Mathematics Specification B - 4MB1 PearsonEdexcel

Number Manipulation

Gbogbo ọrọ náà

Every calculation you do at IGCSE, from a percentage change to a quadratic solution, rests on a small set of number skills: knowing which operation to apply first, breaking numbers into their prime building blocks, and handling roots that refuse to simplify to a whole number. This topic gathers those foundations into one toolkit.

You will practise the order of operations, use prime factorisation to find the highest common factor and lowest common multiple, apply the laws of indices to integer, negative and fractional powers, and learn to simplify and rationalise surds so that every answer is left in its neatest, exact form.

Ebumnobi

  1. Use the ordinary processes of number manipulation including the four operations and combination of them by use of brackets
  2. Understand and use prime numbers, factors and multiples, including finding HCF and LCM in simple cases
  3. Use index notation and index laws for multiplication and division involving integer, fractional and negative powers
  4. Perform simple manipulation of surds, understanding what surds represent and their use for exact answers
  5. Rationalise the denominator
  6. Recognise and use natural numbers, integers, rational and irrational numbers

Maapụ uche

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Kaadị ncheta

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Akwụkwọ Ọmụmụ

A phone signal strength shown as a percentage, an exchange rate quoted to four decimal places, a diagonal measurement that comes out as \(\sqrt{2}\) rather than a tidy decimal: real calculations rarely stay inside the whole numbers you meet first. This topic builds the number toolkit that keeps every later topic, from algebra to trigonometry, working correctly and exactly.

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Nnyocha Ọmụmụ

Ekele diri gi maka imecha ihe karịrị na Number Manipulation. Ugbu a na ị na-enyochakwa isi echiche na echiche ndị dị mkpa, ọ bụ oge iji nwalee ihe ị ma. Ngwa a na-enye ụdị ajụjụ ọmụmụ dị iche iche emebere iji kwado nghọta gị wee nyere gị aka ịmata otú ị ghọtara ihe ndị a kụziri.

Ị ga-ahụ ngwakọta nke ụdị ajụjụ dị iche iche, gụnyere ajụjụ chọrọ ịhọrọ otu n’ime ọtụtụ azịza, ajụjụ chọrọ mkpirisi azịza, na ajụjụ ede ede. A na-arụpụta ajụjụ ọ bụla nke ọma iji nwalee akụkụ dị iche iche nke ihe ọmụma gị na nkà nke ịtụgharị uche.

Jiri akụkụ a nke nyocha ka ohere iji kụziere ihe ị matara banyere isiokwu ahụ ma chọpụta ebe ọ bụla ị nwere ike ịchọ ọmụmụ ihe ọzọ. Ekwela ka nsogbu ọ bụla ị na-eche ihu mee ka ị daa mba; kama, lee ha anya dị ka ohere maka ịzụlite onwe gị na imeziwanye.

  1. What is the value of 4 + 2 x (9 - 6)^2? A) 22 B) 40 C) 46 D) 108 Answer: A
  2. The prime factorisation of 60 is 2^2 x 3 x 5. What is the LCM of 60 and 2^3 x 3^2? A) 12 B) 180 C) 360 D) 720 Answer: C
  3. Which of the following is equal to 5^(-2)? A) -10 B) -25 C) 1/10 D) 1/25 Answer: D
  4. Which number is a surd? A) The square root of 49 B) The square root of 11 C) The square root of 100 D) The cube root of 27 Answer: B
  5. Simplify the square root of 45. A) 3 times the square root of 5 B) 5 times the square root of 3 C) 9 times the square root of 5 D) 15 times the square root of 3 Answer: A

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