IB · Mathematics: Applications & Interpretation SL & HL · Number & algebra

Standard form & errors: IB Mathematics: Applications & Interpretation questions with answers

Free Standard form & errors questions for IB Mathematics: Applications & Interpretation (SL & HL), part of Number & algebra. Each question has the answer and the marking points an examiner would look for.

Generate a full Standard Form & Errors worksheet →All Number & algebra questions

Standard form & errors practice questions

Question 1Structured · 7 marksA* challenge

A rectangular field is measured as 15.6 m long and 7.3 m wide, each correct to one decimal place.

(a)

Write down the upper bound of the length.

[1]
(b)

Find the upper and lower bounds of the area of the field.

[3]
(c)

The area is calculated as length × width using the measured values. Find the greatest possible percentage error in this calculated area.

[3]
Show answers and mark scheme
PartAnswer and marking pointsMarks
(a)15.65 m
15.65 m A1
1
(b)115, 113 m2
upper × upper or lower × lower (M1)
UB 115 m2 A1
LB 113 m2 A1
3
(c)1.01%
calculated area 114 m2 (A1)
largest error is against the lower bound (M1)
1.01% A1
3
Question 2Structured · 5 marks

The mean distance from the Sun to Neptune is 4.50 × 109 km. Light travels at 3.00 × 105 km s−1.

(a)

Find the time taken for light to travel this distance, in seconds. Give your answer in the form a × 10k, where 1 ≤ a < 10 and k ∈ ℤ.

[3]
(b)

Sam estimates the time to be 16000 s. Find the percentage error in Sam’s estimate.

[2]
Show answers and mark scheme
PartAnswer and marking pointsMarks
(a)1.50 × 104 s
4.50 × 1093.00 × 105 (M1)
15000 (A1)
1.50 × 104 s A1
3
(b)6.67%
16000 − 1500015000 × 100% (M1)
6.67% A1
2
Question 3Structured · 7 marksA* challenge

A rectangular field is measured as 18.2 m long and 9.4 m wide, each correct to one decimal place.

(a)

Write down the upper bound of the length.

[1]
(b)

Find the upper and lower bounds of the area of the field.

[3]
(c)

The area is calculated as length × width using the measured values. Find the greatest possible percentage error in this calculated area.

[3]
Show answers and mark scheme
PartAnswer and marking pointsMarks
(a)18.25 m
18.25 m A1
1
(b)172, 170 m2
upper × upper or lower × lower (M1)
UB 172 m2 A1
LB 170 m2 A1
3
(c)0.812%
calculated area 171 m2 (A1)
largest error is against the lower bound (M1)
0.812% A1
3
Question 4Structured · 5 marks

The mean distance from the Earth to the Sun is 1.50 × 108 km. Light travels at 3.00 × 105 km s−1.

(a)

Find the time taken for light to travel this distance, in seconds. Give your answer in the form a × 10k, where 1 ≤ a < 10 and k ∈ ℤ.

[3]
(b)

Sam estimates the time to be 450 s. Find the percentage error in Sam’s estimate.

[2]
Show answers and mark scheme
PartAnswer and marking pointsMarks
(a)4.99 × 102 s
1.50 × 1083.00 × 105 (M1)
499 (A1)
4.99 × 102 s A1
3
(b)9.76%
450 − 499499 × 100% (M1)
9.76% A1
2
Question 5Structured · 7 marksA* challenge

A rectangular field is measured as 15.6 m long and 9.4 m wide, each correct to one decimal place.

(a)

Write down the upper bound of the length.

[1]
(b)

Find the upper and lower bounds of the area of the field.

[3]
(c)

The area is calculated as length × width using the measured values. Find the greatest possible percentage error in this calculated area.

[3]
Show answers and mark scheme
PartAnswer and marking pointsMarks
(a)15.65 m
15.65 m A1
1
(b)148, 145 m2
upper × upper or lower × lower (M1)
UB 148 m2 A1
LB 145 m2 A1
3
(c)0.858%
calculated area 147 m2 (A1)
largest error is against the lower bound (M1)
0.858% A1
3
Question 6Structured · 5 marks

The mean distance from the Earth to the Moon is 3.84 × 105 km. A spacecraft travels at 11.0 km s−1.

(a)

Find the time taken for a spacecraft to travel this distance, in seconds. Give your answer in the form a × 10k, where 1 ≤ a < 10 and k ∈ ℤ.

[3]
(b)

Sam estimates the time to be 33000 s. Find the percentage error in Sam’s estimate.

[2]
Show answers and mark scheme
PartAnswer and marking pointsMarks
(a)3.49 × 104 s
3.84 × 10511.0 (M1)
34909 (A1)
3.49 × 104 s A1
3
(b)5.47%
33000 − 3490934909 × 100% (M1)
5.47% A1
2

More Number & algebra questions

Sequences & seriesFinancial mathematicsExponents & logarithmic scalesSystems of equationsComplex numbersMatrices & eigenvalues

Want a mentor, not just a paper?

Riyaz Shaikh has mentored IGCSE, IB and A Level students for 15+ years, one-on-one, online and in Mumbai. The hardest questions on this site are the ones he uses to find a student's weak points.

Meet Riyaz →

Original IB-style practice questions written for mentorriyaz.in. These are not IB past paper questions, and this site is not affiliated with or endorsed by the International Baccalaureate Organization. Updated 2026-11-04. Paper generator · mentorriyaz.in