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Corbettmaths GCSE 9-1 Practice Papers - Set A, B, C

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Brand: Knowunity

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Corbettmaths GCSE 9-1 Practice Papers - Set A, B, C

ayesha tahir

@ayeshatahir_mlxz

45 Followers

The Corbettmaths GCSE 9-1 Practice Paper Set A Paper 1 Non-Calculator is a comprehensive exam preparation resource for students. This 80-mark paper covers a wide range of mathematical topics and problem-solving skills.

Key features:
• 1 hour 30 minutes duration
• 22 questions of varying difficulty
• Emphasis on showing workings
• Requires standard mathematical equipment

The paper tests students' abilities in areas such as:
• Data interpretation and analysis
• Algebraic manipulation
• Geometry and trigonometry
• Number theory and calculations
• Proportional reasoning
• Graph analysis

This practice paper provides an excellent opportunity for students to familiarize themselves with the exam format and assess their readiness for the actual GCSE 9-1 Foundation Practice Paper.

20/10/2022

1792

Questions 7-8: Mean Calculation and VAT

This section covers statistical calculations and percentage problems:

Question 7: Calculating overall mean • Students must find the mean mark for a class, given separate means for boys and girls. • This involves weighted average calculation.

Example: If 15 boys have a mean of 70 and 10 girls have a mean of 82, the overall mean is calculated as: (15 × 70 + 10 × 82) ÷ 25 = 74.8

Question 8: VAT calculation • The task is to determine the original price of an item before VAT is added. • This tests understanding of percentage increase and decrease.

Vocabulary: VAT (Value Added Tax) - A consumption tax placed on a product whenever value is added at each stage of the supply chain.

These questions assess students' ability to work with averages and percentages in practical contexts, skills that are crucial for many real-world applications of mathematics.

Name: SowTION S
GCSE 9-1
Practice Paper
Set A
Paper 1- Non Calculator
Equipment
1. A black ink ball-point pen.
2. A pencil.
3. An eraser.
4.

Question 1: Umbrella Sales and Rainfall Analysis

This question presents a scatter graph showing the relationship between weekly rainfall and umbrella sales. Students are asked to interpret the data and draw conclusions.

Vocabulary: Scatter graph - A type of graph that shows the relationship between two variables.

Key points: • Students must describe the relationship between rainfall and umbrella sales. • The maximum number of umbrellas sold in one week needs to be identified. • An estimate of umbrella sales for a specific rainfall amount is required.

Highlight: The question tests students' ability to interpret data, identify trends, and make predictions based on graphical information.

This question demonstrates the practical application of statistical analysis in a real-world scenario, reinforcing the relevance of mathematical skills in everyday situations.

View

Questions 9-10: Fractions and Algebraic Expansion

This page covers operations with fractions and algebraic manipulation:

Question 9: Fraction simplification and ordering • Part (a) requires simplifying the fraction 17/5. • Part (b) involves arranging a set of numbers, including fractions and surds, in order.

Vocabulary: Surd - An expression involving square roots or cube roots that cannot be simplified to a whole or rational number.

Question 10: Algebraic expansion • Students must expand and simplify the expression (1 - 2x)(x + 3)(x - 1). • This tests skills in multiplying algebraic terms and collecting like terms.

Example: Expanding (1 - 2x)(x + 3) first gives x + 3 - 2x² - 6x, which then needs to be multiplied by (x - 1).

These questions assess students' ability to work with different number representations and perform complex algebraic manipulations, skills that are fundamental to higher-level mathematics.

View

Questions 19-22: Advanced Mathematical Problems

The final section of the paper likely contains the most challenging questions:

Question 19: May involve advanced algebra, calculus concepts, or complex problem-solving.

Question 20: Could focus on sophisticated geometric proofs or advanced trigonometry.

Question 21: Might require high-level statistical analysis or probability calculations.

Question 22: Typically a multi-part question combining several mathematical concepts.

Highlight: These questions often test students' ability to synthesize multiple mathematical skills and apply them to complex, real-world scenarios.

These final questions are designed to challenge the most capable students and differentiate between higher grade boundaries. They often require creative thinking and the ability to apply mathematical knowledge in novel ways.

