Upper and lower bounds
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The teaching part (1 min) is free to watch. A free account opens the whole lecture: 6 practice questions, 1 real past-paper question with the answer explained, the mistakes that lose marks, the full-marks tip, a one-card summary and a quick quiz.
What this lecture covers
- Measured to the nearest centimetre
- Rounding makes a range
- Writing the error interval
Read the transcript of the teaching part
Last time
Before we start: last time, in Estimating and using a calculator, you learned these points. Here they are again on one card. Keep them in mind, because today builds on them.
Measured to the nearest centimetre
A table is measured as a hundred and twenty centimetres. But that is only correct to the nearest centimetre, so the true length could be a little more or a little less. Bounds tell you the smallest and the largest the true value could be, and how errors add up in a calculation.
Rounding makes a range
When a number is rounded, the true value lies in a range. The range extends half of the rounding unit each way. A length of seven point three centimetres, to one decimal place, is rounded to the nearest tenth. Half a tenth is zero point zero five. So the lower bound is seven point two five, and the upper bound is seven point three five.
Writing the error interval
We write the range as an inequality. The lower bound can be reached, so it has the equals sign. The upper bound is not reached: any number that really is seven point three five rounds up to seven point four. So the interval is seven point two five, less than or equal to l, less than seven point three five.
How often it comes up
How often Cambridge has asked each part, counted by ExamYard from every past paper in its question bank: Upper and lower bounds.
The whole chapter: Estimation, Accuracy and the Calculator.
Chapter 5: Estimation, bounds and the calculator
- Estimating and using a calculator 5 min
- Upper and lower bounds 6 min
Also for O Level Maths 4024
Which topics come up most in O Level Maths 4024 past papers, counted from every paper since 2004.