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1. Tema: Order of operations

   1. Work out 3 + 4 × 5.

   A23B35C27D60
   Solución

   A. 23

   • Multiply before adding: 4 × 5 = 20.
   • 3 + 20 = 23.

2. Tema: Fractions and decimals

   2. Write 0.375 as a fraction in its simplest form.

   A375/100B3/5C37/100D3/8
   Solución

   D. 3/8

   • 0.375 = 375/1000.
   • Divide top and bottom by 125: 3/8.

3. Tema: Rounding

   3. Round 4.876 to 1 decimal place.

   A4.8B5.0C4.9D4.88
   Solución

   C. 4.9

   • Look at the second decimal place: 7.
   • 7 is 5 or more, so round the first decimal place up: 4.9.

4. Tema: Prime factors

   4. Write 56 as a product of its prime factors.

   A2 × 28B2³ × 7C2² × 14D7 × 8
   Solución

   B. 2³ × 7

   • 56 = 2 × 28 = 2 × 2 × 14 = 2 × 2 × 2 × 7.
   • So 56 = 2³ × 7.

5. Tema: HCF

   5. Find the highest common factor of 24 and 36.

   A12B6C72D4
   Solución

   A. 12

   • Factors of 24: 1, 2, 3, 4, 6, 8, 12, 24.
   • Factors of 36: 1, 2, 3, 4, 6, 9, 12, 18, 36.
   • The highest one in both lists is 12.

6. Tema: LCM

   6. Find the lowest common multiple of 6 and 8.

   A48B2C14D24
   Solución

   D. 24

   • Multiples of 6: 6, 12, 18, 24, ...
   • Multiples of 8: 8, 16, 24, ...
   • The first one in both lists is 24.

7. Tema: Fractions

   7. Work out 2/3 + 1/4.

   A3/7B3/12C11/12D2/12
   Solución

   C. 11/12

   • Use a common denominator of 12: 2/3 = 8/12 and 1/4 = 3/12.
   • 8/12 + 3/12 = 11/12.

8. Tema: Standard form

   8. Write 45 000 in standard form.

   A45 × 10³B4.5 × 10⁴C4.5 × 10³D0.45 × 10⁵
   Solución

   B. 4.5 × 10⁴

   • Standard form is A × 10ⁿ with 1 ≤ A < 10.
   • 45 000 = 4.5 × 10 000 = 4.5 × 10⁴.

9. Tema: Powers

   9. Work out 5² − 3³.

   A−2B2C4D−4
   Solución

   A. −2

   • 5² = 25 and 3³ = 27.
   • 25 − 27 = −2.

10. Tema: Negative numbers

    10. The temperature is −4 °C. It rises by 9 °C. What is the new temperature?

    A−13 °CB13 °CC−5 °CD5 °C
    Solución

    D. 5 °C

    • Start at −4 and count up 9.
    • −4 + 9 = 5 °C.