assignment unit 5 number ii

8/9/2019 Assignment Unit 5 Number II

1/13

Name:

Sha Tin College Mathematics Department

Key Stage 4 Extended Level Course

Unit 5 Assignment: Number II Total /90

Need to Know

Laws of Indices :m n m na a a + =

m

m n

n

aa

a

=

( )m n mna a=0 1a =

1m

m

aa

=

A: Indices

#1 no calc

a) Simplify the following: a x a x a x a = [1]

b) 4 x a x a x a x b x b x b

12 x a x a x b[1]

1Sha Tin College Mathematics Department KS 4 Extended ASSIGNMENT Number II


2/13

#2 no calc

Simplify the following expressions, writing your answers in index form:

a) a7 x a 4

b) 11b x 2b3

c)2

3

20

10

ab c

a b

d)2

3

4

8

a b

a b

e) (5x2y)3

f) 3 315 / 5a ab

[6]

#3 no calc

Work out the value of the following:

a) 2-2

b) 361/2

c) 80

d) 271/3

[4]

#4 no calc

Simplify the following expressions (giving your answer in surd form where appropriate).

a)2

3a

b) 1ba

c)1

2a

[3]



3/13

#5 no calcs Write the following surds in index form.

a) 2a

b) 3 5a

c) 5 2a

[3]

#6 Calculate

(a) 32 ,

Answer (a) [1](b) 2 33 2 .

Answer (b) [1]

#7 Solve the equation 3 8x = .

Answer x = [2]

#8 no calc Simplify 2 433 11x x .

Answer [1]

Total for Section A /23



4/13

B: Standard Form

#1 non calc Convert these numbers to standard form:

a) 340

b) 0.006

c) 1.32

d) 7 million[4]

#2 non calc Convert these numbers from standard form to ordinary form:

a) 2.0342 x 102

b) 3.37 x 105

c) 7.072 x 10-2

d) 5.33 x 10 -1

[4]

#3 A dronefly moves its wings 300 times per second.

How many times will it move its wings in1

42

minutes?

Give your answer in standard form.

Answer [2]

#4 In 1985 the population of the Soviet Union was 82.70 10 and the population of

China was 91.02 10 . Calculate the total population of the Soviet Union and

China in 1985, giving your answer in standard form.

Answer [2]



5/13

#5 non calc Insert one of the symbols >, =, < to make each of the statements correct.

(a) ( )2 20.2 .......... 4 10 , [1]

(b) 30 0.507

70. [1]

#6 Marios heart beats 72 times per minute.

(a) Calculate how many times it beats in 1 year. [Use 1 year = 365 days.]

Answer (a) [1]

(b) Write your answer to part (a) in standard form, correct to 2 significant

figures.Answer (b) [1]

#7 The world population is increasing by 3 people per second.

(a) Calculate the increase in world population in 1 year. [1 year = 365 days.]

Answer (a) [1]

(b) The world population was 95.00 10 in 1987.

Assuming that the rate of increase of population remains constant,

calculate an estimate, to 3 significant figures, of the world population

10 years later. Give your answer in standard form.

Answer (b) [2]



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Total for Section B /19

C: Speed, Distance, Time Calculations and Graphs

#1 no calc Roy arrived at the bus station at 10 19. His bus had left half an hour

before.

(a) At what time had his bus left?

Answer (a) [1]

(b) Roys next bus is at 11 05. How long must he wait?

Answer (b) minutes [1]

#2 non calc A family arrives home at 01 10 after a journey that took 71

2hours.

At what time on the previous day did their journey start?

Answer [2]

#3 non calc Penny flies from Lisbon to New York in 7 hours 30 minutes. She departsat 23 40. Lisbon time and has to put her watch back by 5 hours before arrival in New

York.What is the time in New York when her plane lands?

Answer [2]

#4 A videotape is 207 metres long. Its total playing time is three hours.

Find the speed of the tape

(a) in metres per minute,

Answer (a) m/min [1]

(b) in centimetres per second.

Answer (b) cm/s [2]



7/13

#5

The graph shows the first 240 seconds of the motion of a train.

(a) Estimate the speed of the train 90 seconds after it started.

Answer (a) m/s [1]

(b) Calculate the acceleration of the train between 60 and 120 seconds.

Answer (b) m/s2 [2]

#6 A ship sails 465 km across the Adriatic sea, from Ancona to Dubrovnik, at an

average speed of 30 km/h. The departure time from Ancona is 18 40.

Calculate the arrival time at Dubrovnik on the next day.

Answer [3]



8/13

#7

The graph shows the speed, in metres/second, of a car as it comes to rest from

a speed of 10 m/s.

(a) Calculate the rate at which the car is slowing down during the first threeseconds.

Answer (a) m/s2 [1]

(b) Calculate the distance travelled during the 10 second period shown on thegraph.

Answer (b) m [3]



9/13

#8 The distance-time graph below represents Terrys journey from home to school

one morning.

He runs for 10 minutes, rests for 10 minutes and then walks the remaining

distance.

(a) Calculate, in metres per second, his running speed.

Answer (a) m/s [1]

(b) His brother Cliff sets off from home later and runs at a constant speed of

5 m/s for the whole journey to school, arriving at the same time as Terry.

(i) Draw, on the graph above, the line representing

Cliffs journey. [2]

(ii) At what time did Cliff leave home?

Answer (b)(ii) [1]



10/13

#9 The diagram below is a speed-time graph for a car journey.

(a) Calculate the acceleration during the first 20 seconds of the journey.

Answer (a) m/s2 [1]

(b) Calculate the distance travelled in the last 10 seconds of the journey.

Answer (b) m [1]

(c) Calculate the average speed for the whole journey.

Answer (c) m/s [3]

Total for Section C /28



11/13

D: Surds

#1. (a) Evaluate

(i) 32

[1]

(ii)2

1

36

[1]

(iii)3

2

27

[2]

(iv)43

81

16

[2]#2 Simplify the following:

(a) 125

[2]

(b) 50 x 5

[2]

(c) 2 8 - 200 + 4 50

[2]



12/13


13/13

Unit 5 Assignment: Number IICAN DO statements Tick Here

RECAP Calculate powers and roots without a calculator.

RECAP Indices. Simplify expressions using indices.

RECAP Indices. Apply the laws of indices to simplify expressions

NEW Understand what is meant by the zero index and negative indicesNEW Understand what is meant by fractional indices and simplify

expressions involving these indices. Convert from index to surd form.

Investigating checking for completeness

RECAP Standard Form. Convert from ordinary to standard form and vice-

versa using positive indices. Be able to manipulate numbers in standardform.

RECAP Standard Form. Convert from ordinary to standard form and vice-versa using negative indices. Be able to manipulate numbers in standard

form.

RECAP Irrational Numbers

Be able to determine if a number is irrational or not

NEW Irrational Numbers Surds. Manipulation of surds.

Rationalising the denominator.

Surds additional practiceRECAP(A) Calculations involving time: second(s), minutes (min) hours (h) days, months,

years, 1 year = 365 days including the relation between consecutive units.

NEW Speed, distance, time. Solving problems involving finding these

values.RECAP Drawing and interpreting travel graphs. Recognising that the gradient of

a distance time graph represents the rate ie speed

NEW Drawing and interpreting speed time graphs. Recognising that the

gradient represents the acceleration or deceleration.NEW Recognising that the area under a speed time graph is the distance

travelled


assignment unit 5 number ii

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