View

Question 13: Inverse Proportion

This question deals with inverse proportion in the context of magnetic force:

• The force (F) exerted by a magnet is inversely proportional to the square of the distance (d). • Given that F = 50 N when d = 2 cm, students must:

Part (a): Express F in terms of d • This involves forming an equation using the inverse square relationship.

Definition: Inverse proportion occurs when one quantity increases as another decreases in proportion so that their product is constant.

Part (b): Calculate the force when d = 10 cm • Students must use their equation from part (a) to find F for a new value of d.

Example: If F ∝ 1/d², then F = k/d², where k is a constant. In this case, k = 50 × 2² = 200.

This question assesses understanding of inverse proportion and its application in a physical context, demonstrating the relevance of mathematical concepts to real-world phenomena.

View

Questions 5-6: Geometry and Linear Equations

This page focuses on geometric calculations and linear equations:

Question 5: Right-angled triangle area • Students must calculate the area of a right-angled triangle given two side lengths. • This involves using the Pythagorean theorem to find the missing side length.

Highlight: The area of a triangle is calculated using the formula: Area = ½ × base × height.

Question 6: Parallel lines and equations • Students are asked to determine the equation of a line parallel to a given line. • The question tests understanding of gradient and y-intercept in linear equations.

Vocabulary: Gradient - The steepness of a line, calculated as the change in y divided by the change in x.

These questions assess students' ability to apply geometric formulas and understand the properties of parallel lines in the context of linear equations.

View

GCSE 9-1 Practice Paper Set A Paper 1 - Non Calculator

This page provides an overview of the Corbettmaths Practice Paper and essential information for students preparing to take the exam. The document outlines the required equipment, guidance for answering questions, and key information about the paper's structure and scoring.

Highlight: The paper has a maximum score of 80 marks and a duration of 1 hour 30 minutes.

Required equipment includes:

Black ink ball-point pen
Pencil
Eraser
Ruler
Pair of compasses
Protractor

Example: Students are advised to "Always show your workings" when answering questions.

The page also includes a table showing the mark allocation for each of the 22 questions in the paper, helping students understand the relative importance and complexity of different sections.

View

Question 12: Graph Analysis

This question involves interpreting a given graph of the function y = f(x):

Part (a): Identifying turning points • Students must estimate the coordinates of the turning point of the graph.

Vocabulary: Turning point - A point on a graph where the function changes from increasing to decreasing (or vice versa).

Part (b): Reading values from the graph • The task is to use the graph to find the value of f(1.2).

Highlight: This question tests students' ability to read and interpret graphical information accurately.

These skills are essential in many areas of mathematics and science, where data is often presented in graphical form. The ability to extract specific information from graphs is a valuable skill in both academic and real-world contexts.

View

Question 14: Ratio and Algebraic Problem Solving

This complex question involves using ratios and algebraic reasoning to determine the prices of a mobile phone and a television:

• The original prices are denoted as x pounds for the mobile phone and y pounds for the television. • Two scenarios are presented with price changes and resulting ratios.

Key steps:

Form equations based on the given ratios.
Solve the system of equations to find x and y.

Highlight: This question tests students' ability to translate word problems into algebraic equations and solve simultaneous equations.

Example: For the first scenario, the equation would be (x + 40) : (y + 40) = 15 : 22.

This problem assesses advanced problem-solving skills, combining ratio analysis with algebraic manipulation. It demonstrates the application of mathematics in real-world pricing scenarios.

View

Question 15: Volume and Density Calculations

This question focuses on calculating the volume of a sphere and using it to determine density:

Part (a): Estimating sphere volume • Given a radius of 5.97 cm, students must estimate the volume using π. • The question suggests rounding the radius to 6 cm for easier calculation.

Formula: Volume of a sphere = 4/3 × π × r³

Part (b): Density calculation • Using the estimated volume and a given mass of 1002g, students must calculate the density of the wood.

Definition: Density is the mass per unit volume of a substance, typically measured in g/cm³.

Highlight: This question tests students' ability to apply geometric formulas and perform multi-step calculations involving volume and density.

This problem demonstrates the practical application of mathematical concepts in physics and material science, showing how geometry and algebra are used in real-world measurements and calculations.

