Topics › KS3 › Number

Negative numbers

1. neg-01 Present from here

   At midnight the temperature was $-4^\circ\text{C}$. By midday it had risen by $7$ degrees. What was the temperature at midday?

   A Option A: $-11^\circ\text{C}$

   B Option B: $11^\circ\text{C}$

   C Option C: $3^\circ\text{C}$

   D Option D: $-3^\circ\text{C}$
   Answer and misconceptions

   A Option A: $-11^\circ\text{C}$ ✗

   Counts the wrong way on the number lineMoves 7 down from -4 instead of up, as if the temperature fell.

   B Option B: $11^\circ\text{C}$ ✗

   Ignores the negative signTreats -4 as 4 and adds 7.

   C Option C: $3^\circ\text{C}$ ✓ Correct

   D Option D: $-3^\circ\text{C}$ ✗

   Finds the difference and keeps the minus signWorks out 7 - 4 = 3 then copies the negative from -4.
2. neg-02 Present from here

   Work out $-3 - 5$

   A Option A: $-8$

   B Option B: $8$

   C Option C: $2$

   D Option D: $-2$
   Answer and misconceptions

   A Option A: $-8$ ✓ Correct

   B Option B: $8$ ✗

   Thinks two minus signs make the answer positiveApplies the multiplication sign rule to subtraction: sees two minus signs and gives +(3 + 5) = 8.

   C Option C: $2$ ✗

   Moves right on the number line when subtractingStarts at -3 and counts 5 up instead of down.

   D Option D: $-2$ ✗

   Ignores the sign of the first numberWorks out 3 - 5 = -2, treating -3 as 3.
3. neg-03 Present from here

   Work out $5 - (-3)$

   A Option A: $2$

   B Option B: $-8$

   C Option C: $-2$

   D Option D: $8$
   Answer and misconceptions

   A Option A: $2$ ✗

   Treats subtracting a negative as subtractingIgnores the negative on the 3 and works out 5 - 3.

   B Option B: $-8$ ✗

   Thinks a negative anywhere makes the answer negativeCombines 5 and 3 to get 8, then makes it negative because of the minus signs.

   C Option C: $-2$ ✗

   Subtracts the numbers in the wrong orderWorks out 3 - 5, thinking you always take the number after the sign first.

   D Option D: $8$ ✓ Correct
4. neg-04 Present from here

   Work out $-6 + (-4)$

   A Option A: $-2$

   B Option B: $-10$

   C Option C: $10$

   D Option D: $2$
   Answer and misconceptions

   A Option A: $-2$ ✗

   Ignores the sign of the number being addedTreats (-4) as 4 and works out -6 + 4.

   B Option B: $-10$ ✓ Correct

   C Option C: $10$ ✗

   Thinks adding two negatives gives a positiveMisapplies "two negatives make a positive" to addition.

   D Option D: $2$ ✗

   Ignores signs and finds the differenceSees a 6 and a 4 and works out 6 - 4.
5. neg-05 Present from here

   Work out $-20 \div (-4)$

   A Option A: $-5$

   B Option B: $-24$

   C Option C: $5$

   D Option D: $0.2$
   Answer and misconceptions

   A Option A: $-5$ ✗

   Thinks negative divided by negative is negativeBelieves the answer keeps the sign of the numbers being divided.

   B Option B: $-24$ ✗

   Combines two negatives as if adding themSees two negative numbers and works out −20 + (−4) = −24.

   C Option C: $5$ ✓ Correct

   D Option D: $0.2$ ✗

   Divides the smaller number by the largerThinks division always puts the smaller number first: 4 / 20.
6. neg-06 Present from here

   Find the value of $3x^2$ when $x = -2$.

   A Option A: $36$

   B Option B: $-12$

   C Option C: $-6$

   D Option D: $12$
   Answer and misconceptions

   A Option A: $36$ ✗

   Squares $3x$ instead of just $x$Works out $(3 \times -2)^2 = (-6)^2 = 36$; the power applies only to $x$, so it is $3 \times (-2)^2$.

   B Option B: $-12$ ✗

   Thinks a negative number squared is negativeWorks out $(-2)^2 = -4$, then $3 \times -4 = -12$; $(-2) \times (-2) = +4$.

   C Option C: $-6$ ✗

   Ignores the powerWorks out $3 \times -2 = -6$ without squaring $x$ at all.

   D Option D: $12$ ✓ Correct