Standard Form: Fluency and Exam Drill (GCSE Maths) - Worksheets, Questions and Revision

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GCSE · Number - Standard Form

5.4D Standard Form: Fluency and Exam Drill

EDEXCEL 1MA1 · Calculators not allowed · about 60 minutes

Total Marks

Name: _______________________________ Date: ____ / ____ / ______

Answer ALL questions. Show all your working.

Write the number 68000 in standard form.

(Total for Question 1 is 1 mark)

Write the number 0.000047 in standard form.

(Total for Question 2 is 1 mark)

Write 9.1 x 10⁴ as an ordinary number.

(Total for Question 3 is 1 mark)

Write 2.06 x 10^-3 as an ordinary number.

(Total for Question 4 is 1 mark)

Four students each write the number 84000 in standard form.

Amir writes 8.4 x 10⁴
Ben writes 84 x 10³
Chloe writes 0.84 x 10⁵
Dev writes 8.4 x 10³

Exactly one student has written the number correctly in standard form. Write down the name of that student.

(Total for Question 5 is 1 mark)

Write the number 0.0000059 in standard form.

(Total for Question 6 is 1 mark)

Write 7.2 x 10^-4 as an ordinary number.

(Total for Question 7 is 1 mark)

Write 3.15 x 10⁶ as an ordinary number.

(Total for Question 8 is 1 mark)

Which is larger, 6.4 x 10³ or 5.9 x 10⁴? Write down the larger number, in standard form.

(Total for Question 9 is 1 mark)

Here are four numbers written in standard form.

7.1 x 10² 6 x 10³ 8.4 x 10¹ 2.3 x 10³

Put the numbers in order of size, starting with the smallest.

(Total for Question 10 is 2 marks)

Write the number 0.000000083 in standard form.

(Total for Question 11 is 1 mark)

Write 4 x 10^-1 as an ordinary number.

(Total for Question 12 is 1 mark)

Work out (3 x 10⁴) x (2 x 10³). Give your answer in standard form.

(Total for Question 13 is 2 marks)

Work out (9 x 10⁷) / (3 x 10²). Give your answer in standard form.

(Total for Question 14 is 2 marks)

Work out (4 x 10⁵) x (5 x 10³). Give your answer in standard form.

(Total for Question 15 is 2 marks)

Work out (6 x 10²) / (1.5 x 10^-3). Give your answer in standard form.

(Total for Question 16 is 2 marks)

A bacterium has a diameter of 4 x 10^-6 m.
A dust mite has a diameter of 2 x 10^-4 m.
Work out how many times bigger the diameter of the dust mite is than the diameter of the bacterium.

(Total for Question 17 is 3 marks)

Work out (5.4 x 10⁵) + (6 x 10⁴). Give your answer in standard form.

(Total for Question 18 is 3 marks)

A scientist collects a sample of fine sand.
Each grain of sand has a mass of 4 x 10^-4 g.
The sample contains 5 x 10⁶ grains of sand.

(a)Work out the total mass of the sample. Give your answer, in grams, in standard form.(3)

(b)Given that 1 kg = 1000 g, work out the total mass of the sample in kg.(2)

(Total for Question 19 is 5 marks)

Three stars have these distances from Earth, in light-years.

Star P: 3.6 x 10² Star Q: 9 x 10¹ Star R: 1.4 x 10³

Put the stars in order of distance from Earth, starting with the nearest. Show how you have compared the distances.

(Total for Question 20 is 2 marks)

The wavelength of a particular red light is 6.5 x 10^-7 m.
The wavelength of a particular radio wave is 1.3 x 10¹ m.
Work out how many times longer the wavelength of the radio wave is than the wavelength of the red light. Give your answer in standard form.

(Total for Question 21 is 3 marks)

(4 x 10ⁿ) x (2 x 10³) = 8 x 10⁸

Find the value of n.

(Total for Question 22 is 2 marks)

A pupil says that 0.00038 is equal to 38 x 10^-5 written in standard form.
A second pupil says the first pupil is wrong, and that the correct standard form is 3.8 x 10^-4.
By writing both expressions as ordinary numbers, determine which pupil (if either) is correct, and explain any error in the incorrect statement.

(Total for Question 23 is 3 marks)

M² = 4 x 10¹⁰, where M > 0.
Find the value of M. Give your answer in standard form.

(Total for Question 24 is 3 marks)

Solve the equation (5 x 10ⁿ)² = 2.5 x 10¹⁵, where n is an integer.

