Using a Calculator (Copy)
Practice Questions — 1.14 Using a Calculator
Question 1
A car travels 315 km in 4 hours 30 minutes.
(a) Enter the time in hours on your calculator.
(b) Find the average speed in km/h.
Question 2
Evaluate on a calculator:
(a) (45.67 × 23.8) ÷ 19.4
(b) √(245.76)
(c) (3.2 × 10⁵) ÷ (8 × 10²)
Question 3
A train leaves at 08:45 and arrives at 11:25.
(a) Enter the journey time in hours.
(b) If the distance was 185 km, find the average speed.
Question 4
Use your calculator to evaluate and give the answer to 3 significant figures:
(a) (56.7² − 43.2²) ÷ 12.5
(b) (3.1416 × 12.8²) ÷ 2
(c) 5.9³ ÷ 14.25
Question 5
Convert correctly for calculator entry:
(a) 2 hours 45 minutes into hours
(b) 3 hours 20 minutes into hours
(c) 1 hour 15 minutes into hours
Written and Compiled By Sir Hunain Zia, World Record Holder With 154 Total A Grades, 7 Distinctions and 11 World Records For Educate A Change O Level And IGCSE Mathematics Full Scale Course
Question 6
A rectangular field measures 48.5 m by 32.7 m.
Use your calculator to find:
(a) the perimeter to 1 decimal place
(b) the area to 2 decimal places.
Question 7
Evaluate the following, leaving your answer in standard form to 2 significant figures:
(a) (4.7 × 10⁶) ÷ (9.4 × 10³)
(b) (6.3 × 10⁴) × (2.8 × 10⁻²)
Question 8
Enter carefully into your calculator and find:
(a) sin 37°
(b) cos 52°
(c) tan 68°
Give answers to 3 significant figures.
Question 9
A sum of Rs. 72 000 earns 8.5% compound interest per year.
Find the total amount after 2 years, giving your answer to the nearest rupee.
Question 10
A runner completes a race in 1 hour 18 minutes 45 seconds.
Express this time in hours correct to 4 decimal places.
Written and Compiled By Sir Hunain Zia, World Record Holder With 154 Total A Grades, 7 Distinctions and 11 World Records For Educate A Change O Level And IGCSE Mathematics Full Scale Course
Answer key and explanations — 1.14 Using a Calculator
1.
(a) 4 h 30 min = 4.5 h (since 30 min = 0.5 h)
(b) Speed = 315 ÷ 4.5 = 70 km/h
Explanation: Convert time correctly into decimal hours before division.
2.
(a) (45.67 × 23.8) ÷ 19.4 = 1086.946 ÷ 19.4 ≈ 56.0
(b) √245.76 = 15.696 ≈ 15.7 (3 s.f.)
(c) (3.2 × 10⁵) ÷ (8 × 10²) = 3.2 ÷ 8 × 10^(5−2) = 0.4 × 10³ = 4.0 × 10²
Explanation: Enter carefully; apply index laws where helpful.
3.
Journey time = 2 h 40 min = 2.667 h
Speed = 185 ÷ 2.667 ≈ 69.3 km/h
Explanation: Convert minutes to a fraction of an hour: 40 ÷ 60 = 0.667.
4.
(a) (56.7² − 43.2²) ÷ 12.5 = (3216.09 − 1866.24) ÷ 12.5 = 1349.85 ÷ 12.5 = 108 ≈ 108 (3 s.f.)
(b) (3.1416 × 12.8²) ÷ 2 = (3.1416 × 163.84) ÷ 2 = 514.718 ÷ 2 = 257 ≈ 257 (3 s.f.)
(c) 5.9³ ÷ 14.25 = 205.379 ÷ 14.25 = 14.4 (3 s.f.)
5.
(a) 2 h 45 min = 2.75 h
(b) 3 h 20 min = 3.333 h
(c) 1 h 15 min = 1.25 h
Explanation: Convert minutes into fraction of hour (minutes ÷ 60).
Written and Compiled By Sir Hunain Zia, World Record Holder With 154 Total A Grades, 7 Distinctions and 11 World Records For Educate A Change O Level And IGCSE Mathematics Full Scale Course
6.
Perimeter = 2(48.5 + 32.7) = 2 × 81.2 = 162.4 m
Area = 48.5 × 32.7 = 1587.95 ≈ 1587.95 m² → 1587.95 rounded = 1587.95 (to 2 d.p.)
Answer: Perimeter = 162.4 m, Area = 1587.95 m²
7.
(a) (4.7 × 10⁶) ÷ (9.4 × 10³) = (4.7 ÷ 9.4) × 10^(6−3) = 0.5 × 10³ = 5.0 × 10²
(b) (6.3 × 10⁴) × (2.8 × 10⁻²) = (6.3 × 2.8) × 10^(4−2) = 17.64 × 10² = 1.76 × 10³ (2 s.f.)
8.
(a) sin 37° ≈ 0.601
(b) cos 52° ≈ 0.616
(c) tan 68° ≈ 2.61
Explanation: Ensure calculator is in degree mode.
9.
Compound interest: A = P(1 + r/100)ⁿ
= 72 000(1.085)² = 72 000 × 1.177225 = Rs. 84 759 (nearest rupee)
10.
1 h 18 min 45 s = 1 + 18/60 + 45/3600
= 1 + 0.3 + 0.0125 = 1.3125 h
To 4 d.p. = 1.3125 h
Written and Compiled By Sir Hunain Zia, World Record Holder With 154 Total A Grades, 7 Distinctions and 11 World Records For Educate A Change O Level And IGCSE Mathematics Full Scale Course