Negative Numbers (GCSE Maths) - Worksheets, Questions and Revision

18 original exam-style questions - 8 pages of questions with a full mark scheme - free printable PDF.

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1.8 Negative Numbers

EDEXCEL 1MA1 · Calculator allowed · about 90 minutes

Total Marks

Name: _______________________________ Date: ____ / ____ / ______

Answer ALL questions. Show all your working.

Revision notes: Negative Numbers

Negative numbers are numbers less than zero. GCSE questions test the four operations with negative numbers, where the key skill is applying the correct sign rules, especially when two negative signs appear next to each other.

Adding a negative number is the same as subtracting: e.g. 5 + (-3) = 5 - 3.
Subtracting a negative number is the same as adding: e.g. 5 - (-3) = 5 + 3.
For multiplying and dividing: same signs give a POSITIVE answer (e.g. negative x negative = positive); different signs give a NEGATIVE answer (e.g. positive x negative = negative).
On a number line, moving right corresponds to a positive result and moving left to a negative result; use this to check an answer makes sense.

Worked example. Work out (a) -8 - (-3), and (b) -6 x (-4).

(a) Subtracting a negative becomes adding: -8 - (-3) = -8 + 3 = -5.
(b) Two negative numbers multiplied together give a positive answer: -6 x (-4) = 24.

Answer: (a) -5; (b) 24.

Here is a number line.

(a)Write down the number that the arrow is pointing to.(1)

(b)Write these numbers in order, starting with the smallest: 3, -5, 0, -8, 6(1)

(Total for Question 1 is 2 marks)

Insert < or > to make each statement correct.

(a)-3 [ ] -7(1)

(b)-2 [ ] 5(1)

(Total for Question 2 is 2 marks)

Work out the value of each of the following.

(a)-3 + 7(1)

(b)-5 - 2(1)

(Total for Question 3 is 3 marks)

The temperature at midnight in Kendal was -6 degrees C. The temperature at midday was 9 degrees C.

(a)Work out the difference between the two temperatures.(2)

(b)By 6pm the temperature had fallen by 14 degrees C from midday. Work out the temperature at 6pm.(2)

(Total for Question 4 is 4 marks)

Here are the first five terms of a number sequence: 7, 4, 1, -2, -5

(a)Write down the next two terms in the sequence.(1)

(b)The rule for the sequence is 'subtract 3 from the previous term'. Work out the 8th term of the sequence.(2)

(Total for Question 5 is 3 marks)

Priya's bank account balance is -35 pounds sterling.

(a)She pays in 50 pounds sterling. Work out her new balance.(2)

(b)She then spends 68 pounds sterling on a train ticket. Work out her new balance.(2)

(Total for Question 6 is 4 marks)

Work out the value of each of the following.

(a)-4 x 3(1)

(b)-20 / -5(1)

(d)-18 / 3(1)

(Total for Question 7 is 4 marks)

Work out the value of each of the following.

(a)-2 + 3 x (-4)(2)

(b)(-6 + 2) x (-5)(2)

(Total for Question 8 is 4 marks)

The table shows the midday temperature in five UK cities on 7 January 2026.
Aberdeen: -3 degrees C, Cardiff: 2 degrees C, Leeds: -1 degrees C, Belfast: 0 degrees C, Truro: 4 degrees C

(a)Write down the name of the city with the lowest temperature.(1)

(b)Work out the difference in temperature between Leeds and Belfast.(2)

(c)Work out the range of the five temperatures.(2)

(Total for Question 9 is 5 marks)

A lift in a shopping centre starts at floor 3. It goes down 5 floors, then up 2 floors.

(a)Work out which floor the lift is on now.(2)

(b)The car park is on floor -2. Work out how many floors the lift must now travel down to reach the car park.(2)

(Total for Question 10 is 4 marks)

a = -3, b = 5, c = -2

(a)Work out a + b(1)

(b)Work out b - a(1)

(c)Work out a x c(1)

(d)Work out bc - a(2)

(Total for Question 11 is 5 marks)

Ben was asked to work out -8 + 3. Ben's answer was 11.