(Total for Question 25 is 3 marks)

Mark scheme · 5.4D Standard Form: Fluency and Exam Drill

Question 1

B1 6.8 x 10⁴ oe
Answer: 6.8 x 10⁴

Question 2

B1 4.7 x 10^-5 oe
Answer: 4.7 x 10^-5

Question 3

B1 91000 cao
Answer: 91000

Question 4

B1 0.00206 cao
Answer: 0.00206

Question 5

B1 Amir
Answer: Amir (8.4 x 10⁴ is correctly in standard form, since 1 ≤ 8.4 < 10, and 8.4 x 10⁴ = 84000)

Question 6

B1 5.9 x 10^-6 oe
Answer: 5.9 x 10^-6

Question 7

B1 0.00072 cao
Answer: 0.00072

Question 8

B1 3150000 cao
Answer: 3150000

Question 9

B1 5.9 x 10⁴ oe (59000)
Answer: 5.9 x 10⁴

Question 10

M1 converts numbers to a comparable form, e.g. as ordinary numbers 84, 710, 2300, 6000 oe
A1 8.4 x 10¹, 7.1 x 10², 2.3 x 10³, 6 x 10³ cao, all four in correct order
Answer: 8.4 x 10¹, 7.1 x 10², 2.3 x 10³, 6 x 10³

Question 11

B1 8.3 x 10^-8 oe
Answer: 8.3 x 10^-8

Question 12

B1 0.4 cao
Answer: 0.4

Question 13

M1 3 x 2 = 6 and 10⁴ x 10³ = 10⁷ seen, or 6 x 10⁷ oe unsimplified
A1 6 x 10⁷ cao
Answer: 6 x 10⁷

Question 14

M1 9 / 3 = 3 and 10⁷ / 10² = 10⁵ seen, or 3 x 10⁵ oe unsimplified
A1 3 x 10⁵ cao
Answer: 3 x 10⁵

Question 15

M1 4 x 5 = 20 and 10⁵ x 10³ = 10⁸ seen, or 20 x 10⁸ oe unsimplified
A1 2 x 10⁹ cao (converts 20 x 10⁸ to correct standard form)
Answer: 2 x 10⁹

Question 16

M1 6 / 1.5 = 4 and 10² / 10^-3 = 10⁵ seen, or 4 x 10⁵ oe unsimplified
A1 4 x 10⁵ cao
Answer: 4 x 10⁵

Question 17

M1 sets up (2 x 10^-4) / (4 x 10^-6)
M1 2 / 4 = 0.5 and 10^-4 / 10^-6 = 10² seen, or 0.5 x 10² oe unsimplified
A1 50 cao
Answer: 50 (times bigger)

Question 18

M1 writes both numbers to the same power of 10, e.g. 54 x 10⁴ + 6 x 10⁴ oe
M1 dependent, adds correctly to give 60 x 10⁴ oe
A1 6 x 10⁵ cao
Answer: 6 x 10⁵

Question 19

(a) M1 multiplies coefficients, 4 x 5 = 20
(a) M1 dependent, adds powers of 10, -4 + 6 = 2, giving 20 x 10²
(a) A1 2 x 10³ cao (g)
(a) Answer: 2 x 10³ g
(b) M1 ft, divides their part (a) answer by 1000, e.g. (2 x 10³) / (1 x 10³)
(b) A1 ft, 2 cao (kg)
(b) Answer: 2 kg

Question 20

M1 converts distances to a comparable form, e.g. as ordinary numbers 360, 90, 1400 oe
A1 Q, P, R cao, all three in correct order (nearest first)
Answer: Star Q, Star P, Star R

Question 21

M1 sets up (1.3 x 10¹) / (6.5 x 10^-7)
M1 1.3 / 6.5 = 0.2 and 10¹ / 10^-7 = 10⁸ seen, or 0.2 x 10⁸ oe unsimplified
A1 2 x 10⁷ cao
Answer: 2 x 10⁷

Question 22

M1 multiplies coefficients, 4 x 2 = 8, matching the given coefficient, so equates powers of 10, giving n + 3 = 8
A1 n = 5 cao
Answer: n = 5

Question 23

M1 converts 38 x 10^-5 and/or 3.8 x 10^-4 to an ordinary number, showing both equal 0.00038
B1 states the second pupil is correct
B1 dependent on M1, explains that although 38 x 10^-5 is numerically equal to 0.00038, it is not in standard form because 38 is not between 1 and 10, whereas 3.8 x 10^-4 is correctly in standard form because 3.8 is between 1 and 10
Answer: The second pupil is correct; 3.8 x 10^-4 is the correctly written standard form of 0.00038.

Question 24

M1 finds the square root of the coefficient, √4 = 2
M1 finds the square root of the power of 10, √10¹⁰ = 10⁵, e.g. by writing 10¹⁰ as (10⁵)²
A1 2 x 10⁵ cao
Answer: M = 2 x 10⁵

Question 25

M1 squares the left-hand side, (5 x 10ⁿ)² = 25 x 10²ⁿ oe unsimplified
M1 dependent, converts to standard form and equates powers, 25 x 10²ⁿ = 2.5 x 10^{2n + 1}, so 2n + 1 = 15
A1 n = 7 cao
Answer: n = 7

Question 25

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Standard Form: Fluency and Exam Drill (GCSE Maths) - Worksheets, Questions and Revision

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