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Free Non-Calculator GCSE Maths Practice Papers & Answers

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Free Non-Calculator GCSE Maths Practice Papers & Answers

yuma

@blueyberrymuffin

183 Followers

This document covers key topics for GCSE Maths non Calculator questions higher and Foundation levels. It includes practice questions and solutions for various mathematical concepts, helping students prepare for their exams.

The paper is a Pearson Edexcel Level 1/Level 2 GCSE (9-1) Mathematics Paper 1 (Non-Calculator)
It covers a range of topics including ratios, geometry, algebra, and probability
Solutions are provided for each question, demonstrating step-by-step problem-solving techniques
The paper is designed to test students' mathematical skills without the use of a calculator

25/10/2022

3608

.
Pearson Edexcel
Level 1/Level 2 GCSE (9-1)
Mathematics
Paper 1 (Non-Calculator)
Instructions
.
Time: 1 hour 30 minutes
Use black ink or ba

View

Question 1: Ratio Problem

This page presents a ratio problem, which is a common type of Non Calculator Maths questions Year 9 and above. The question asks students to divide £280 between Ali and Beth in the ratio 2:5.

The solution demonstrates the step-by-step process:

Add the ratio parts: 2 + 5 = 7
Divide the total amount by the sum of ratio parts: £280 ÷ 7 = £40
Multiply each ratio part by the value of one part:
- Ali's share: 2 × £40 = £80
- Beth's share: 5 × £40 = £200

This question tests students' understanding of ratios and their ability to perform calculations without a calculator.

Example: In real-life scenarios, ratios are often used for sharing profits, dividing resources, or mixing ingredients in recipes.

View

Question 2: Circle Geometry

This page features a geometry question involving a circle, which is a typical topic in GCSE Maths Non Calculator revision Foundation and Higher tiers. The question provides a diagram of a circle with points A, B, and C on its circumference, and a tangent line at point A.

Students are asked to calculate the size of angle CAO, given that:

Angle BAE = 56°
Angle CBO = 35°

The solution involves several steps using circle theorems:

Angle BCA = 56° (angle between tangent and chord)
Angle BOA = 56° × 2 = 112° (angle at center is twice angle at circumference)
360° - 112° = 248° (remaining angle in the circle)
360° - 56° - 35° - 248° = 21° (final calculation for angle CAO)

Vocabulary: Tangent - a line that touches a curve at a single point without crossing it.

Highlight: Understanding circle theorems is crucial for solving geometry problems without a calculator.

View

Question 3: Volume and Rate Problem

This page presents a complex problem involving volume calculations and rates, which is characteristic of GCSE Maths non calculator topics Foundation and Higher levels. The question describes a swimming pool and asks whether it can be filled in 10 hours at a given rate.

Key information:

Swimming pool dimensions: 10m × 10m × 1m
Fill rate: 5 litres per second
1 m³ = 1000 litres

The solution involves multiple steps:

Calculate the volume of the pool: 10m × 10m × 1m = 100m³
Convert volume to litres: 100m³ = 100,000 litres
Calculate total seconds in 10 hours: 10 × 60 × 60 = 36,000 seconds
Calculate total litres filled in 10 hours: 36,000 × 5 = 180,000 litres

The conclusion is that the pool will not be completely filled in 10 hours, as it requires 200,000 litres but only 180,000 litres will be filled.

Example: This type of problem combines real-world applications with mathematical concepts, preparing students for practical problem-solving.

View

Question 4: Work Rate Problem

This page features a work rate problem, which is a common type of Non Calculator maths questions and answers Foundation and Higher tiers. The question states that 12 men can complete a job in 5 days and asks how long it would take 3 men to complete the same job.

The solution uses the concept of man-days:

Calculate total man-days: 12 men × 5 days = 60 man-days
Divide total man-days by new number of men: 60 ÷ 3 = 20 days

The question also asks students to state an assumption made in the calculation and how the answer would be affected if the assumption is not correct.

Highlight: Assumptions in mathematical modeling are crucial for problem-solving but can affect the accuracy of results if not valid.

Example: A common assumption in work rate problems is that all workers work at the same rate, which may not always be true in real-life scenarios.

