Revision mat · Negative Numbers

No calculator10 marks

Question mix weighted by 63 real exam questions from 52 GCSE papers (2017–24), so the most common question types get the most space. Show your working.

Two signs together $+\,- = -\quad -\,- = +$Multiply / divide $\text{same signs}\to+,\ \text{different}\to-$Ordering $\ldots -3<-2<-1<0<1\ldots$BIDMAS still applies $\times,\div\text{ before }+,-$
Ordering≈32% of real exam Qs
1The arrow on the number line points to a number.
Write down the number shown by the arrow.
Number line ()-20-15-10-50
Answer: (1 mark)
2The arrow on the number line points to a number.
Write down the number shown by the arrow.
Number line ()-8-6-4-20
Answer: (1 mark)
Add & subtract≈13% of real exam Qs
3Work out $-6 + 3 + (-9)$.
Answer: (2 marks)
In context≈13% of real exam Qs
4The temperature in Helsinki is $-13°C$.
London is $8°C$.
How many degrees warmer is London than Helsinki?
Answer: (2 marks)
Multiply & divide≈8% of real exam Qs
5Work out $2 \times (-2) \div (-4)$.
Answer: (2 marks)
★ Exam capstonemixed & other forms ≈29% of real exam Qs
6$n$ is a number with $n < -1$.
Which one of these expressions has the largest value?
Answer: (2 marks)

Mark scheme · Negative Numbers

Total: 10 marks

Award the marks shown for each correct step, then add up the total out of 10. A method mark counts even if the final answer is wrong.

1The arrow on the number line points to a number.
Write down the number shown by the arrow.[1 mark]
Method
Each large gap of 5 is split into 5 equal parts, so each small step is 1.
The arrow is 3 small steps to the right of -20, so it shows -17.
Answer: $-17$
Marks
✔1 markValue = -17
2The arrow on the number line points to a number.
Write down the number shown by the arrow.[1 mark]
Method
Each large gap of 2 is split into 2 equal parts, so each small step is 1.
The arrow is 1 small step to the right of -2, so it shows -1.
Answer: $-1$
Marks
✔1 markValue = -1
3Work out $-6 + 3 + (-9)$.[2 marks]
Method
Work left to right. $-6 + 3 = -3$.
$-3 + (-9) = -12$.
Answer: $-12$
Marks
✔1 markFirst step -3
✔1 markFinal answer -12
4The temperature in Helsinki is $-13°C$.
London is $8°C$.
How many degrees warmer is London than Helsinki?[2 marks]
Method
Difference $= 8 - (-13) = 8 + 13 = 21°C$.
Answer: $21$
Marks
✔1 markCorrect directed calculation
✔1 markAnswer 21°C
5Work out $2 \times (-2) \div (-4)$.[2 marks]
Method
$2 \times (-2) = -4$.
$-4 \div (-4) = 1$.
Answer: $1$
Marks
✔1 markProduct -4
✔1 markFinal answer 1
6$n$ is a number with $n < -1$.
Which one of these expressions has the largest value?[2 marks]
Method
When $n < -1$: $n^2$ is positive and bigger than $1$; $-n$ is positive but smaller than $n^2$; $\dfrac{1}{n}$ is between $-1$ and $0$; $n$ and $n^3$ are negative.
So $n^2$ is the largest.
Answer: $$n^2$$
Marks
✔1 markCompares the expressions for a < −1
✔1 markn² is largest
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