(a)Ben's answer is wrong. Write down the correct answer.(1)

(b)Explain the mistake that Ben has made.(1)

(Total for Question 12 is 2 marks)

A submarine is at a depth of -120 metres. It rises 45 metres, then dives a further 68 metres.

(a)Work out the depth of the submarine now.(3)

(b)The submarine must stay no lower than -150 metres to avoid a reef. Determine, showing your working, whether the submarine is above the reef.(2)

(Total for Question 13 is 5 marks)

Work out the value of each of the following.

(a)(-5)²(1)

(b)-(5²)(1)

(c)(-2)³(2)

(Total for Question 14 is 4 marks)

Work out the value of each of the following.

(a)-2.5 + 6.8(2)

(b)-0.6 x 5(2)

(Total for Question 15 is 4 marks)

A freezer is set to a temperature of -18 degrees C. A fault causes the temperature to rise by 2 degrees C every hour.

(a)Work out the temperature in the freezer after 2 hours.(2)

(b)Food in the freezer becomes unsafe once the temperature reaches -12 degrees C or higher. Work out after how many whole hours the food becomes unsafe.(3)

(Total for Question 16 is 5 marks)

Priya and Tomasz are comparing scores in a quiz. A wrong answer scores negative points.
Priya's scores in four rounds: -3, 5, -2, 6
Tomasz's scores in four rounds: 2, -1, 4, -3

(a)Work out Priya's total score.(2)

(b)Work out Tomasz's total score.(2)

(c)Priya says: 'I scored more than double Tomasz's total.' Is Priya correct? Show working to justify your answer.(2)

(Total for Question 17 is 6 marks)

p = -4, q = -6, r = 3

(a)Work out p + q - r(1)

(b)Work out pq(1)

(c)Work out q / r(1)

(d)Work out pr - q(2)

(Total for Question 18 is 5 marks)

Mark scheme · 1.8 Negative Numbers

Question 1

(a) B1 -6 cao
(a) Answer: -6
(b) B1 -8, -5, 0, 3, 6 oe (all five numbers correctly ordered)
(b) Answer: -8, -5, 0, 3, 6

Question 2

(a) B1 > cao
(a) Answer: -3 > -7
(b) B1 < cao
(b) Answer: -2 < 5

Question 3

(a) B1 4 cao
(a) Answer: 4
(b) B1 -7 cao
(b) Answer: -7
(c) B1 -5 cao
(c) Answer: -5

Question 4

(a) M1 9 - (-6) oe, or correct method shown on a number line/scale
(a) A1 15 (degrees C) cao
(a) Answer: 15 degrees C
(b) M1 9 - 14 oe
(b) A1 -5 (degrees C) cao
(b) Answer: -5 degrees C

Question 5

(a) B1 -8 and -11 oe (both correct)
(a) Answer: -8, -11
(b) M1 correct method continuing the sequence to the 8th term, e.g. 7, 4, 1, -2, -5, -8, -11, -14
(b) A1 -14 cao
(b) Answer: -14

Question 6

(a) M1 -35 + 50 oe
(a) A1 15 (pounds) cao, or GBP15
(a) Answer: 15 pounds sterling
(b) M1 15 - 68 oe, ft from (a)
(b) A1 -53 (pounds) cao ft
(b) Answer: -53 pounds sterling

Question 7

(a) B1 -12 cao
(a) Answer: -12
(b) B1 4 cao
(b) Answer: 4
(c) B1 -12 cao
(c) Answer: -12
(d) B1 -6 cao
(d) Answer: -6

Question 8

(a) M1 3 x (-4) = -12 seen, showing multiplication done before addition
(a) A1 -14 cao
(a) Answer: -14
(b) M1 -6 + 2 = -4 seen, showing bracket evaluated first
(b) A1 20 cao
(b) Answer: 20