View

Question 5: Algebraic Fraction and Expansion

This page presents an algebraic problem involving fractions and expansion, which is typical of GCSE Maths Non Calculator questions higher tier. The question asks students to work out an expression involving algebraic fractions.

The solution demonstrates step-by-step algebraic manipulation:

Find a common denominator
Add fractions
Simplify the resulting expression

Vocabulary: Algebraic fraction - a fraction where the numerator, denominator, or both contain algebraic expressions.

Highlight: Mastering algebraic fractions is essential for higher-level mathematics and is a key skill tested in non-calculator exams.

View

Question 6: Probability Tree Diagram

This page features a probability question using tree diagrams, which is a common topic in Non Calculator Maths Topics. The question involves a red 6-sided dice and a blue 8-sided dice, asking students to complete a probability tree diagram and calculate a specific probability.

Key points:

The red dice can land on numbers 1 to 6
The blue dice can land on numbers 1 to 8
Students must calculate the probability that neither dice will land on a 6

The solution involves:

Completing the probability tree diagram with correct fractions
Calculating the probability of not landing on 6 for each dice
Multiplying these probabilities to find the combined probability

Definition: A probability tree diagram is a visual representation of all possible outcomes of an event and their probabilities.

Example: Probability tree diagrams are useful in various real-world scenarios, such as analyzing game strategies or predicting weather patterns.

View

Question 7: Percentage Increase Problem

This page presents a percentage increase problem, which is a key topic in GCSE Maths past papers PDF with answers. The question describes three rectangles (A, B, and C) where each subsequent rectangle has an area 10% greater than the previous one.

Students are asked to calculate by what percentage the area of rectangle C is greater than the area of rectangle A.

The solution involves:

Expressing the area of B in terms of A: B = A × 1.1
Expressing the area of C in terms of B: C = B × 1.1
Combining these to express C in terms of A: C = A × 1.1 × 1.1 = A × 1.21
Calculating the percentage increase: (1.21 - 1) × 100 = 21%

Highlight: Understanding compound percentage increases is crucial for many real-world applications, including financial calculations and population growth models.

View

Question 8: Mean Value Problem

This page features a problem involving mean values, which is a common topic in AQA GCSE Mathematics Foundation Tier Paper 1 (Non Calculator answers). The question provides information about the mean number of counters in bags and boxes and asks students to verify a statement about the mean number of counters per box.

Key information:

18 bags and 12 boxes of counters
Mean number of counters in all 30 bags and boxes is 14
Mean number of counters in the 18 bags is 10

The solution involves:

Calculating the total number of counters: 30 × 14 = 420
Calculating the number of counters in bags: 18 × 10 = 180
Deducing the number of counters in boxes: 420 - 180 = 240
Calculating the mean number of counters per box: 240 ÷ 12 = 20

Example: Mean value calculations are essential in various fields, including statistics, data analysis, and quality control.

Highlight: This question tests students' ability to work backwards from given mean values to deduce unknown quantities.

View

Questions 9-11: Advanced Mathematical Proofs and Algebraic Manipulation

These pages cover advanced topics typically found in Maths Paper 1 Non Calculator Topics Edexcel Higher tier. The questions involve:

Proving that a recurring decimal equals a specific fraction
Calculating complex expressions involving powers and roots
Rearranging a complex formula to make a specific variable the subject
Proving a statement about the sum of squares of consecutive odd numbers

These questions test students' ability to:

Manipulate algebraic expressions
Work with recurring decimals and fractions
Understand and apply mathematical proofs
Solve complex equations without a calculator

Vocabulary: Recurring decimal - a decimal number that repeats infinitely after a certain point.

Highlight: These advanced topics prepare students for higher-level mathematics and develop critical thinking skills essential for problem-solving in various scientific and engineering fields.

View

Pearson Edexcel GCSE Mathematics Paper 1 (Non-Calculator) Instructions

This page provides essential information about the exam paper and instructions for candidates. The paper is a Non Calculator maths questions and answers assessment for the Higher Tier of GCSE Mathematics.

