627 + 183 = ?
20 – 3 × 5 = ?
Put these numbers in order of magnitude from biggest to smallest:
0.5 0.03 1 0.1 1.5 0.3 0.55 0.05
0.001 is equal to which of the following?
1 1
1
(a) –––
(b) –––– (c) –––––
10 100 1000
¾ + 0.6 = ?
If y = x – 2, what is the value of x when y = 6?
Write 3.75 million in figures.
√(3^{2} + 4^{2}) = ?
What is 2½% of £10?
If cheese is £2.20 per kilogramme, what should I pay for 400 grammes?
The answers are:
627 + 183 = 810
20 – 3 × 5 = 5.
Note that the order of operations in maths is
brackets, powers of, divide, multiply, add, subtract.
Put these numbers in order of magnitude from biggest to smallest:
0.5 0.03 1 0.1 1.5 0.3 0.55 0.05
gives us
1.5 1 0.55 0.5 0.3 0.1 0.05 0.03.
I carelessly gave:
0.03 0.05 0.1 0.3 0.5 0.55 1 1.5,
arranged in ascending order. I counted either as correct.
0.001 is equal to which of the following?
1 1
1
(a) –––
(b) –––– (c) –––––
10 100 1000
The answer is c.
¾ + 0.6 = 0.75 + 0.6 = 1.35.
I would also accept 1 7/20 or 27/20.
If y = x – 2, the value of x when y = 6 is 8.
Write 3.75 million in figures: 3,750,000.
√(3^{2} + 4^{2}) = √(9 + 16) = √25 = 5.
2½% of £10 = £0.25 = 25p.
If cheese is £2.20 per kilogramme, for 400 grammes I should pay £2.20 × 400/1000 = £0.88 = 88p.
There were 80 students altogether. The numbers getting each possible score out of 10 were:
Score | Count | % |
---|---|---|
0 | 0 | 0.00 |
1 | 0 | 0.00 |
2 | 0 | 0.00 |
3 | 1 | 1.25 |
4 | 2 | 2.50 |
5 | 4 | 5.00 |
6 | 8 | 10.00 |
7 | 12 | 15.00 |
8 | 17 | 21.25 |
9 | 23 | 28.75 |
10 | 13 | 16.25 |
We can present this graphically:
Hence 27 students got 7 or less, the score that I suggested meant that they should brush up their maths.
The question which caused most trouble was 2: 20 – 3 × 5 = ?. 62% got this wrong, almost all giving the answer 85. They got this by first subtracting 3 from 20 then multiplying 17 by 5. The rules of arithmetic are that we multiply before we add. We do not need brackets to make this clear. See part 1 of Brush up your maths.
We asked whether you panicked when you saw all those numbers. 37 said 'yes' to this, 35 said 'no', and 8 did not reply. Not surprisingly, the panickers did worst, with mean score = 7.3, compared to 8.6 for those who did not panic and 8.3 for those who did not answer.
I was disappointed that only 41 identified themselves, making it difficult for us to see how this test might predict student performance. Anonymous students were more likely to panic, 59.0% compared to 34.2% of identified students. Anonymous students had a lower average score, 7.3 compared to 8.5 for identified students.
Martin Bland
15 October, 2007.
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Last updated: 18 October, 2007.