Negative Numbers (Part 2) - Worksheets, Questions and Revision

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

Download PDF Jump to mark scheme (page 9)Read the revision guide

Next in this strand

Revision Library

revisionlibrary.co.uk

FOUNDATION

1.8B Negative Numbers (Part 2)

EDEXCEL 1MA1 · Calculator allowed · about 90 minutes

Total Marks

Name: _______________________________ Date: ____ / ____ / ______

Answer ALL questions. Show all your working.

Find the missing number in each calculation.

(a)-4 + ___ = 3(1)

(b)___ - 6 = -9(1)

(Total for Question 1 is 2 marks)

Write True or False for each statement.

(a)-15 < -20(1)

(b)-3 > -3.5(1)

(Total for Question 2 is 2 marks)

Work out the value of each of the following.

(a)-6 + 9(1)

(b)-8 - 5(1)

(d)-10 + (-4)(1)

(Total for Question 3 is 4 marks)

Work out the value of each of the following.

(a)-7 x 4(1)

(b)-36 / -9(1)

(d)-45 / 5(1)

(Total for Question 4 is 4 marks)

In golf, a player's score is given relative to par. A score below par is negative and a score above par is positive. After the front nine holes, Jamal's score is -4 (4 under par).

(a)On the back nine holes, Jamal scores 7 over par. Work out Jamal's total score for the round, relative to par.(2)

(b)A rival team, Wales, has a total score of -11 for the round. Determine, showing working, whether Jamal's total score from part (a) is better or worse than the Wales team score, and by how many strokes.(2)

(Total for Question 5 is 4 marks)

A cave system in the Yorkshire Dales has its highest point at 45 m above sea level and its lowest chamber at -68 m (68 m below sea level).

(a)Work out the vertical distance between the highest point and the lowest chamber.(2)

(b)A nearby pothole reaches -95 m. Work out how much further below sea level the pothole reaches, compared with the cave's lowest chamber.(2)

(Total for Question 6 is 4 marks)

Here is a thermometer.

Figure (to be drawn): A vertical thermometer scale from -20 to 20 degrees C, marked in steps of 2, with an arrow pointing to the -14 mark.

(a)Write down the temperature shown on the thermometer.(1)

(b)The temperature is forecast to rise by 20 degrees C by midday. Work out the midday temperature.(2)

(Total for Question 7 is 3 marks)

Here are the first five terms of a number sequence: 15, 9, 3, -3, -9

(a)Write down the next term in the sequence.(1)

(b)By continuing the pattern backwards, work out the term that comes immediately before 15 in the sequence.(2)

(Total for Question 8 is 3 marks)

Work out the value of each of the following.

(a)-5 x (-2) + 3(2)

(b)20 / (-4) - (-6)(2)

(Total for Question 9 is 4 marks)

Work out the value of each of the following.

(a)(-3)⁴(2)

(b)Chidi says: 'Since (-3)⁴ = 81, I know (-3)⁵ must also be positive.' Explain why Chidi is wrong, and work out the correct value of (-3)⁵.(2)

(Total for Question 10 is 4 marks)

The table shows five players' scores relative to par in a golf tournament.
Erin: -5, Kwame: 2, Oliwia: -1, Noah: 0, Callum: -8

(a)Write down the name of the player with the best (lowest) score.(1)

(b)Work out the total combined score of Erin and Callum.(2)

(c)Put all five scores in order, starting with the best (lowest) score. Write down the middle (median) score.(2)

(Total for Question 11 is 5 marks)

x = -5, y = 4, z = -2

(a)Work out yz(1)

(b)Work out x - y(1)

(c)Work out z²(1)

(d)Work out xy + z(2)

(Total for Question 12 is 5 marks)

Zara's working for -12 / (-4) is shown below.
Step 1: 12 / 4 = 3
Step 2: A negative divided by a negative gives a negative answer.
Step 3: Answer: -3

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

(b)Identify the step where Zara's reasoning is wrong, and explain the mistake she has made.(1)

(Total for Question 13 is 2 marks)

A research drone's pressure sensor gives a reading of -32 units relative to the surface calibration point.

(a)The drone rises, and its reading increases by 50 units. Work out the drone's new reading.(2)

(b)The drone then descends again, and its reading decreases by 6 units every minute for 4 minutes. Work out the drone's reading after these 4 minutes.(2)

(Total for Question 14 is 4 marks)

A function machine works like this: input -> multiply by -3 -> add 7 -> output.

(a)The input is -4. Work out the output.(2)

(b)The output is -2. Work out the input.(2)

(Total for Question 15 is 4 marks)

Work out the value of each of the following.

(a)-7.4 - 2.6(2)

(b)-1.2 x (-0.5)(2)

(Total for Question 16 is 4 marks)

A scientist records the temperature of a chemical sample during an experiment. The sample starts at 18 degrees C. During cooling stage 1, the temperature falls by 25 degrees C. During cooling stage 2, the temperature falls by a further 9 degrees C.

