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Negative numbers

Free Printable Negative numbers PDF Worksheets, Revision Guide & GCSE Past Paper Questions (Grade 1)

Download free negative numbers worksheets (PDF), GCSE maths past paper questions and worked solutions for Negative numbers (1J). This is a Grade 1 number topic from the GCSE questions by topic collection for Foundation and Higher tier GCSE Maths (Edexcel, AQA, OCR and IGCSE).

The free PDF worksheets table below brings together printable question booklets (Qs) and worked answers or mark schemes (Ans) from Maths Genie, Corbett Maths, Maths Takeaway, Dr Austin, Maths4EveryOne, GCSE Maths Rocket, E Classroom and PMT, along with past paper question booklets.

Below the worksheet links you can read our negative numbers revision notes and worked examples with diagrams, try real GCSE past paper negative numbers questions with step-by-step solutions, or download a PDF of all negative numbers worksheet links.

Free Negative numbers PDF Worksheets & Answers

Grade 1 • Topic 1J
Resource Questions Answers
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Graded exam questions & solutions
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Practice Questions & answers
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Textbook Exercise & answers
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GCSE Maths Takeaway exam questions
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KS2 SATs questions & solutions
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Practice questions & answers
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Practice questions & answers
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GCSE topic booklet & answers
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PMT (Edxl)
Edexcel GCSE topic questions & solutions
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PMT (AQA)
AQA GCSE topic questions & solutions
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PMT (IGCSE)
Edexcel IGCSE topic questions & solutions
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Interactive 10-question revision grid
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MathsBot interactive resource
Interactive online resource
 Open
Self-marking online worksheet
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Grade 1 topics
1A - Addition1B - Subtraction
1C - Multiplication1D - Division
1E - Time1F - Ordering FDP
1G - Place Value1H - Rounding
1J - Negative numbers1K - Powers and roots
1L - BIDMAS1M - Factors, multiples and primes
1N - Coordinates1P - Pictograms
1Q - 2D shapes1R - 3D shapes
GCSE Maths Grade 1 Revision Notes & Method

Guide to Negative numbers: Explanation, Diagrams & Worked Examples

Download Printable One Page Guide (PDF)

Explanation:

When adding or subtracting negative numbers, picture a vertical thermometer or number line: adding a positive number moves up (right), while subtracting a positive number moves down (left). If two signs sit right next to each other, combine them first: same signs make a plus (+ + or − − → +) and different signs make a minus (+ − or − + → −).

When multiplying or dividing two numbers, calculate the size first, then apply the sign rule: same signs give a positive answer, and different signs give a negative answer.

Example 1: Work out: (a) −6 + 9  (b) 4 − (−7)  (c) −3 + (−8)

+ 9 (across 0) -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6
(a) Start at −6 and move right 9 across zero → 3
(b) Two minuses make a plus: 4 − (−7) = 4 + 7 = 11
(c) Plus & minus make a minus: −3 − 8 = −11

Example 2: Work out:
(a) (−6) × 4   (b) (−35) ÷ (−7)   (c) (−5)2

Solution:

(a) Different signs (− and +) give negative: 6 × 4 = −24
(b) Same signs (− and −) give positive: 35 ÷ 7 = 5
(c) Squaring multiplies a number by itself:
• (−5)2 = (−5) × (−5) = 25
Answers: (a) −24   (b) 5   (c) 25
Scanned GCSE Exam Questions & Worked Solutions

GCSE Past Paper Negative numbers Questions & Answers

Past Paper Example 1 IGCSE Nov 2024 1F Q4 3 marks
Full Paper (PDF) • Mark Scheme (PDF)
The table shows information about the temperatures at different heights above sea level.
Height above sea level(metres)Temperature(°C)14 000−6012 000−589000−507000−406000−324000−172000−1012
(a) Work out the difference in temperature between a height of 0 m and a height of 12 000 m [1 mark]
(b) Work out the difference in temperature between a height of 4000 m and a height of 6000 m [1 mark]
(c) At what height is the temperature 10°C warmer than the temperature at a height of 9000 m? [1 mark]
Worked Solution & Mark Scheme (3 marks)
Part (a) Solution:
12 − (−58) = 70 B1
Answer (a): 70 °C
Part (b) Solution:
−17 − (−32) = 15 B1
Answer (b): 15 °C
Part (c) Solution:
−50 + 10 = −40°C, which is at 7000 m B1
Answer (c): 7000 m
Past Paper Example 2 IGCSE Jan 2019 2FR Q5 4 marks
Full Paper (PDF) • Mark Scheme (PDF)
The table gives the midnight temperatures on 1st January for five cities in the USA.
CityMidnight temperatureBoston–5 °CPhiladelphia–4 °COrlando10 °CChicago–6 °CPhoenix8 °C
(a) Here are the five temperatures.
-5   -4   10   -6   8
Write these numbers in order of size.
Start with the smallest number. [1 mark]
(b) Work out the difference between the midnight temperature in Orlando and the midnight temperature in Boston. [1 mark]
(c) Work out the temperature that is exactly halfway between 8 °C and −6 °C. [1 mark]
(d) On 1st January the midnight temperature in Minneapolis was 10 °C lower than the midnight temperature in Philadelphia.
Work out the midnight temperature in Minneapolis. [1 mark]
Worked Solution & Mark Scheme (4 marks)
Part (a) Solution:
−6, −5, −4, 8, 10
Answer (a): −6, −5, −4, 8, 10
Part (b) Solution:
15
Answer (b): 15 °C
Part (c) Solution:
1
Answer (c): 1 °C
Part (d) Solution:
−14
Answer (d): −14 °C
Past Paper Example 3 GCSE Jun 2025 2F Q4 1 mark
Full Paper (PDF) • Mark Scheme (PDF)
Here are some temperatures in °C.
–3 5 –6 7 2
Write the temperatures in order.
Start with the lowest temperature.
Worked Solution & Mark Scheme (1 mark)
Order from coldest to warmest: –6, –3, 2, 5, 7. B1
Answer: –6, –3, 2, 5, 7

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