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)

……………………………… (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)

………………………………….. (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&#x2014; 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

Standard Form Exam Questions: Grade B

Standard Form Exam Questions: Grade B