View

Question 11: Exponents and Roots

This question focuses on operations involving exponents and roots:

Part (a): Percentage calculation • Students must find the value of 100%/1.

Part (b): Negative exponents • The task is to calculate 4^(-3/2).

Definition: A negative exponent indicates the reciprocal of a number raised to the positive exponent. For example, 4^(-3/2) = 1 / (4^(3/2)).

Part (c): Simplification of roots • Students need to simplify (27^(1/3))^2.

Highlight: This question tests understanding of the laws of exponents, particularly how exponents behave when raised to powers.

These problems assess students' ability to work with various forms of numerical expressions, including percentages, fractions, and exponents. Such skills are crucial for more advanced mathematical concepts and real-world applications.

View

Questions 16-18: Various Mathematical Concepts

This section covers a range of mathematical topics:

Question 16: Likely involves algebraic or geometric problem-solving.

Question 17: May focus on statistical analysis, probability, or data interpretation.

Question 18: Could be related to trigonometry, further algebra, or number theory.

Highlight: These questions are designed to test a broad range of mathematical skills and knowledge.

While specific details are not provided, these questions typically assess students' ability to apply various mathematical concepts and techniques to solve complex problems. They often require a combination of skills learned throughout the GCSE mathematics curriculum.

View

Questions 2-4: Prime Factors, Division, and Algebraic Expressions

This section covers a range of mathematical concepts:

Question 2: Prime factorization • Students must express 60 as a product of its prime factors.

Definition: Prime factors are the prime numbers that, when multiplied together, give the original number.

Question 3: Division with decimals • The task is to calculate 412.8 ÷ 2.4.

Question 4: Algebraic expressions • Students need to form an expression for the area of a rectangle with given dimensions in terms of x.

Example: For a rectangle with length (x + 9) cm and width (x - 1) cm, the area expression would be x² + 8x - 9 cm².

These questions assess students' understanding of fundamental mathematical operations and their ability to apply algebraic concepts to geometric problems.

View

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.

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 11 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.

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.

Download in

Google Play

Download in

App Store

4.9+

Average app rating

13 M

Pupils love Knowunity

#1

In education app charts in 11 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.

Subjects

Maths

Geometry & measures

Angles

Corbettmaths GCSE 9-1 Practice Papers - Set A, B, C

ayesha tahir

@ayeshatahir_mlxz

45 Followers

Key features:
• 1 hour 30 minutes duration
• 22 questions of varying difficulty
• Emphasis on showing workings
• Requires standard mathematical equipment

This practice paper provides an excellent opportunity for students to familiarize themselves with the exam format and assess their readiness for the actual GCSE 9-1 Foundation Practice Paper.

20/10/2022

1792

Questions 7-8: Mean Calculation and VAT

This section covers statistical calculations and percentage problems:

Question 7: Calculating overall mean • Students must find the mean mark for a class, given separate means for boys and girls. • This involves weighted average calculation.

Example: If 15 boys have a mean of 70 and 10 girls have a mean of 82, the overall mean is calculated as: (15 × 70 + 10 × 82) ÷ 25 = 74.8

Question 8: VAT calculation • The task is to determine the original price of an item before VAT is added. • This tests understanding of percentage increase and decrease.

Vocabulary: VAT (Value Added Tax) - A consumption tax placed on a product whenever value is added at each stage of the supply chain.

These questions assess students' ability to work with averages and percentages in practical contexts, skills that are crucial for many real-world applications of mathematics.

Sign up to get unlimited access to thousands of study materials. It's free!

Access to all documents

Join milions of students

Improve your grades

By signing up you accept Terms of Service and Privacy Policy

Question 1: Umbrella Sales and Rainfall Analysis

This question presents a scatter graph showing the relationship between weekly rainfall and umbrella sales. Students are asked to interpret the data and draw conclusions.

Vocabulary: Scatter graph - A type of graph that shows the relationship between two variables.

Highlight: The question tests students' ability to interpret data, identify trends, and make predictions based on graphical information.

This question demonstrates the practical application of statistical analysis in a real-world scenario, reinforcing the relevance of mathematical skills in everyday situations.

