Brush up your maths: Simple maths test 2007

The test

There were ten questions:

  1. 627 + 183 = ?

  2. 20 – 3 × 5 = ?

  3. 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

  4. 0.001 is equal to which of the following?
            1               1                   1
    (a) –––     (b) ––––     (c) –––––
          10             100             1000

  5. ¾ + 0.6 = ?

  6. If y = x – 2, what is the value of x when y = 6?

  7. Write 3.75 million in figures.

  8. √(32 + 42) = ?

  9. What is 2½% of £10?

  10. If cheese is £2.20 per kilogramme, what should I pay for 400 grammes?

The answers are:

  1. 627 + 183 = 810

  2. 20 – 3 × 5 = 5.
    Note that the order of operations in maths is brackets, powers of, divide, multiply, add, subtract.

  3. 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.

  4. 0.001 is equal to which of the following?
            1               1                   1
    (a) –––     (b) ––––     (c) –––––
          10             100             1000
    The answer is c.

  5. ¾ + 0.6 = 0.75 + 0.6 = 1.35.
    I would also accept 1 7/20 or 27/20.

  6. If y = x – 2, the value of x when y = 6 is 8.

  7. Write 3.75 million in figures: 3,750,000.

  8. √(32 + 42) = √(9 + 16) = √25 = 5.

  9. 2½% of £10 = £0.25 = 25p.

  10. 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.

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