Key details include:

Time allowed: 1 hour 30 minutes
Total marks: 50
Required equipment: Ruler, protractor, compasses, pen, HB pencil, eraser
Tracing paper may be used

Candidates are instructed to answer all questions in the spaces provided and show all working out. The marks for each question are shown in brackets, serving as a guide for time management.

Highlight: Calculators may not be used in this paper.

Definition: Higher Tier refers to the more advanced level of GCSE Mathematics, typically aimed at students targeting grades 5-9.

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

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#1

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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.

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Subjects

Maths

Number

Place value

Free Non-Calculator GCSE Maths Practice Papers & Answers

yuma

@blueyberrymuffin

183 Followers

The paper is a Pearson Edexcel Level 1/Level 2 GCSE (9-1) Mathematics Paper 1 (Non-Calculator)
It covers a range of topics including ratios, geometry, algebra, and probability
Solutions are provided for each question, demonstrating step-by-step problem-solving techniques
The paper is designed to test students' mathematical skills without the use of a calculator

25/10/2022

3608

10/11

Maths

Question 1: Ratio Problem

This page presents a ratio problem, which is a common type of Non Calculator Maths questions Year 9 and above. The question asks students to divide £280 between Ali and Beth in the ratio 2:5.

The solution demonstrates the step-by-step process:

Add the ratio parts: 2 + 5 = 7
Divide the total amount by the sum of ratio parts: £280 ÷ 7 = £40
Multiply each ratio part by the value of one part:
- Ali's share: 2 × £40 = £80
- Beth's share: 5 × £40 = £200

This question tests students' understanding of ratios and their ability to perform calculations without a calculator.

Example: In real-life scenarios, ratios are often used for sharing profits, dividing resources, or mixing ingredients in recipes.

Question 2: Circle Geometry

Students are asked to calculate the size of angle CAO, given that:

Angle BAE = 56°
Angle CBO = 35°

The solution involves several steps using circle theorems:

Angle BCA = 56° (angle between tangent and chord)
Angle BOA = 56° × 2 = 112° (angle at center is twice angle at circumference)
360° - 112° = 248° (remaining angle in the circle)
360° - 56° - 35° - 248° = 21° (final calculation for angle CAO)

Vocabulary: Tangent - a line that touches a curve at a single point without crossing it.

Highlight: Understanding circle theorems is crucial for solving geometry problems without a calculator.

Question 3: Volume and Rate Problem

Key information:

Swimming pool dimensions: 10m × 10m × 1m
Fill rate: 5 litres per second
1 m³ = 1000 litres

The solution involves multiple steps:

Calculate the volume of the pool: 10m × 10m × 1m = 100m³
Convert volume to litres: 100m³ = 100,000 litres
Calculate total seconds in 10 hours: 10 × 60 × 60 = 36,000 seconds
Calculate total litres filled in 10 hours: 36,000 × 5 = 180,000 litres

The conclusion is that the pool will not be completely filled in 10 hours, as it requires 200,000 litres but only 180,000 litres will be filled.

Example: This type of problem combines real-world applications with mathematical concepts, preparing students for practical problem-solving.

Question 4: Work Rate Problem

The solution uses the concept of man-days:

Calculate total man-days: 12 men × 5 days = 60 man-days
Divide total man-days by new number of men: 60 ÷ 3 = 20 days

The question also asks students to state an assumption made in the calculation and how the answer would be affected if the assumption is not correct.

Highlight: Assumptions in mathematical modeling are crucial for problem-solving but can affect the accuracy of results if not valid.

Example: A common assumption in work rate problems is that all workers work at the same rate, which may not always be true in real-life scenarios.

Question 5: Algebraic Fraction and Expansion

The solution demonstrates step-by-step algebraic manipulation:

Find a common denominator
Add fractions
Simplify the resulting expression

Vocabulary: Algebraic fraction - a fraction where the numerator, denominator, or both contain algebraic expressions.

Highlight: Mastering algebraic fractions is essential for higher-level mathematics and is a key skill tested in non-calculator exams.

Question 6: Probability Tree Diagram

Key points:

The red dice can land on numbers 1 to 6
The blue dice can land on numbers 1 to 8
Students must calculate the probability that neither dice will land on a 6

The solution involves:

Completing the probability tree diagram with correct fractions
Calculating the probability of not landing on 6 for each dice
Multiplying these probabilities to find the combined probability

Definition: A probability tree diagram is a visual representation of all possible outcomes of an event and their probabilities.