Sign up to get unlimited access to thousands of study materials. It's free!

Access to all documents

Join milions of students

Improve your grades

By signing up you accept Terms of Service and Privacy Policy

Questions 9-10: Fractions and Algebraic Expansion

This page covers operations with fractions and algebraic manipulation:

Question 9: Fraction simplification and ordering • Part (a) requires simplifying the fraction 17/5. • Part (b) involves arranging a set of numbers, including fractions and surds, in order.

Vocabulary: Surd - An expression involving square roots or cube roots that cannot be simplified to a whole or rational number.

Question 10: Algebraic expansion • Students must expand and simplify the expression (1 - 2x)(x + 3)(x - 1). • This tests skills in multiplying algebraic terms and collecting like terms.

Example: Expanding (1 - 2x)(x + 3) first gives x + 3 - 2x² - 6x, which then needs to be multiplied by (x - 1).

These questions assess students' ability to work with different number representations and perform complex algebraic manipulations, skills that are fundamental to higher-level mathematics.

Sign up to get unlimited access to thousands of study materials. It's free!

Access to all documents

Join milions of students

Improve your grades

By signing up you accept Terms of Service and Privacy Policy

Questions 19-22: Advanced Mathematical Problems

The final section of the paper likely contains the most challenging questions:

Question 19: May involve advanced algebra, calculus concepts, or complex problem-solving.

Question 20: Could focus on sophisticated geometric proofs or advanced trigonometry.

Question 21: Might require high-level statistical analysis or probability calculations.

Question 22: Typically a multi-part question combining several mathematical concepts.

Highlight: These questions often test students' ability to synthesize multiple mathematical skills and apply them to complex, real-world scenarios.

Sign up to get unlimited access to thousands of study materials. It's free!

Access to all documents

Join milions of students

Improve your grades

By signing up you accept Terms of Service and Privacy Policy

Question 13: Inverse Proportion

This question deals with inverse proportion in the context of magnetic force:

• The force (F) exerted by a magnet is inversely proportional to the square of the distance (d). • Given that F = 50 N when d = 2 cm, students must:

Part (a): Express F in terms of d • This involves forming an equation using the inverse square relationship.

Definition: Inverse proportion occurs when one quantity increases as another decreases in proportion so that their product is constant.

Part (b): Calculate the force when d = 10 cm • Students must use their equation from part (a) to find F for a new value of d.

Example: If F ∝ 1/d², then F = k/d², where k is a constant. In this case, k = 50 × 2² = 200.

This question assesses understanding of inverse proportion and its application in a physical context, demonstrating the relevance of mathematical concepts to real-world phenomena.

Sign up to get unlimited access to thousands of study materials. It's free!

Access to all documents

Join milions of students

Improve your grades

By signing up you accept Terms of Service and Privacy Policy

Questions 5-6: Geometry and Linear Equations

This page focuses on geometric calculations and linear equations:

Highlight: The area of a triangle is calculated using the formula: Area = ½ × base × height.

Vocabulary: Gradient - The steepness of a line, calculated as the change in y divided by the change in x.

These questions assess students' ability to apply geometric formulas and understand the properties of parallel lines in the context of linear equations.

Sign up to get unlimited access to thousands of study materials. It's free!

Access to all documents

Join milions of students

Improve your grades

By signing up you accept Terms of Service and Privacy Policy

GCSE 9-1 Practice Paper Set A Paper 1 - Non Calculator

Highlight: The paper has a maximum score of 80 marks and a duration of 1 hour 30 minutes.

Required equipment includes:

Black ink ball-point pen
Pencil
Eraser
Ruler
Pair of compasses
Protractor

Example: Students are advised to "Always show your workings" when answering questions.

The page also includes a table showing the mark allocation for each of the 22 questions in the paper, helping students understand the relative importance and complexity of different sections.

Sign up to get unlimited access to thousands of study materials. It's free!

Access to all documents

Join milions of students

Improve your grades

By signing up you accept Terms of Service and Privacy Policy

Question 12: Graph Analysis

This question involves interpreting a given graph of the function y = f(x):

Part (a): Identifying turning points • Students must estimate the coordinates of the turning point of the graph.

