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HIGHER

5.4H Standard Form: Higher Tier Practice

EDEXCEL Edexcel 1MA1 · Calculator allowed · about 60 minutes

Total Marks

Name: _______________________________ Date: ____ / ____ / ______

Answer ALL questions. Show all your working.

Write 0.000742 in standard form.

(Total for Question 1 is 1 mark)

Write 4.06 x 10⁵ as an ordinary number.

(Total for Question 2 is 1 mark)

Work out (3.5 x 10⁴) x (2.2 x 10^-3). Give your answer in standard form.

(Total for Question 3 is 2 marks)

Work out (6.0 x 10⁷) / (2.5 x 10³). Give your answer in standard form.

(Total for Question 4 is 2 marks)

Work out 4.2 x 10⁶ + 3.6 x 10⁵. Give your answer in standard form.

(Total for Question 5 is 2 marks)

Estimate the product of 9.8 x 10² and 4.05 x 10^-1 to 2 significant figures. Give your answer in standard form.

(Total for Question 6 is 2 marks)

Show that if 2.5 x 10^-3 x = 6.25 x 10¹ then x = 2.5 x 10⁴.

(Total for Question 7 is 3 marks)

Which is larger, 3.6 x 10⁸ or 2.9 x 10⁹? Explain your answer briefly.

(Total for Question 8 is 1 mark)

The luminosity of a distant star is 3.2 x 10²⁶ W. The luminosity of the Sun is 3.828 x 10²⁶ W. Find the ratio star : Sun to 2 significant figures and give your answer in standard form.

(Total for Question 9 is 3 marks)

A quantity y and x are related by y/x = k, where when x = 3.2 x 10³, y = 6.4 x 10^-2. Work out k and give your answer in standard form.

(Total for Question 10 is 4 marks)

Write 0.000000432 in engineering notation (a power of 10 with exponent a multiple of 3).

(Total for Question 11 is 2 marks)

Given A = 5.12 x 10³ and B = 3.87 x 10², calculate (A + B) / (A - B). Give your answer to 4 significant figures.

(Total for Question 12 is 4 marks)

Mark scheme · 5.4H Standard Form: Higher Tier Practice

Question 1

B1 7.42 x 10^-4 cao
Answer: 7.42 x 10^-4

Question 2

B1 406000 cao
Answer: 406000

Question 3

M1 multiply coefficients and add powers: 3.5 x 2.2 and 10^{4 + -3} method
A1 7.7 x 10¹ cao
Answer: 7.7 x 10¹

Question 4

M1 divide coefficients and subtract powers: 6.0/2.5 and 10^{7 - 3}
A1 2.4 x 10⁴ cao
Answer: 2.4 x 10⁴

Question 5

M1 convert to same power of 10 and add (e.g. 4.2 x 10⁶ + 0.36 x 10⁶ or equivalent shown)
A1 4.56 x 10⁶ cao
Answer: 4.56 x 10⁶

Question 6

M1 multiply the numbers: 9.8 x 4.05 x 10^{2 + -1} or equivalent method
A1 4.0 x 10² cao (396.9 rounded to 2 s.f.)
Answer: 4.0 x 10²

Question 7

M1 divide both sides by 2.5 x 10^-3 showing 6.25/2.5 and 10^{1 - -3} or equivalent
M1 evaluate 6.25/2.5 = 2.5
A1 2.5 x 10⁴ cso
Answer: 2.5 x 10⁴

Question 8

B1 2.9 x 10⁹ is larger, because exponent 9 > 8 so it is 10 times larger order of magnitude oe
Answer: 2.9 x 10⁹ is larger because its power of 10 is greater (10⁹ vs 10⁸).

Question 9

M1 divide 3.2 x 10²⁶ by 3.828 x 10²⁶ or show equivalent calculation
M1 evaluate ratio 3.2/3.828 = 0.8360... shown
A1 8.4 x 10^-1 cao (0.84 to 2 s.f.)
Answer: 8.4 x 10^-1

Question 10

M1 substitute and divide: k = (6.4 x 10^-2) / (3.2 x 10³) shown
M1 divide coefficients 6.4/3.2 = 2.0 and subtract exponents -2 - 3 = -5 or equivalent exponent step
A1 2.0 x 10^-5 cao
B1 statement that k = 2.0 x 10^-5 (coefficient in standard form between 1 and 10) oe
Answer: 2.0 x 10^-5

Question 11

M1 express number with exponent multiple of 3, e.g. move decimal to give 432 x 10^-9 shown
A1 432 x 10^-9 cao
Answer: 432 x 10^-9

Question 12

M1 convert to ordinary numbers or show sum and difference in standard form: A + B = 5120 + 387 and A - B = 5120 - 387
M1 evaluate sum 5507 and difference 4733 or show correct intermediate values
A1 5507 / 4733 = 1.163532... correct to at least 4 s.f.
A1 1.164 cao (answer rounded to 4 significant figures)
Answer: 1.164

Standard Form: Higher Tier Practice - Worksheets, Questions and Revision