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GCSE Maths Higher Tier Practice PDF (Free + Answered)

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GCSE Maths Higher Tier Practice PDF (Free + Answered)
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yuma

@blueyberrymuffin

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I'll help create SEO-optimized summaries for this GCSE Maths exam transcript. Let me process it page by page and provide the summaries as requested.

This comprehensive GCSE higher tier maths practice exam PDF from January 2022 covers essential mathematical concepts and problem-solving techniques. The exam is designed for calculator use and spans 80 marks over 90 minutes.

Key features:

  • Full calculator paper with detailed solutions
  • Covers advanced mathematical concepts
  • Includes geometry, algebra, and probability questions
  • Comprehensive marking scheme
  • Perfect for GCSE Maths past papers practice

26/10/2023

2498

GCSE Mock Exam (Jan 2022) Maths 2 (Higher) - Calc Materials Use a blue/black pen. You must have a ruler, protractor, pencil and eraser. Trac

View

Page 2: Algebra and Equations

This page focuses on algebraic manipulation and equation solving, key skills for the GCSE higher tier maths practice exam. Question 1 asks students to simplify algebraic expressions and solve an inequality. Part (a) requires simplification of 14y/3, part (b) involves simplifying p^t × p^(-t), and part (c) asks to solve the inequality 7y > 9 × 3.

Example: For part (b), students need to apply the laws of exponents to simplify p^t × p^(-t) to 1.

Vocabulary: Simplify - To reduce an expression to its simplest form by combining like terms or cancelling out factors.

GCSE Mock Exam (Jan 2022) Maths 2 (Higher) - Calc Materials Use a blue/black pen. You must have a ruler, protractor, pencil and eraser. Trac

View

Page 3: Speed, Distance, and Time

This page presents a problem involving speed, distance, and time calculations, a common topic in GCSE Maths past papers with answers. Question 2 describes Andrea's journey, which consists of driving 110 km at 40 km/h and then running 14 km at 8 km/h. Students must calculate the total time taken for both parts of the journey, giving the answer in hours and minutes.

Example: To solve this, students should:

  1. Calculate time for driving: 110 km ÷ 40 km/h = 2.75 hours
  2. Calculate time for running: 14 km ÷ 8 km/h = 1.75 hours
  3. Add the times: 2.75 + 1.75 = 4.5 hours
  4. Convert to hours and minutes: 4 hours 30 minutes
GCSE Mock Exam (Jan 2022) Maths 2 (Higher) - Calc Materials Use a blue/black pen. You must have a ruler, protractor, pencil and eraser. Trac

View

Page 4: Transformations

This page focuses on geometric transformations, a key topic in the GCSE higher tier maths practice exam 2020 and other years. Question 3(a) requires students to translate shape P by the vector (-9, 5). The question provides a coordinate grid with shape P already drawn.

Definition: Translation - A transformation that moves every point of a shape the same distance in the same direction.

Highlight: Understanding transformations is crucial for success in the geometry sections of GCSE Maths past papers Foundation and Higher tiers.

GCSE Mock Exam (Jan 2022) Maths 2 (Higher) - Calc Materials Use a blue/black pen. You must have a ruler, protractor, pencil and eraser. Trac

View

Page 5: Transformations (continued)

This page continues with transformations, asking students to describe a single transformation that maps shape A onto shape B. The correct answer is a reflection in the line y = x. This type of question is common in GCSE Maths past papers PDF with answers AQA and other exam boards.

Vocabulary: Reflection - A transformation that flips a shape over a line, creating a mirror image.

Highlight: Being able to identify and describe transformations is a key skill tested in GCSE Maths past papers Foundation and Higher tiers.

GCSE Mock Exam (Jan 2022) Maths 2 (Higher) - Calc Materials Use a blue/black pen. You must have a ruler, protractor, pencil and eraser. Trac

View

Page 6: Compound and Simple Interest

This page presents a problem comparing compound and simple interest, a topic frequently appearing in GCSE higher tier maths practice exam free resources. Question 4 describes two investments of £4000 over 3 years, one with compound interest at 1.8% per year and one with simple interest at the same rate. Students must calculate how much more interest the compound interest investment earns.

Definition:

  • Compound Interest: Interest calculated on the initial principal and the accumulated interest from previous periods.
  • Simple Interest: Interest calculated only on the principal amount.

