[discia] GCSE Maths › Number › Negative Numbers › Practise
  1. Either paper 1 mark

    Write these numbers in order, starting with the smallest.

    \(8,\ -9,\ 3,\ -1,\ -11\)

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    \(-11,\ -9,\ -1,\ 3,\ 8\)

    On a number line the smallest number is the one furthest to the left, so every negative number comes before every positive one, and the most negative comes first.

    \(-11,\ -9,\ -1,\ 3,\ 8\)

  2. Either paper 1 mark

    The temperature in a cold store is below \(-13.5\)°C.

    Write down a possible temperature, in °C.

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    Any number less than \(-13.5\), for example \(-16\)

    Below \(-13.5\)°C means further left than \(-13.5\) on a number line, so colder than \(-13.5\)°C.

    A temperature such as \(-13\)°C is nearer zero, so it is warmer than \(-13.5\)°C, not colder.

    For example \(-16\)°C.

  3. Either paper 2 marks
    (a)

    Find the value of \(-11 + 7\)

    (b)

    Find the value of \(2 - (-8)\)

    Show answer
    (a) \(-4\)
    (b) \(10\)

    Start at \(-11\) on a number line and count 7 places to the right:

    \(-11 + 7 = -4\)

    Subtracting a negative number is the same as adding:

    \(2 - (-8) = 2 + 8 = 10\)

  4. Either paper 4 marks

    At 4 am the temperature in Bangor was \(-13^\circ\text{C}\).

    (a)

    By 2 pm the temperature had risen by \(16^\circ\text{C}\). Work out the temperature at 2 pm.

    (b)

    By midnight the temperature had fallen to \(-14^\circ\text{C}\). Work out the fall in temperature between 2 pm and midnight.

    Show answer
    (a) \(3^\circ\text{C}\)
    (b) \(17^\circ\text{C}\)

    Counting 16 up from \(-13\) passes through zero:

    \(-13 + 16 = 3\)

    The fall is the difference between the two temperatures:

    \(3 - (-14) = 3 + 14 = 17\)

    • (a) M1adds 16 to \(-13\) or counts up through zero
    • (a) A1temperature \(3^\circ\text{C}\)
    • (b) M1difference between \(3\) and \(-14\)
    • (b) A1fall \(17^\circ\text{C}\)
  5. Either paper 3 marks

    The diagram shows part of a number line.

    -20-16-12-8-4048121620AB
    (a)

    State the number that the point labelled A is marking.

    (b)

    Calculate the difference between the numbers marked by A and B.

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    (a) \(-10\)
    (b) \(18\)

    The line is numbered in 4s, and A sits halfway between \(-12\) and \(-8\).

    A is marking \(-10\).

    Counting from \(-10\) up to zero is 10, and from zero up to \(8\) is another 8.

    \(8 - (-10) = 8 + 10 = 18\)

    • (b) M1distances from A and B to zero, \(10\) and \(8\), added or \(8 - (-10)\)
    • (b) A1difference \(18\)
  6. Either paper 1 mark

    \(n\) is a negative even number.

    Circle the words that describe \(n^3\).

    - negative and odd - negative and even - positive and odd - positive and even

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    negative and even

    \(n\) is a negative even number.

    Sign: An odd power of a negative number is negative, because one negative sign is left over.

    Odd or even: \(n\) is even. A whole number and its powers are both odd or both even.

    So \(n^3\) is negative and even.

  7. Either paper 2 marks
    (a)

    Work out the value of \(-9 \times 6\)

    (b)

    Work out the value of \(-40 \div (-10)\)

    Show answer
    (a) \(-54\)
    (b) \(4\)

    A negative multiplied by a positive gives a negative.

    \(9 \times 6 = 54\), so \(-9 \times 6 = -54\)

    A negative divided by a negative gives a positive.

    \(40 \div 10 = 4\), so \(-40 \div (-10) = 4\)

  8. Either paper 4 marks

    Erin has £45 in a bank account. A bill for £170 is taken out of the account.

    (a)

    Calculate the balance of the account after the £170 bill is taken out.

    (b)

    Erin then pays £460 into the account. Work out how much she now has in the account.

    Show answer
    (a) \(-£125\)
    (b) \(\text{£}335\)

    The bill is bigger than the money in the account, so the balance goes below zero.

    \(£45 - £170 = -£125\)

    The account is overdrawn by £125.

    Start from the negative balance and add the payment:

    \(-£125 + £460 = £335\)

    • (a) M1subtracting the bill from the balance \(£45 - £170\)
    • (a) A1balance \(-£125\)
    • (b) M1adding the payment to the negative balance \(-£125 + £460\)
    • (b) A1balance \(£335\)
  9. Either paper 3 marks
    (a)

    Work out \((-11)^2\)

    (b)

    Work out \((-5)^3\)

    (c)

    Work out \((-4) \times (-2) \times (-3)\)

    Show answer
    (a) \(121\)
    (b) \(-125\)
    (c) \(-24\)

    Squaring means multiplying the number by itself, and a negative multiplied by a negative gives a positive.

    \((-11) \times (-11) = 121\)

    \((-5) \times (-5) = 25\), a positive.

    A cube is three of them multiplied together, so that positive is multiplied by \(-5\) once more, which makes it negative again.

    \(25 \times (-5) = -125\)

    Take the first two: \((-4) \times (-2) = 8\), a positive.

    Multiplying that by a third negative makes the answer negative.

    \(8 \times (-3) = -24\)

  10. Either paper 6 marks

    In a quiz, every correct answer scores \(2\) points and every wrong answer scores \(-6\) points.

    (a)

    Tomas answers 3 questions correctly and 10 questions wrongly.

    Calculate Tomas's total score.

    (b)

    In a second quiz Tomas answers 7 questions correctly and scores -22 points.

    Calculate how many questions he answered wrongly.

    Show answer
    (a) \(-54\)
    (b) \(6\)

    Each wrong answer loses 6 points.

    Points gained: \(3 \times 2 = 6\)

    Points lost: \(10 \times 6 = 60\)

    \(6 - 60 = -54\)

    Points gained: \(7 \times 2 = 14\)

    The score is what is left after the lost points are taken off the gained points, so the points lost are the gained points minus the score.

    \(14 - (-22) = 36\)

    Each wrong answer loses 6 points, so \(36 \div 6 = 6\) questions were answered wrongly.

    • (a) M1points gained \(6\)
    • (a) M1points lost \(60\)
    • (a) A1total score \(-54\)
    • (b) M1points gained \(14\)
    • (b) M1points lost \(36\) (gained minus score)
    • (b) A1wrong answers \(6\)