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2³ × 2⁴ works out to 128 and log₁₀ 1000 is 3, so this IB sheet opens with an exponent product and a logarithm. The key records 4.5 × 10⁻⁴ in standard form, 5√2 as a surd and 4 as a later value.
Key Takeaways
2³ × 2⁴ = 128 (Q1).
log₁₀ 1000 = 3 (Q2).
Q3 records 4.5 × 10⁻⁴ as a standard form answer.
Section A: Multiple Choice Questions (1 Mark Each)
Choose the correct option for each question.
1.
What is 2³ × 2⁴?
(a) 128 (b) 64 (c) 16 (d) 256
2.
What is log₁₀ 1000?
(a) 10 (b) 100 (c) 3 (d) 4
3.
Write 0.00045 in scientific notation.
(a) 4.5 × 10⁻⁴ (b) 4.5 × 10⁴ (c) 45 × 10⁻⁵ (d) 0.45 × 10⁻³
4.
Simplify 6x³ ÷ 2x where x is not zero.
(a) 3x³ (b) 3x² (c) 12x² (d) 8x
5.
Simplify √50.
(a) 2√5 (b) 5√2 (c) 10√5 (d) 25√2
6.
Evaluate 8 to the power 2/3.
(a) 2 (b) 4 (c) 16 (d) 64
Section B: Short Answer Type Questions (2 Marks Each)
Show all steps clearly.
7.
Evaluate 5² × 5³ without a calculator.
8.
Write 3.4 × 10⁶ in ordinary decimal form.
9.
Simplify log₃ 81.
10.
Simplify √72.
11.
Evaluate (10²)³ ÷ 10⁴.
12.
Solve 2ˣ = 32.
13.
Write 0.0072 in standard form.
14.
Simplify (2a³b²)².
Section C: Numericals & Word Problems (3 Marks Each)
Apply the concepts to solve the problems. Show all working.
15.
A population starts at 50 000 and grows at 4% per year. Find the population after 5 years.
16.
A phone worth $1200 loses 15% of its value each year. Find its value after 3 years.
17.
A bacteria colony starts with 1000 cells and doubles every 2 hours. Find the number of cells after 8 hours.
18.
Anya invests $8000 at 5% interest compounded annually. Find the balance after 4 years.
19.
An earthquake has amplitude 1000 times the reference level. If M = log₁₀(A ÷ A₀), find the magnitude M.
20.
A radioactive sample starts at 40 g and has a half-life of 10 years. Find the mass remaining after 30 years.
Answer Key
1. a) 128
2. c) 3
3. a) 4.5 × 10⁻⁴
4. b) 3x²
5. b) 5√2
6. b) 4
7. Refer to solution guide.
8. Refer to solution guide.
9. Refer to solution guide.
10. Refer to solution guide.
11. Refer to solution guide.
12. Refer to solution guide.
13. Refer to solution guide.
14. Refer to solution guide.
15. Refer to solution guide.
16. Refer to solution guide.
17. Refer to solution guide.
18. Refer to solution guide.
19. Refer to solution guide.
20. Refer to solution guide.
End of Worksheet
People Also Ask
What is 2³ × 2⁴?
128, option (a) in this worksheet (Q1).
What is log₁₀ 1000?
3, option (c) in this worksheet (Q2).
How is 0.00045 written in standard form?
4.5 × 10⁻⁴, option (a) in this worksheet (Q3).