Where can I download free standard form PDF worksheets with answers?

On this MathsLinks page you can download free printable standard form PDF worksheets (Qs) and full worked solutions or mark schemes (Ans) from Ken Stafford, IGCSE MT, Maths Genie, Maths4Everyone, Corbett Practice, plus a printable one-page standard form revision guide.

What GCSE grade is standard form (5D)?

Standard form (topic code 5D) is a Grade 5 number topic in GCSE Maths for Edexcel, AQA, OCR, Eduqas and IGCSE specifications.

Free Standard form Worksheets (PDF) with Answers — GCSE Maths

Free Standard form PDF Worksheets & Answers

Grade 5 • Topic 5D

Resource	Questions	Answers
Ken Stafford (F) GCSE past paper questions & solutions	Qs	Ans
Ken Stafford (H) GCSE past paper questions & solutions	Qs	Ans
IGCSE MT IGCSE (9–1) past paper booklet	Qs	Ans
Maths Genie Graded exam questions & solutions	Qs	Ans
Maths4Everyone GCSE 9–1 practice booklet & solutions	Qs	Ans
Corbett Practice Practice Questions & answers	Qs	Ans
Corbett Textbook Textbook Exercise & answers	Qs	Ans
Maths Made Easy MME worksheet & model answers	Qs	Ans
Naiker Maths Exam question booklet & solutions	Qs	Ans
Hannah Kettle Practice sheet & answers	Qs	Ans
Dr Austin (1) Practice grid / worksheet & answers	Qs	Ans
Dr Austin (2) Practice grid / worksheet & answers	Qs	Ans
1st Class Maths (Edxl) Edexcel exam questions & solutions	Qs	Ans
1st Class Maths (AQA) AQA exam questions & solutions	Qs	Ans
Dr Austin Practice grid / worksheet & answers	Qs	Ans
Metatutor Topic worksheet & worked solutions	Qs	Ans
GCSE Maths Rocket Practice questions & answers	Qs	Ans
E Classroom GCSE topic booklet & answers	Qs	Ans
PMT (Edxl) Edexcel GCSE topic questions & solutions	Qs	Ans
PMT (AQA) AQA GCSE topic questions & solutions	Qs	Ans
PMT (IGCSE) Edexcel IGCSE topic questions & solutions	Qs	Ans
The Maths Room Online topic notes & examples	Page
Cognito F Interactive online lesson & practice	Page
Cognito H Interactive online lesson & practice	Page
esheets Self-marking online worksheet	Page

Grade 5 topics
5A - Combining ratios	5B - Direct and inverse proportion
5C - Reverse percentages	5D - Standard form
5E - Speed	5F - Changing the subject
5G - Quadratic expressions	5H - Solving quadratic equations
5J - Drawing quadratic graphs	5K - Cubic/reciprocal graphs
5L - Simultaneous equations	5M - Sector areas and arc lengths
5N - Sim. equ. graphically	5P - Midpoint of a line segment
5Q - Gradient of a line	5R - Equation of a line
5S - Spheres and cones	5T - Similar shapes (lengths)
5U - Trigonometry (SOHCAHTOA)	5V - Exact trig. values
5W - Probability trees	5X - Vectors
5Y - Venn diagrams	5Z - Density
5AA - Pressure

Explanation:

A number in standard form is written as A × 10ⁿ, where 1 ≤ A < 10 and n is a whole number (positive for large numbers, negative for small decimals less than 1).

To multiply or divide in standard form, multiply or divide the front numbers and use index laws on the powers of 10 (adjusting the final answer if A is not between 1 and 10). To add or subtract, convert both numbers into ordinary numbers (or the same power of 10) first.

Example 1: Work out (4.5 × 10⁴) × (6 × 10⁵). Give your answer in standard form.

Solution:

Multiply front numbers: 4.5 × 6 = 27

Add powers of 10: 10⁴ × 10⁵ = 10⁹ → 27 × 10⁹

Adjust so 1 ≤ A < 10: 27 = 2.7 × 10¹

2.7 × 10¹ × 10⁹ = 2.7 × 10¹⁰

Answer: 2.7 × 10¹⁰

Example 2: Work out (3.2 × 10⁻³) + (4.8 × 10⁻⁴). Give your answer in standard form.

Solution:

Write as ordinary decimals:

3.2 × 10⁻³ = 0.0032 and 4.8 × 10⁻⁴ = 0.00048

Add decimals: 0.0032 + 0.00048 = 0.00368

Convert back to standard form:

Answer: 3.68 × 10⁻³

Scanned GCSE Exam Questions & Worked Solutions

GCSE Past Paper Standard form Questions & Answers

10-Question Interactive Quiz More Past Paper Questions

Past Paper Example 1 IGCSE Jan 2022 2HR Q10 3 marks

Full Paper (PDF) • Mark Scheme (PDF)

The table gives information about the population and the total amount of money, in dollars, spent on healthcare for two countries in 2016

Work out how much more was spent per person on healthcare in Luxembourg than in Austria.
Give your answer correct to the nearest whole number.

Worked Solution & Mark Scheme (3 marks)

Luxembourg per person = (3.7 × 10⁹) ÷ (6.3 × 10⁵) = $5873.0158.. M1
Austria per person = (4.2 × 10¹⁰) ÷ (8.7 × 10⁶) = $4827.5862.. M1
Difference = 5873.0158 – 4827.5862 = 1045.429... → 1045 dollars. A1

Answer: 1045 dollars

Past Paper Example 2 IGCSE Jun 2024 1F Q24 / 1H Q9 3 marks

Full Paper (PDF) • Mark Scheme (PDF)

The table gives the amount of rice produced by each of two countries in 2020

(a) Write 3.5 × 10⁷ as an ordinary number. [1 mark]

(b) Work out the amount of rice Japan produced in 2020
Give your answer in standard form. [2 marks]

Worked Solution & Mark Scheme (3 marks)

Part (a) Solution:

35 000 000

Answer (a): 35 000 000

Part (b) Solution:

820 000 + 6 780 000 = 7 600 000 = 7.6 × 10⁶ tonnes M1 A1

Answer (b): 7.6 × 10⁶ tonnes

Past Paper Example 3 GCSE Jun 2017 2H Q10 4 marks

Full Paper (PDF) • Mark Scheme (PDF)

The table shows some information about eight planets.

(a) Write down the name of the planet with the greatest mass. [1 mark]

(b) Find the difference between the mass of Venus and the mass of Mercury. [1 mark]

Worked Solution & Mark Scheme (4 marks)

Part (a) Solution:

1.898 × 10²⁷ is highest power of 10 -> Jupiter B1

Answer (a): Jupiter

Part (b) Solution:

4.869 × 10²⁴ – 3.302 × 10²³ = 4.5388 × 10²⁴ kg B1

Answer (b): 4.5388 × 10²⁴ kg

Part (c) Solution:

(4.35 × 10⁹) ÷ (4.14 × 10⁷) = 105.07... > 100, so Yes M1 A1

Answer (c): Yes, (4.35 × 10⁹) ÷ (4.14 × 10⁷) = 105.07... > 100

← 5C Reverse percentages

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Standard form

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GCSE Past Paper Standard form Questions & Answers