Example: Probability tree diagrams are useful in various real-world scenarios, such as analyzing game strategies or predicting weather patterns.

Question 7: Percentage Increase Problem

Students are asked to calculate by what percentage the area of rectangle C is greater than the area of rectangle A.

The solution involves:

Expressing the area of B in terms of A: B = A × 1.1
Expressing the area of C in terms of B: C = B × 1.1
Combining these to express C in terms of A: C = A × 1.1 × 1.1 = A × 1.21
Calculating the percentage increase: (1.21 - 1) × 100 = 21%

Highlight: Understanding compound percentage increases is crucial for many real-world applications, including financial calculations and population growth models.

Question 8: Mean Value Problem

Key information:

18 bags and 12 boxes of counters
Mean number of counters in all 30 bags and boxes is 14
Mean number of counters in the 18 bags is 10

The solution involves:

Calculating the total number of counters: 30 × 14 = 420
Calculating the number of counters in bags: 18 × 10 = 180
Deducing the number of counters in boxes: 420 - 180 = 240
Calculating the mean number of counters per box: 240 ÷ 12 = 20

Example: Mean value calculations are essential in various fields, including statistics, data analysis, and quality control.

Highlight: This question tests students' ability to work backwards from given mean values to deduce unknown quantities.

Questions 9-11: Advanced Mathematical Proofs and Algebraic Manipulation

These pages cover advanced topics typically found in Maths Paper 1 Non Calculator Topics Edexcel Higher tier. The questions involve:

Proving that a recurring decimal equals a specific fraction
Calculating complex expressions involving powers and roots
Rearranging a complex formula to make a specific variable the subject
Proving a statement about the sum of squares of consecutive odd numbers

These questions test students' ability to:

Manipulate algebraic expressions
Work with recurring decimals and fractions
Understand and apply mathematical proofs
Solve complex equations without a calculator

Vocabulary: Recurring decimal - a decimal number that repeats infinitely after a certain point.

Highlight: These advanced topics prepare students for higher-level mathematics and develop critical thinking skills essential for problem-solving in various scientific and engineering fields.

Pearson Edexcel GCSE Mathematics Paper 1 (Non-Calculator) Instructions

Key details include:

Time allowed: 1 hour 30 minutes
Total marks: 50
Required equipment: Ruler, protractor, compasses, pen, HB pencil, eraser
Tracing paper may be used

Candidates are instructed to answer all questions in the spaces provided and show all working out. The marks for each question are shown in brackets, serving as a guide for time management.

Highlight: Calculators may not be used in this paper.

Definition: Higher Tier refers to the more advanced level of GCSE Mathematics, typically aimed at students targeting grades 5-9.

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

15 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

Free Non-Calculator GCSE Maths Practice Papers & Answers

Question 1: Ratio Problem

Question 2: Circle Geometry

Question 3: Volume and Rate Problem

Question 4: Work Rate Problem

Question 5: Algebraic Fraction and Expansion

Question 6: Probability Tree Diagram

Question 7: Percentage Increase Problem

Question 8: Mean Value Problem

Questions 9-11: Advanced Mathematical Proofs and Algebraic Manipulation

Pearson Edexcel GCSE Mathematics Paper 1 (Non-Calculator) Instructions

Similar content

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.

4.9+

15 M

#1

950 K+

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

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

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

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

Free Non-Calculator GCSE Maths Practice Papers & Answers

Question 1: Ratio Problem

Question 2: Circle Geometry

Question 3: Volume and Rate Problem

Question 4: Work Rate Problem

Question 5: Algebraic Fraction and Expansion

Question 6: Probability Tree Diagram

Question 7: Percentage Increase Problem

Question 8: Mean Value Problem

Questions 9-11: Advanced Mathematical Proofs and Algebraic Manipulation

Pearson Edexcel GCSE Mathematics Paper 1 (Non-Calculator) Instructions

Similar content

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.

4.9+

15 M

#1

950 K+

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

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

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

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