(a)Work out the temperature of the sample after both cooling stages.(3)

(b)The experiment is only valid if the final temperature is below -20 degrees C. Chen says the experiment is valid. Determine, showing your working, whether Chen is correct.(2)

(Total for Question 17 is 5 marks)

m = -4, n = 3, k = -5

(a)Work out m + nk(2)

(b)Work out (m - k)²(2)

(c)Sam says: 'mk is definitely greater than m + k.' Determine, with working, whether Sam is correct.(2)

(Total for Question 18 is 6 marks)

Mark scheme · 1.8B Negative Numbers (Part 2)

Question 1

(a) B1 7 cao
(a) Answer: 7
(b) B1 -3 cao
(b) Answer: -3

Question 2

(a) B1 False cao
(a) Answer: False
(b) B1 True cao
(b) Answer: True

Question 3

(a) B1 3 cao
(a) Answer: 3
(b) B1 -13 cao
(b) Answer: -13
(c) B1 -5 cao
(c) Answer: -5
(d) B1 -14 cao
(d) Answer: -14

Question 4

(a) B1 -28 cao
(a) Answer: -28
(b) B1 4 cao
(b) Answer: 4
(c) B1 -40 cao
(c) Answer: -40
(d) B1 -9 cao
(d) Answer: -9

Question 5

(a) M1 -4 + 7 oe
(a) A1 3 cao
(a) Answer: 3 (3 over par)
(b) M1 3 - (-11) oe, ft from (a)
(b) A1 correct conclusion with reason, e.g. 'Worse, since 3 is 14 more than -11 and a lower golf score is better' cso ft
(b) Answer: Worse, by 14 strokes

Question 6

(a) M1 45 - (-68) oe
(a) A1 113 (m) cao
(a) Answer: 113 metres
(b) M1 -68 - (-95) oe
(b) A1 27 (m) cao
(b) Answer: 27 metres

Question 7

(a) B1 -14 cao
(a) Answer: -14
(b) M1 -14 + 20 oe, ft from (a)
(b) A1 6 (degrees C) cao ft
(b) Answer: 6 degrees C

Question 8

(a) B1 -15 cao
(a) Answer: -15
(b) M1 correct method reversing the term-to-term rule, e.g. 15 + 6
(b) A1 21 cao
(b) Answer: 21

Question 9

(a) M1 -5 x (-2) = 10 seen, showing multiplication done before addition
(a) A1 13 cao
(a) Answer: 13
(b) M1 20 / (-4) = -5 seen, showing division done before subtraction
(b) A1 1 cao
(b) Answer: 1

Question 10

(a) M1 (-3) x (-3) x (-3) x (-3) oe, or (-3)² = 9 seen
(a) A1 81 cao
(a) Answer: 81
(b) B1 correct explanation oe, e.g. '(-3)⁵ has an odd number (5) of negative factors, so the result stays negative, unlike the even number of factors in (-3)⁴' or equivalent valid reasoning
(b) B1 -243 cao
(b) Answer: Chidi is wrong; (-3)⁵ = -243 because an odd power of a negative number is negative.

Question 11

(a) B1 Callum cao
(a) Answer: Callum
(b) M1 -5 + (-8) oe
(b) A1 -13 cao
(b) Answer: -13
(c) M1 scores ordered correctly, e.g. -8, -5, -1, 0, 2 seen
(c) A1 -1 cao
(c) Answer: -1

Question 12

(a) B1 -8 cao
(a) Answer: -8
(b) B1 -9 cao
(b) Answer: -9
(c) B1 4 cao
(c) Answer: 4
(d) M1 xy = -5 x 4 = -20 seen
(d) A1 -22 cao
(d) Answer: -22

Question 13

(a) B1 3 cao
(a) Answer: 3
(b) B1 correct step identified with correct explanation oe, e.g. 'Step 2 is wrong: a negative divided by a negative gives a positive answer, not a negative one' or equivalent valid reasoning
(b) Answer: Step 2 is wrong: dividing a negative number by a negative number gives a positive answer, not a negative one, so the answer should be 3, not -3.

Question 14

(a) M1 -32 + 50 oe
(a) A1 18 cao
(a) Answer: 18
(b) M1 18 - 6 x 4 oe, ft from (a)
(b) A1 -6 cao ft
(b) Answer: -6

Question 15

(a) M1 -4 x (-3) = 12 seen
(a) A1 19 cao
(a) Answer: 19
(b) M1 correct reverse method, e.g. -2 - 7 = -9 seen
(b) A1 3 cao
(b) Answer: 3

Question 16

(a) M1 correct method e.g. 7.4 + 2.6 shown
(a) A1 -10 cao (accept -10.0)
(a) Answer: -10
(b) M1 1.2 x 0.5 = 0.6 seen
(b) A1 0.6 cao (accept 0.60)
(b) Answer: 0.6

Question 17

(a) M1 18 - 25 (= -7) oe
(a) M1 their value - 9 oe
(a) A1 -16 (degrees C) cao
(a) Answer: -16 degrees C
(b) M1 correct comparison of -16 and -20 shown, ft from (a)
(b) A1 correct conclusion with reason, e.g. 'No, -16 is greater than -20 so the final temperature is not below -20 degrees C and the experiment is not valid' cso ft
(b) Answer: No; Chen is not correct, since -16 is greater than -20 so the temperature is not below -20 degrees C.