# 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 p−q x = pq 1. p = 4 × 105 q = 1.25 × 104 Calculate the value of x. Give your answer in standard form. ………………………………. (Total 2 marks) 2. The engine of a new aircraft had a major inspection after 1.2 × 10 4 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. ……………….… km (3) In 2000 the aircraft carried a total of 1.2 × 105 passengers. In 2001 the aircraft carried a total of 9 ×104 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 ……………….……. (2) (Total 5 marks) The Winston Churchill School 2 x= 3. p−q pq p = 4 × 105 q = 1.25 × 104 (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 × 102 hours at a speed of 8 × 104 km/h. (a) Calculate the distance travelled by the spaceship. Give your answer in standard form. ........................... km (3) The Winston Churchill School 3 One month an aircrfat travelled 2 × 105 km. The next month the aircraft travelled 3 × 104 km. (b) Calculate the total distance travelled by the aircraft in the two months. Give your answer as an ordinary number. ........................... km (2) (Total 5 marks) ab y =a+b 2 5. a = 3 × 108 b = 2 × 107 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) The Winston Churchill School 4 A hard disk can store 2.4 × 109 bytes of data. (b) Calculate the number of floppy disks needed to store the 2.4 × 10 9 bytes of data. …………………………………… (3) (Total 4 marks) 7. (a) (i) Write 40 000 000 in standard form. ................................... (ii) Write 3 × 10–5 as an ordinary number. ................................... (2) The Winston Churchill School 5 (b) Work out the value of 3 × 10–5 × 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 × 10–5 as an ordinary number. ................................. (1) (c) Work out (5 × 104) × (6 × 109) Give your answer in standard form. ................................. (2) (Total 4 marks) The Winston Churchill School 6 9. Work out (9.88 × 108) ÷ (2.6 × 102) Give your answer in standard form. ………………………………….. (Total 2 marks) 10. (a) Write 0.000 000 000 054 in standard form. ....................................... (1) S = 12.6 R2 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 –5 B2 for 7.75 × 10 (B1 for either 7.75 or 3.875 × 105 or 5 × 109) [2] 2. (a) 1.08 × 107 3 Distance = 900 × 1.2 ×104 = 1080 × 104 M1 for 900 × 1.2 ×104 A2 for 1.08 × 107 (A1 for either 1080 × 104 or for k × 107, 1≤k<10) (b) 30 000 2 12 × 104 – 9 × 104 = 120 000 – 90 000 M1 for either 12 × 104 or 120 000 or 90 000 seen A1 for 30 000 [5] 3. (a) 7.75 × 10–5 2 –5 B2 for 7.75 × 10 (B1 for either 7.75 or 3.875 × 105 or 5 × 109) (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 × 107 3 6 × 102 × 8 × 104 48 × 106 = 4.8 × 107 M1 for 6 × 10a × 8 × 10b oe, a and b integers including 0 A1 for 48 × 106 oe The Winston Churchill School 8 A1 cao The Winston Churchill School 9 (b) 230000 2 200 000 + 30 000 = 230000 B2 cao (B1 for sight of 200 000 or 30 000 or 2.3 × 105 or 23 × 104) [5] 5. 4.3 × 10 3 3 6 × 1015 3.2 × 10 8 1.875 × 107 3 3 B3 for 4.3 × 10 to 4.34 × 10 7 (B2 for 1.875 × 10 oe or 4300 to 4340 or final answer of 1.9 × 107) 15 8 (B1 for sight of 6 × 10 oe or 3.2 × 10 oe) [3] 6. (a) 1.44 × 106 1 B1 cao (b) 1667 3 (2.4 × 109) ÷ (1.44 × 106) M1 for 2.4 × 109 ÷ “1.44 × 106” oe A1 for 1666 or 1666.6… or 1666.7 A1 (dep) for 1667 cao [4] 7. (a) 4 × 107 0.000 03 2 B1 cao B1 cao (b) 1.2 × 10³ 2 12 × 10² 1.2 × 10³ M1 for 12 × 10² or 1200 ft from “(a)” A1 for 1.2 × 10³ ft [4] The Winston Churchill School 10 8. (a) 4.0 Ă— 107 1 B1 cao (b) 0.000014 1 B1 cao The Winston Churchill School 11 (c) 3.0 × 1014 2 14 B2 cao accept 3 × 10 (B1 for 30 × 1013 or 5 × 6 × 104+9) SC: B1 for correct answer as an ordinary number [4] 9. 3.8 × 106 2 n B1 3.8 × 10 B1 cao [2] 10. (a) 5.4 × 10–11 1 12.6 × (5.4 × 10–11)2 (b) 3.67 × 10–20 2 B1 cao M1 for digits 2916 or 367(416) A1 for 3.67(416) × 10–20 [3] The Winston Churchill School 12