Standard Form Exam Questions Grade B (Includes Mark Scheme)
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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)
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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)
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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)
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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)
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(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)
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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)
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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
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A1 cao
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(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]
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8.
(a)
4.0 × 107
1 B1 cao
(b)
0.000014
1 B1 cao
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(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]
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