Example: For compound interest: £4000 × (1.018)³ = £4219.91 For simple interest: £4000 + (£4000 × 0.018 × 3) = £4216.00 Difference: £4219.91 - £4216.00 = £3.91

GCSE Mock Exam (Jan 2022) Maths 2 (Higher) - Calc Materials Use a blue/black pen. You must have a ruler, protractor, pencil and eraser. Trac

View

Page 7: Rounding and Trigonometry

This page covers two distinct topics: rounding and trigonometry, both common in GCSE Maths past papers with answers. Question 5 asks students to complete a statement about the range of possible values for a height given as 184 meters to the nearest meter. Question 6 involves using trigonometry to calculate the perimeter of a rectangle given one side length and an angle.

Vocabulary: Significant figures - The digits in a number that carry meaning contributing to its precision.

Example: For Question 6, students need to use tan(35°) = opposite/adjacent to find the unknown side length, then add all sides to find the perimeter.

GCSE Mock Exam (Jan 2022) Maths 2 (Higher) - Calc Materials Use a blue/black pen. You must have a ruler, protractor, pencil and eraser. Trac

View

Page 8: Mean Calculations and Ratio

This page focuses on calculating means and working with ratios, essential skills for the GCSE higher tier maths practice exam. Question 7 requires students to calculate the overall mean age of an orchestra given the mean ages and numbers of men and women separately. Question 8 asks students to prove a relationship between ratios.

Definition: Mean - The average of a set of numbers, calculated by summing all values and dividing by the count of values.

Highlight: Questions involving means and ratios are common in GCSE Maths past papers Foundation and Higher tiers, often requiring multi-step solutions.

GCSE Mock Exam (Jan 2022) Maths 2 (Higher) - Calc Materials Use a blue/black pen. You must have a ruler, protractor, pencil and eraser. Trac

View

Page 9: Probability

This page presents a probability problem, a topic frequently tested in GCSE Maths past papers PDF with answers. Question 9 describes a bag of colored counters and provides some probability information. Students must use this information to calculate the number of red counters in the bag.

Vocabulary: Probability - The likelihood of an event occurring, expressed as a number between 0 and 1.

Example: To solve this, students need to:

  1. Find the probability of yellow counters
  2. Use this to find the probability of red counters
  3. Calculate the number of red counters out of 500 total
GCSE Mock Exam (Jan 2022) Maths 2 (Higher) - Calc Materials Use a blue/black pen. You must have a ruler, protractor, pencil and eraser. Trac

View

Page 10: Percentage Increase and Algebra

This page covers percentage increase calculations and algebraic expansion, both key topics in GCSE higher tier maths practice exam free resources. Question 10 involves working backwards from a house value after two years of 1.5% annual increases to find the original value. Question 11 asks students to expand and simplify a product of three linear expressions.

Highlight: These types of multi-step problems are common in GCSE Maths past papers with answers, testing students' ability to apply multiple concepts.

GCSE Mock Exam (Jan 2022) Maths 2 (Higher) - Calc Materials Use a blue/black pen. You must have a ruler, protractor, pencil and eraser. Trac

View

Page 11: Solving Equations

This page focuses on solving a complex equation, a skill frequently tested in GCSE Maths past papers PDF with answers AQA and other exam boards. Question 12 requires students to solve the equation (8-3x)/4 = 8-2x. This involves algebraic manipulation and fraction operations.

Example: To solve this equation, students should:

  1. Multiply both sides by 4 to eliminate fractions
  2. Expand brackets
  3. Collect like terms
  4. Isolate the variable

Highlight: Equation solving is a fundamental skill assessed in all GCSE Maths past papers Foundation and Higher tiers.

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Lena, iOS user

I love this app ❤️ I actually use it every time I study.

Subjects

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Maths

/

Probability

/

Sets & venn diagrams

GCSE Maths Higher Tier Practice PDF (Free + Answered)

user profile picture

yuma

@blueyberrymuffin

·

181 Followers

Follow

I'll help create SEO-optimized summaries for this GCSE Maths exam transcript. Let me process it page by page and provide the summaries as requested.

This comprehensive GCSE higher tier maths practice exam PDF from January 2022 covers essential mathematical concepts and problem-solving techniques. The exam is designed for calculator use and spans 80 marks over 90 minutes.

Key features:

  • Full calculator paper with detailed solutions
  • Covers advanced mathematical concepts
  • Includes geometry, algebra, and probability questions
  • Comprehensive marking scheme
  • Perfect for GCSE Maths past papers practice

26/10/2023

2498

 

10/11

 

Maths

69

GCSE Mock Exam (Jan 2022) Maths 2 (Higher) - Calc Materials Use a blue/black pen. You must have a ruler, protractor, pencil and eraser. Trac

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Page 2: Algebra and Equations

This page focuses on algebraic manipulation and equation solving, key skills for the GCSE higher tier maths practice exam. Question 1 asks students to simplify algebraic expressions and solve an inequality. Part (a) requires simplification of 14y/3, part (b) involves simplifying p^t × p^(-t), and part (c) asks to solve the inequality 7y > 9 × 3.

