Question 1
LEVEL 4
Jane’s height was measured to be 185 cm to the nearest cm. Work out the interval within which h, Jane’s height, lies.
Select the correct answer from the list below:
A: 185.5\leq h<186.5
B: 184\leq h<186
C: 180\leq h<190
D: 184.5\leq h<185.5
CORRECT ANSWER: D: 184.5\leq h<185.5
WORKED SOLUTION:
To find the interval we need to do \pm5 lots of the units to the right of where the value was rounded to. Here, the value was rounded to the nearest cm, so we need to look at the tenths.
\pm0.5We use -0.5 for the lower bound and +0.5 for the upper bound.
185-0.5=184.5
185+0.5=185.5
We can now create our interval, remembering that the lower bound uses a non-strict inequality and the upper bounds uses a strict inequality.
184.5\leq h<185.5Question 2
LEVEL 4
The cost of a government scheme is projected to cost £2.45 billion, rounded to 2 dp. Find the interval for where the cost, C, of this scheme lies.
Select the correct answer from the list below:
A: 2.455 \leq C<2.445
B: 2.445 \leq C<2.455
C: 2.4 \leq C<2.5
D: 2 \leq C<3
CORRECT ANSWER: B: 2.445 \leq C<2.455
WORKED SOLUTION:
To find the interval we need to do \pm5 lots of the units to the right of where the value was rounded to. Here, the value was rounded to 2dp, so we need to look at the thousandths.
\pm0.005We use -0.005 for the lower bound and +0.005 for the upper bound.
2.45 -0.005=2.445
2.45+0.005=2.455
We can now create our interval, remembering that the lower bound uses a non-strict inequality and the upper bounds uses a strict inequality.
2.445 \leq C<2.455Question 3
LEVEL 4
Tyrone walked for 32 minutes to the nearest minute. Work out the interval within which t, the time Tyrone walked for, lies.
Select the correct answer from the list below:
A: 31.5\leq t < 32.5
B: 31\leq t < 33
C: 30\leq t < 34
D: 32\leq t < 32.1
CORRECT ANSWER: A: 31.5\leq t < 32.5
WORKED SOLUTION:
To find the interval we need to do \pm5 lots of the units to the right of where the value was rounded to. Here, the value was rounded to the nearest minute, so we need to look at the tenths.
\pm0.5We use -0.5 for the lower bound and +0.5 for the upper bound.
32-0.5 = 31.5
32+0.5=32.5
Question 4
LEVEL 4
Barbara drove her car from her home to her friends house. The distance she travelled was 6.4 miles to the nearest 0.1 miles. Work out the interval within which d, the distance Barbara travelled, lies.
Select the correct answer from the list below:
A: 6.35\leq d < 6.45
B: 6.3\leq d < 6.5
C: 6.375\leq d < 6.425
D: 6\leq d < 7
CORRECT ANSWER: A: 6.35\leq d < 6.45
WORKED SOLUTION:
To find the interval we need to do \pm5 lots of the units to the right of where the value was rounded to. Here, the value was rounded to the nearest 0.1 miles, so we need to look at the hundredths.
\pm 0.05We use -0.05 for the lower bound and +0.05 for the upper bound.
6.4-0.05 = 6.35
6.4+0.05= 6.45
Question 5
LEVEL 4
Shaun took his casserole out of the oven and checked its temperature. It measured 75 \degree C to the nearest 5 \degree C. Work out the interval within which T, the temperature of the casserole, lies.
Select the correct answer from the list below:
A: 72.5\leq T < 77.5
B: 70\leq T < 80
C: 74\leq T< 76
D: 74.5\leq T < 75.5
CORRECT ANSWER: A: 72.5\leq T < 77.5
WORKED SOLUTION:
To find the interval we need to do \pm5 lots of the units to the right of where the value was rounded to. Here, the value was rounded to the nearest 5 \degree C, so we do \pm 2.5 .
We use -2.5 for the lower bound and +2.5 for the upper bound.
75-2.5 = 72.5
75+2.5= 77.5