup and view all the answers

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

<p>Quadratic (A)</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 (D)</p> Signup and view all the answers

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

<p>0 (B)</p> Signup and view all the answers

Flashcards

Exam duration

The examination lasts 1 hour and 30 minutes.

Unnecessary material

Graph paper is not required for the exam.

Total exam marks

The maximum score attainable on the exam is 80 marks.

Pencil type for diagrams

Use a dark pencil (HB or B) for diagrams.

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Missing name/candidate number

If you forget your name or candidate number, ask the invigilator for help.

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π value (no π button)

If your calculator doesn't have π, use 3.142.

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Extra time action

Check your answers if you have extra time.

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Exam tier

This exam is categorized under the Foundation Tier.

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Spinner sections

Majid's spinner has 3 sections.

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Probability of one section

The probability of landing on any one section is 1/3.

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Correct probability of section 2

The probability of landing on section 2 must be 1/3.

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Majid's statement accuracy

Majid is correct because the spinner is fair.

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Probability of not landing on section 2

The probability of not landing on section 2 is 2/3.

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Probability of section 1 or 3

The probability of landing on section 1 or 3 is 2/3.

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Expected landing on section 2

Majid would expect to land on section 2 3 times in 9 spins.

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Spinner equal probability

Each section on the spinner has an equal probability.

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Side CB length

Side CB is approximately 16.4 cm.

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Prime factors of 90

The prime factors of 90 are 2, 3, and 5.

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Triangle ABC type

Triangle ABC is a right-angled triangle.

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Longest side of triangle

Side AB is the longest side if the triangle is right-angled.

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Significant figures for CB

The length of CB should be rounded to 3 significant figures (16.4 cm).

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Pythagorean theorem equation

AB² + AC² = CB² represents the relationship in a right-angled triangle.

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Approximate area of triangle ABC

The approximate area of triangle ABC is 95 cm².

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Possible AC length

AC could be 12 cm if using Pythagorean theorem to calculate CB.

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Total chocolate bars

Saira bought 24 chocolate bars.

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White chocolate bars

There are 2 white chocolate bars.

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Milk chocolate bars

There are 22 milk chocolate bars.

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Fraction of white chocolate

The fraction of white chocolate bars is 1/12.

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Percentage of milk chocolate

75% of the bars are milk chocolate.

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White chocolate bars (12 bars)

If Saira had 12 bars, 2 would be white chocolate.

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Bars after giving away white chocolate

Saira has 22 bars left after giving away the white ones.

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Total bars with extra 12

If Saira buys 12 more bars, she will have 36 bars in total.

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Value of y (x=1)

When x=1, y=0 for the function y = x² - x.

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Maximum y (x² - x)

The value x=0.5 gives the maximum value of y = x² - x.

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Quadratic equation form

The function y = x² - x can be represented by a quadratic equation like ax² + bx + c = 0.

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y value (x=-2)

When x is -2, y is 6, for the function y = x² - x.

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Graphical solutions (x² - x = 4)

Solutions can be found at the points where the graph of y = x² - x intersects with the line y = 4.

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Graph nature (x² - x)

The graph of y = x² - x is a parabola.

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Minimum y value (x² - x)

The lowest output for y=x² - x occurs when x=0.5.

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Y-intercept (x² - x)

The y-intercept for y = x² - x is 0.

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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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