Question 9

(a) B1 Aberdeen cao
(a) Answer: Aberdeen
(b) M1 0 - (-1) oe
(b) A1 1 (degree C) cao
(b) Answer: 1 degree C
(c) M1 4 - (-3) oe, identifying highest (Truro, 4) and lowest (Aberdeen, -3)
(c) A1 7 (degrees C) cao
(c) Answer: 7 degrees C

Question 10

(a) M1 3 - 5 + 2 oe, or correct intermediate value -2 seen
(a) A1 0 (ground floor) cao
(a) Answer: 0 (ground floor)
(b) M1 0 - (-2) oe, ft from (a)
(b) A1 2 (floors) cao ft
(b) Answer: 2 floors

Question 11

(a) B1 2 cao
(a) Answer: 2
(b) B1 8 cao
(b) Answer: 8
(c) B1 6 cao
(c) Answer: 6
(d) M1 bc = 5 x (-2) = -10 seen
(d) A1 -7 cao
(d) Answer: -7

Question 12

(a) B1 -5 cao
(a) Answer: -5
(b) B1 correct explanation oe, e.g. 'he added 8 and 3 instead of finding the difference between them, and did not keep the negative sign' or equivalent valid reasoning
(b) Answer: Ben added 8 and 3 (getting 11) instead of correctly combining -8 and +3, which gives -5.

Question 13

(a) M1 -120 + 45 (= -75) oe
(a) M1 -75 - 68 (their value - 68) oe
(a) A1 -143 (m) cao
(a) Answer: -143 metres
(b) M1 correct comparison of -143 and -150 shown, ft from (a)
(b) A1 correct conclusion with reason, e.g. 'Yes, -143 > -150 so the submarine is above the reef' cso ft
(b) Answer: Yes; -143 is greater than -150 (7 m above the reef).

Question 14

(a) B1 25 cao
(a) Answer: 25
(b) B1 -25 cao
(b) Answer: -25
(c) M1 (-2) x (-2) x (-2) oe, or -2 x -2 = 4 seen
(c) A1 -8 cao
(c) Answer: -8

Question 15

(a) M1 correct method e.g. 6.8 - 2.5 shown
(a) A1 4.3 cao
(a) Answer: 4.3
(b) M1 0.6 x 5 = 3 seen
(b) A1 -3 cao (accept -3.0)
(b) Answer: -3

Question 16

(a) M1 -18 + 2 x 2 oe
(a) A1 -14 (degrees C) cao
(a) Answer: -14 degrees C
(b) M1 correct equation or systematic trial, e.g. -18 + 2h = -12 oe, or table of values shown
(b) M1 correct method to solve for h, e.g. 2h = 6
(b) A1 3 (hours) cao
(b) Answer: 3 hours

Question 17

(a) M1 -3 + 5 - 2 + 6 oe, or correct partial sum shown
(a) A1 6 cao
(a) Answer: 6
(b) M1 2 - 1 + 4 - 3 oe, or correct partial sum shown
(b) A1 2 cao
(b) Answer: 2
(c) M1 double of Tomasz's total found, 2 x 2 = 4, ft from (b)
(c) A1 correct conclusion with comparison shown, e.g. 'Yes, since 6 > 4' cso ft
(c) Answer: Yes, Priya is correct; double Tomasz's total is 4, and Priya's total of 6 is more than 4.

Question 18

(a) B1 -13 cao
(a) Answer: -13
(b) B1 24 cao
(b) Answer: 24
(c) B1 -2 cao
(c) Answer: -2
(d) M1 pr = -4 x 3 = -12 seen
(d) A1 -6 cao
(d) Answer: -6

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Negative Numbers (GCSE Maths) - Worksheets, Questions and Revision

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1.8 Negative Numbers

Revision notes: Negative Numbers

Question 1

Question 2

Question 3

Question 4

Question 5

Question 6

Question 7

Question 8

Question 9

Question 10

Question 11

Question 12

Question 13

Question 14

Question 15

Question 16

Question 17

Question 18

Question 1

Question 2

Question 3

Question 4

Question 5

Question 6

Question 7

Question 8

Question 9

Question 10

Question 11

Question 12

Question 13

Question 14

Question 15

Question 16

Question 17

Question 18