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Pack B — Fluency

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Ecolint Campus des NationsMathematics
Year 7 · 7.1 Positive Integers

Pack B · Fluency

Name: _________________________________
Date: _________________ Class: ___________

Answer all questions. Show your working. Questions are grouped by challenge level.

BronzeQuestions 1–10
  1. 1.
    Fill in the missing digit: 4_3 + 378 = 841. Which digit is missing and in which place? Justify your answer.
     
  2. 2.
    Round 7819 to the nearest thousand and name the digit that decided the rounding. Justify.
     
  3. 3.
    If 741 − ?? = 448, what is the missing number? Show how you would check your answer.
     
  4. 4.
    Without fully calculating, decide: is 47 × 8 closer to 350 or 400? Justify.
     
  5. 5.
    Is 5913 divisible by 3? Use short division to check. Show your working and state whether there is a remainder.
     
  6. 6.
    Is 135 divisible by 9? Use short division to find out. Show enough working to be sure.
     
  7. 7.
    Find ONE factor of 48 (other than 1 and 48) and justify that it is a factor.
     
  8. 8.
    Which is the smallest multiple of 9 that is greater than 50? Justify.
     
  9. 9.
    Is 43 a prime number? Justify with at least one trial division.
     
  10. 10.
    Without working out the exact value of 727^2, decide: is 727^2 greater or less than 50? Justify.
     
SilverQuestions 11–20
  1. 11.
    Round 8352 to the nearest hundred.
     
  2. 12.
    Calculate 5384 + 2769.
     
  3. 13.
    Calculate 7104 − 3857.
     
  4. 14.
    Calculate 2484 ÷ 9.
     
  5. 15.
    Work out 12 + 4 × 7 using the correct order of operations.
     
  6. 16.
    Find the HCF of 30 and 42.
     
  7. 17.
    Find the LCM of 4 and 10.
     
  8. 18.
    What is 5 cubed? Write n3{{n}}^3.
     
  9. 19.
    Write 30 as a product of prime factors.
     
  10. 20.
    Each notebook costs £7. How much do 12 notebooks cost?
     
GoldQuestions 21–30
  1. 21.
    Work out (8+6)×3−20÷4(8 + 6) \times 3 - 20 \div 4.
     
  2. 22.
    Find the HCF of 20, 28 and 36.
     
  3. 23.
    Express 120 as a product of prime factors in index form.
     
  4. 24.
    Work out n3\sqrt[3]{{{n}}}.
     
  5. 25.
    Without calculating exactly, decide which is larger: 31 × 34 or 32 × 33. Explain your reasoning.
     
  6. 26.
    Calculate b2×5{{b}}^2 \times 5.
     
  7. 27.
    Find a number that is both a multiple of 4 and a factor of 48.
     
  8. 28.
    Estimate 63 × 29 by rounding each number to 1 significant figure.
     
  9. 29.
    Apples cost 45p each. Oranges cost 60p each. Sam buys 3 apples and 4 oranges and pays with a £5 note. How much change does he receive?
     
  10. 30.
    Work out (82−4)÷6+3(8^2 - 4) \div 6 + 3.
     
PlatinumQuestions 31–40
  1. 31.
    Given p=23×3×5p = 2^3 \times 3 \times 5 and q=22×32×7q = 2^2 \times 3^2 \times 7, find the HCF and LCM of pp and qq.
     
  2. 32.
    Find the largest prime factor of 156.
     
  3. 33.
    In the multiplication below, each letter stands for a different digit. Find A and B.
    4A‾×3=14B‾\overline{4A} \times 3 = \overline{14B}
     
  4. 34.
    Two whole numbers have HCF = 4 and LCM = 48. Find all possible pairs of numbers.
     
  5. 35.
    Is 97 a prime number? Show your reasoning.
     
  6. 36.
    A number satisfies all of these: it is two-digit, it is prime, and the sum of its digits is 8. Find all such numbers.
     
  7. 37.
    Two whole numbers aa and bb satisfy a×b=60a \times b = 60 and a+b=17a + b = 17, with a>ba > b. Find aa and bb.
     
  8. 38.
    Explain why the product of any two consecutive even numbers is always divisible by 8.
     
  9. 39.
    Work out (102−(3+2)2)÷((10−3−2)×5)(10^2 - (3 + 2)^2) \div ((10 - 3 - 2) \times 5).
     
  10. 40.
    A school raises £2200 for a trip. Transport costs £640. The remaining money is split equally among 40 students. Each student pays £12 on top of their share. How much does each student have in total to spend?