# Standard Form Exam Questions: Grade B

Standard Form Exam Questions: Grade B

Standard Form Exam Questions Grade B (Includes Mark Scheme) The Winston Churchill School 1 1. p = 4 � 10 4 q = 1.25 � 10 Calculate the value of x. Give your answer in standard form. ..................................... (Total 2 marks) 5 p-q x = pq 2. The engine of a new aircraft had a major inspection after 1.2 � 10 hours flying time. The aircraft flies at an average speed of 900 km/h. (a) Calculate the distance travelled by the new aircraft before its engine had a major inspection. Give your answer in standard form. 4 ...................... km (3) In 2000 the aircraft carried a total of 1.2 � 10 passengers. 4 In 2001 the aircraft carried a total of 9 �10 passengers. (b) Calculate the difference in the number of passengers the aircraft carried in 2000 and in 2001. Give your answer as an ordinary number 5 .......................... (2) (Total 5 marks) x= 3. 5 p-q pq p = 4 � 10 4 q = 1.25 � 10 (a) Calculate the value of x. Give your answer in standard form. .................................... (2) (b) Make q the subject of the formula x= p-q pq q = .................................. (4) (Total 6 marks) 4. A spaceship travelled for 6 � 10 hours at a speed of 8 � 10 km/h. (a) Calculate the distance travelled by the spaceship. Give your answer in standard form. 2 4 ........................... km (3) The Winston Churchill School 3 One month an aircrfat travelled 2 � 10 km. 4 The next month the aircraft travelled 3 � 10 km. (b) Calculate the total distance travelled by the aircraft in the two months. Give your answer as an ordinary number. 5 ........................... km (2) (Total 5 marks) 5. a = 3 � 10 7 b = 2 � 10 8 ab y =a+b 2 Find y. Give your answer in standard form correct to 2 significant figures. y = ................................... (Total 3 marks) 6. A floppy disk can store 1 440 000 bytes of data. (a) Write the number 1 440 000 in standard form. .......................................... (1) A hard disk can store 2.4 � 10 bytes of data. (b) Calculate the number of floppy disks needed to store the 2.4 � 10 bytes of data. 9 9 .......................................... (3) (Total 4 marks) 7. (a) (i) Write 40 000 000 in standard form. ................................... (ii) Write 3 � 10 as an ordinary number. �5 ................................... (2) The Winston Churchill School 5 (b) �5 Work out the value of 3 � 10 � 40 000 000 Give your answer in standard form. ................................... (2) (Total 4 marks) 8. (a) Write the number 40 000 000 in standard form. ................................. (1) (b) Write 1.4 � 10 as an ordinary number. �5 ................................. (1) (c) Work out (5 � 10 ) � (6 � 10 ) Give your answer in standard form. 4 9 ................................. (2) (Total 4 marks) 9. Work out (9.88 � 10 ) � (2.6 � 10 ) 8 2 Give your answer in standard form. ......................................... (Total 2 marks) 10. (1) (a) Write 0.000 000 000 054 in standard form. ....................................... S = 12.6 R 2 R = 0.000 000 000 054 (b) Use the formula to calculate the value of S. Give your answer in standard form, correct to 3 significant figures. S = .......................... (2) (Total 3 marks) The Winston Churchill School 7 1. 7.75 � 10 �5 2 B2 for 7.75 � 10 5 9 (B1 for either 7.75 or 3.875 � 10 or 5 � 10 ) �5 [2] 2. (a) 1.08 � 10 7 4 4 3 Distance = 900 � 1.2 �10 = 1080 � 10 4 M1 for 900 � 1.2 �10 7 A2 for 1.08 � 10 4 7 (A1 for either 1080 � 10 or for k � 10 , 1k<10) (b) 30 000 4 2 4 12 � 10 � 9 � 10 = 120 000 � 90 000 4 M1 for either 12 � 10 or 120 000 or 90 000 seen A1 for 30 000 [5] 3. (a) 7.75 � 10 �5 B2 for 7.75 � 10 5 9 (B1 for either 7.75 or 3.875 � 10 or 5 � 10 ) �5 2 (b) p xp + 1 4 xpq = p � q xpq + q = p q(xp + 1) = p M1 for correct elimination of fractions M1 for a correct isolation M1 for q(xp + 1) = p p A1 for xp + 1 [6] 4. (a) 4.8 � 10 2 7 4 3 6 � 10 � 8 � 10 6 7 48 � 10 = 4.8 � 10 a b M1 for 6 � 10 � 8 � 10 oe, a and b integers including 0 6 A1 for 48 � 10 oe A1 cao (b) 230000 2 200 000 + 30 000 = 230000 B2 cao 5 4 (B1 for sight of 200 000 or 30 000 or 2.3 � 10 or 23 � 10 ) [5] 5. 4.3 � 103 3 6 � 1015 3.2 � 108 7 3 3 B3 for 4.3 � 10 to 4.34 �10 7 7 (B2 for 1.875 � 10 oe or 4300 to 4340 or final answer of 1.9 � 10 ) 15 8 (B1 for sight of 6 � 10 oe or 3.2 � 10 oe) 1.875 � 10 [3] 6. (a) 1.44 � 10 B1 cao 3 9 6 6 1 (b) 1667 (2.4 � 10 ) � (1.44 � 10 ) 9 6 M1 for 2.4 � 10 � "1.44 � 10 " oe A1 for 1666 or 1666.6... or 1666.7 A1 (dep) for 1667 cao [4] 7. (a) 4 � 10 0.000 03 2 B1 cao B1 cao (b) 1.2 � 10� 2 7 12 � 10� 1.2 � 10� M1 for 12 � 10� or 1200 ft from "(a)" A1 for 1.2 � 10� ft [4] 8. (a) 4.0 � 10 7 1 9 The Winston Churchill School B1 cao (b) 0.000014 1 B1 cao (c) 3.0 � 10 14 2 14 B2 cao accept 3 � 10 13 4+9 (B1 for 30 � 10 or 5 � 6 � 10 ) SC: B1 for correct answer as an ordinary number [4] 9. 3.8 � 10 6 2 B1 3.8 � 10 B1 cao n [2] 10. (a) 5.4 � 10 �11 �11 2 1 ) 12.6 � (5.4 � 10 (b) 3.67 � 10 �20 2 B1 cao M1 for digits 2916 or 367(416) �20 A1 for 3.67(416) � 10 [3] The Winston Churchill School 11