Example: For part (b), students need to apply the laws of exponents to simplify p^t × p^(-t) to 1.

Vocabulary: Simplify - To reduce an expression to its simplest form by combining like terms or cancelling out factors.

GCSE Mock Exam (Jan 2022) Maths 2 (Higher) - Calc Materials Use a blue/black pen. You must have a ruler, protractor, pencil and eraser. Trac

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Access to all documents

Improve your grades

Join milions of students

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Page 3: Speed, Distance, and Time

This page presents a problem involving speed, distance, and time calculations, a common topic in GCSE Maths past papers with answers. Question 2 describes Andrea's journey, which consists of driving 110 km at 40 km/h and then running 14 km at 8 km/h. Students must calculate the total time taken for both parts of the journey, giving the answer in hours and minutes.

Example: To solve this, students should:

  1. Calculate time for driving: 110 km ÷ 40 km/h = 2.75 hours
  2. Calculate time for running: 14 km ÷ 8 km/h = 1.75 hours
  3. Add the times: 2.75 + 1.75 = 4.5 hours
  4. Convert to hours and minutes: 4 hours 30 minutes
GCSE Mock Exam (Jan 2022) Maths 2 (Higher) - Calc Materials Use a blue/black pen. You must have a ruler, protractor, pencil and eraser. Trac

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Page 4: Transformations

This page focuses on geometric transformations, a key topic in the GCSE higher tier maths practice exam 2020 and other years. Question 3(a) requires students to translate shape P by the vector (-9, 5). The question provides a coordinate grid with shape P already drawn.

Definition: Translation - A transformation that moves every point of a shape the same distance in the same direction.

Highlight: Understanding transformations is crucial for success in the geometry sections of GCSE Maths past papers Foundation and Higher tiers.

GCSE Mock Exam (Jan 2022) Maths 2 (Higher) - Calc Materials Use a blue/black pen. You must have a ruler, protractor, pencil and eraser. Trac

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By signing up you accept Terms of Service and Privacy Policy

Page 5: Transformations (continued)

This page continues with transformations, asking students to describe a single transformation that maps shape A onto shape B. The correct answer is a reflection in the line y = x. This type of question is common in GCSE Maths past papers PDF with answers AQA and other exam boards.

Vocabulary: Reflection - A transformation that flips a shape over a line, creating a mirror image.

Highlight: Being able to identify and describe transformations is a key skill tested in GCSE Maths past papers Foundation and Higher tiers.

GCSE Mock Exam (Jan 2022) Maths 2 (Higher) - Calc Materials Use a blue/black pen. You must have a ruler, protractor, pencil and eraser. Trac

Sign up to see the content. It's free!

Access to all documents

Improve your grades

Join milions of students

By signing up you accept Terms of Service and Privacy Policy

Page 6: Compound and Simple Interest

This page presents a problem comparing compound and simple interest, a topic frequently appearing in GCSE higher tier maths practice exam free resources. Question 4 describes two investments of £4000 over 3 years, one with compound interest at 1.8% per year and one with simple interest at the same rate. Students must calculate how much more interest the compound interest investment earns.

Definition:

  • Compound Interest: Interest calculated on the initial principal and the accumulated interest from previous periods.
  • Simple Interest: Interest calculated only on the principal amount.

Example: For compound interest: £4000 × (1.018)³ = £4219.91 For simple interest: £4000 + (£4000 × 0.018 × 3) = £4216.00 Difference: £4219.91 - £4216.00 = £3.91

GCSE Mock Exam (Jan 2022) Maths 2 (Higher) - Calc Materials Use a blue/black pen. You must have a ruler, protractor, pencil and eraser. Trac

Sign up to see the content. It's free!

Access to all documents

Improve your grades

Join milions of students

By signing up you accept Terms of Service and Privacy Policy

Page 7: Rounding and Trigonometry

This page covers two distinct topics: rounding and trigonometry, both common in GCSE Maths past papers with answers. Question 5 asks students to complete a statement about the range of possible values for a height given as 184 meters to the nearest meter. Question 6 involves using trigonometry to calculate the perimeter of a rectangle given one side length and an angle.

