CAMBRIDGE IGCSE MATHS (0580)

Question 1:

Find the lowest common multiple (LCM) of 36 and 48.
................................................... [2]

Question 2:

(a) From this list of numbers: 30, 32, 35, 36, 48, 49, 51, 3, 6, 19, 20, 24, 27, write down:
(i) a factor of 15, .................................................. [1]
(ii) a multiple of 18, .................................................. [1]
(iii) an odd square number, .................................................. [1]
(iv) a cube number. .................................................. [1]

(b) Write as a percentage:
(i) 0.43 ..................................................% [1]
(ii) 1/2 ..................................................% [1]

(c) Write 42/28 in its lowest terms. .................................................. [1]

(d) (i) Write 45 as a product of its prime factors. .................................................. [2]
(ii) Find the highest common factor (HCF) of 45 and 105. .................................................. [2]

Question 3:

Write 3.5897 correct to 4 significant figures. .................................................. [1]

Question 4 (a): Here are five number cards: 1, 2, 6, 7, 8. Place two cards side-by-side to show:

(i) a two-digit multiple of 7 .................................................. [1]

(ii) a two-digit square number .................................................. [1]

(iii) a two-digit cube number .................................................. [1]

(iv) a two-digit prime number .................................................. [1]

Question 4 (b):

Solve the following and write down all the numbers in the list that are irrational.

• √2
• 5.85
• (4.1)²
• π

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Question 4 (c): Put one pair of brackets into this calculation to make it correct: 7 × 5 – 2 + 3 = 42
.................................................. [1]

Question 4 (d): Work out:

(i) 3^0.729 .................................................. [1]

(ii) 54 .................................................. [1]

(iii) 4^−2 .................................................. [1]

Question 4 (e):

(i) Write 60 as a product of its prime factors .................................................. [2]

(ii) Find the lowest common multiple (LCM) of 36 and 60 .................................................. [2]

Question 5: Write in figures the number nine million eighty-two thousand five hundred and seven.
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Question 6: Write 71 496 correct to 2 significant figures.
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Question 7: From the list of numbers: 2, 3, –4, –6, –8

(a) Write down three numbers whose sum is –12.
................. , ................. , ................. [1]

(b) Write down two numbers whose product is –24.
........................... , ........................... [1]

Question 8: (a) For the integers from 40 to 70, write down:
(i) a multiple of 19.
.................................................. [1]

(ii) a common multiple of 6 and 8.
.................................................. [1]

(iii) the square root of 2500.
.................................................. [1]

(iv) a factor of 106.
.................................................. [1]

(v) an odd number where the tens digit is double the units digit.
.................................................. [1]

(vi) a number that is both a square number and a cube number.
.................................................. [1]

(vii) a number that has exactly 3 factors.
.................................................. [1]

(viii) three prime numbers.
................ , ................ , ................ [2]

(b) Write 234 as a product of its prime factors.
.................................................. [2]

(c) Write the answer to 34 × 37:
(i) in the form 3^x.
.................................................. [1]

(ii) as an integer.
.................................................. [1]

(iii) in standard form.
.................................................. [1]

(d) (i) Write 3⁻² as a fraction.
.................................................. [1]

(ii) Find the value of 3^x where x = 5.
.................................................. [1]

Question 9:
Write down, in figures, seventeen thousand and seventeen.
................................................... [1]

Question 10:
(a) Write 6789 correct to the nearest 100.
................................................... [1]

(b) Write 6789 correct to 3 significant figures.
................................................... [1]

Question 11:
(a) Write 2016 as the product of prime factors.
................................................... [3]

(b) Write 2016 in standard form.
................................................... [1]

Question 12:
The temperature in Berlin is –7 °C and the temperature in Istanbul is –3 °C.
(a) Write down how many degrees colder it is in Berlin than it is in Istanbul.
Answer(a) ........................................... °C [1]

(b) Sydney is 23 degrees warmer than Berlin. Write down the temperature in Sydney.
Answer(b) ........................................... °C [1]

Question 13:
Six donkeys are each given two 5 ml spoons of medicine three times each day. Calculate the number of whole days a 2 litre bottle of medicine will last.
Answer ........................................ days [3]

Question 14:
(a) Write 30 as a product of its prime factors.
Answer(a) ................................................ [2]

(b) Find the lowest common multiple (LCM) of 30 and 45.
Answer(b) ................................................ [2]

Question 15:
(a) Write down:
(i) two factors of 12,
Answer(a)(i) .................................................. [1]

(ii) the next prime number after 19,
Answer(a)(ii) ................................................ [1]

(iii) the cube root of 64,
Answer(a)(iii) ............................................... [1]

(iv) two million five hundred and seven in figures,
Answer(a)(iv) ................................................ [1]

(v) two multiples of 75,
Answer(a)(v) .................................................. [1]

(vi) the value of π correct to 5 significant figures.
Answer(a)(vi) .................................................. [1]

(b) Write as a percentage.
(i) 1.63
Answer(b)(i) ............................................... % [1]

(ii) 40 3
Answer(b)(ii) ............................................... % [1]

(c) (i) Write 63,521.769 correct to 1 decimal place.
Answer(c)(i) .................................................. [1]

(ii) Write 63,521.769 correct to the nearest hundred.
Answer(c)(ii) ................................................ [1]

(d) (i) Change 234 mm into metres.
Answer(d)(i) ................................................ m [1]

(ii) Change 876 m² into square centimetres.
Answer(d)(ii) ............................................... cm² [1]