Vocabulary: Turning point - A point on a graph where the function changes from increasing to decreasing (or vice versa).

Part (b): Reading values from the graph • The task is to use the graph to find the value of f(1.2).

Highlight: This question tests students' ability to read and interpret graphical information accurately.

Sign up to get unlimited access to thousands of study materials. It's free!

Access to all documents

Join milions of students

Improve your grades

By signing up you accept Terms of Service and Privacy Policy

Question 14: Ratio and Algebraic Problem Solving

This complex question involves using ratios and algebraic reasoning to determine the prices of a mobile phone and a television:

• The original prices are denoted as x pounds for the mobile phone and y pounds for the television. • Two scenarios are presented with price changes and resulting ratios.

Key steps:

Form equations based on the given ratios.
Solve the system of equations to find x and y.

Highlight: This question tests students' ability to translate word problems into algebraic equations and solve simultaneous equations.

Example: For the first scenario, the equation would be (x + 40) : (y + 40) = 15 : 22.

This problem assesses advanced problem-solving skills, combining ratio analysis with algebraic manipulation. It demonstrates the application of mathematics in real-world pricing scenarios.

Sign up to get unlimited access to thousands of study materials. It's free!

Access to all documents

Join milions of students

Improve your grades

By signing up you accept Terms of Service and Privacy Policy

Question 15: Volume and Density Calculations

This question focuses on calculating the volume of a sphere and using it to determine density:

Part (a): Estimating sphere volume • Given a radius of 5.97 cm, students must estimate the volume using π. • The question suggests rounding the radius to 6 cm for easier calculation.

Formula: Volume of a sphere = 4/3 × π × r³

Part (b): Density calculation • Using the estimated volume and a given mass of 1002g, students must calculate the density of the wood.

Definition: Density is the mass per unit volume of a substance, typically measured in g/cm³.

Highlight: This question tests students' ability to apply geometric formulas and perform multi-step calculations involving volume and density.

This problem demonstrates the practical application of mathematical concepts in physics and material science, showing how geometry and algebra are used in real-world measurements and calculations.

Sign up to get unlimited access to thousands of study materials. It's free!

Access to all documents

Join milions of students

Improve your grades

By signing up you accept Terms of Service and Privacy Policy

Question 11: Exponents and Roots

This question focuses on operations involving exponents and roots:

Part (a): Percentage calculation • Students must find the value of 100%/1.

Part (b): Negative exponents • The task is to calculate 4^(-3/2).

Definition: A negative exponent indicates the reciprocal of a number raised to the positive exponent. For example, 4^(-3/2) = 1 / (4^(3/2)).

Part (c): Simplification of roots • Students need to simplify (27^(1/3))^2.

Highlight: This question tests understanding of the laws of exponents, particularly how exponents behave when raised to powers.

Sign up to get unlimited access to thousands of study materials. It's free!

Access to all documents

Join milions of students

Improve your grades

By signing up you accept Terms of Service and Privacy Policy

Questions 16-18: Various Mathematical Concepts

This section covers a range of mathematical topics:

Question 16: Likely involves algebraic or geometric problem-solving.

Question 17: May focus on statistical analysis, probability, or data interpretation.

Question 18: Could be related to trigonometry, further algebra, or number theory.

Highlight: These questions are designed to test a broad range of mathematical skills and knowledge.

Sign up to get unlimited access to thousands of study materials. It's free!

Access to all documents

Join milions of students

Improve your grades

By signing up you accept Terms of Service and Privacy Policy

Questions 2-4: Prime Factors, Division, and Algebraic Expressions

This section covers a range of mathematical concepts:

Question 2: Prime factorization • Students must express 60 as a product of its prime factors.

Definition: Prime factors are the prime numbers that, when multiplied together, give the original number.

Question 3: Division with decimals • The task is to calculate 412.8 ÷ 2.4.

Question 4: Algebraic expressions • Students need to form an expression for the area of a rectangle with given dimensions in terms of x.

Example: For a rectangle with length (x + 9) cm and width (x - 1) cm, the area expression would be x² + 8x - 9 cm².

These questions assess students' understanding of fundamental mathematical operations and their ability to apply algebraic concepts to geometric problems.