Vocabulary: Significant figures - The digits in a number that carry meaning contributing to its precision.

Example: For Question 6, students need to use tan(35°) = opposite/adjacent to find the unknown side length, then add all sides to find the perimeter.

GCSE Mock Exam (Jan 2022) Maths 2 (Higher) - Calc Materials Use a blue/black pen. You must have a ruler, protractor, pencil and eraser. Trac

Sign up to see the content. It's free!

Access to all documents

Improve your grades

Join milions of students

By signing up you accept Terms of Service and Privacy Policy

Page 8: Mean Calculations and Ratio

This page focuses on calculating means and working with ratios, essential skills for the GCSE higher tier maths practice exam. Question 7 requires students to calculate the overall mean age of an orchestra given the mean ages and numbers of men and women separately. Question 8 asks students to prove a relationship between ratios.

Definition: Mean - The average of a set of numbers, calculated by summing all values and dividing by the count of values.

Highlight: Questions involving means and ratios are common in GCSE Maths past papers Foundation and Higher tiers, often requiring multi-step solutions.

GCSE Mock Exam (Jan 2022) Maths 2 (Higher) - Calc Materials Use a blue/black pen. You must have a ruler, protractor, pencil and eraser. Trac

Sign up to see the content. It's free!

Access to all documents

Improve your grades

Join milions of students

By signing up you accept Terms of Service and Privacy Policy

Page 9: Probability

This page presents a probability problem, a topic frequently tested in GCSE Maths past papers PDF with answers. Question 9 describes a bag of colored counters and provides some probability information. Students must use this information to calculate the number of red counters in the bag.

Vocabulary: Probability - The likelihood of an event occurring, expressed as a number between 0 and 1.

Example: To solve this, students need to:

  1. Find the probability of yellow counters
  2. Use this to find the probability of red counters
  3. Calculate the number of red counters out of 500 total
GCSE Mock Exam (Jan 2022) Maths 2 (Higher) - Calc Materials Use a blue/black pen. You must have a ruler, protractor, pencil and eraser. Trac

Sign up to see the content. It's free!

Access to all documents

Improve your grades

Join milions of students

By signing up you accept Terms of Service and Privacy Policy

Page 10: Percentage Increase and Algebra

This page covers percentage increase calculations and algebraic expansion, both key topics in GCSE higher tier maths practice exam free resources. Question 10 involves working backwards from a house value after two years of 1.5% annual increases to find the original value. Question 11 asks students to expand and simplify a product of three linear expressions.

Highlight: These types of multi-step problems are common in GCSE Maths past papers with answers, testing students' ability to apply multiple concepts.

GCSE Mock Exam (Jan 2022) Maths 2 (Higher) - Calc Materials Use a blue/black pen. You must have a ruler, protractor, pencil and eraser. Trac

Sign up to see the content. It's free!

Access to all documents

Improve your grades

Join milions of students

By signing up you accept Terms of Service and Privacy Policy

Page 11: Solving Equations

This page focuses on solving a complex equation, a skill frequently tested in GCSE Maths past papers PDF with answers AQA and other exam boards. Question 12 requires students to solve the equation (8-3x)/4 = 8-2x. This involves algebraic manipulation and fraction operations.

Example: To solve this equation, students should:

  1. Multiply both sides by 4 to eliminate fractions
  2. Expand brackets
  3. Collect like terms
  4. Isolate the variable

Highlight: Equation solving is a fundamental skill assessed in all GCSE Maths past papers Foundation and Higher tiers.

Similar content

Maths - Venn Diagrams

Venn Diagrams notation

22

709

0

Know Venn Diagrams thumbnail

Can't find what you're looking for? Explore other subjects.

Knowunity is the #1 education app in five European countries

Knowunity has been named a featured story on Apple and has regularly topped the app store charts in the education category in Germany, Italy, Poland, Switzerland, and the United Kingdom. Join Knowunity today and help millions of students around the world.

Ranked #1 Education App

Download in

Google Play

Download in

App Store

Knowunity is the #1 education app in five European countries

4.9+

Average app rating

13 M

Pupils love Knowunity

#1

In education app charts in 12 countries

950 K+

Students have uploaded notes

Still not convinced? See what other students are saying...

iOS User

I love this app so much, I also use it daily. I recommend Knowunity to everyone!!! I went from a D to an A with it :D

Philip, iOS User

The app is very simple and well designed. So far I have always found everything I was looking for :D

Lena, iOS user

I love this app ❤️ I actually use it every time I study.