Name:
Sha Tin College Mathematics Department
Key Stage 4 CORE Level Course
Unit 5 Assignment: Number II
Total
/ 85
Formulae
Need to Know
Laws of Indices :
a m  a n  a mn
am
 a mn
an
(a m )n  a mn
a0  1
am 
1
am
A: Powers and Roots
1. (no calc) Work out the value of each of these powers or roots – without a
calculator
Sha Tin College Mathematics Department KS 4 CORE ASSIGNMENT Number II
1
43
25
10 4
20 2
10000
3
27
81
4
16
0.52
43
62
169
400
4
1
23 x 25
225
3
125
4
81
7
3
5
32
Total for Section A
/20
B: Indices
#1(no calc)
Express 4
1
as a fraction.
Answer
#2(no calc)
(a)
[1]
Calculate 32 , giving your answer as a fraction.
Answer (a)
Sha Tin College Mathematics Department KS 4 CORE ASSIGNMENT Number II
[1]
2
(b)
#3
(a)
(b)
Calculate 60 .
Evaluate
Answer (b)
[1]
Answer (a)
[2]
26  23  20 .
Write 52 as the sum of three different powers of 2.
Answer (b)
#4 no calc
a) Simplify the following: a x a x a x a =
[2]
[1]
b) 4 x a x a x a x b x b x b
12 x a x a x b
[1]
#5 no calc
Simplify the following expressions, writing your answers in index form:
a) a7 x a 4
b) 11b x 2b3
20ab 2c
c)
10a3b
d)
4 a 2 b
8a 3b
e) (5x2y)3
f) 15a 3 / 5ab3
[6]
Sha Tin College Mathematics Department KS 4 CORE ASSIGNMENT Number II
3
#6 no calc
Work out the value of the following:
a) 2-2
c) 80
[4]
Total for Section B
/19
C: Standard Form
#1(no calc) In 1993 the United States of America tried to cut its budget deficit by
$450 000 000 000. Write this figure in standard form.
Answer $
#2
In 1985 the population of the Soviet Union was 2.70 108 and the population of
China was 1.02  109 . Calculate the total population of the Soviet Union and
China in 1985, giving your answer in standard form.
Answer
#3
[2]
[2]
The populations of six countries, in 1985, are shown in the table below.
Guyana
Jamaica
Laos
Liberia
Mauritius
Sierra Leone
(a)
798 000
2 032 000
3 364 000
1 716 000
1 049 000
2 715 000
What is the difference between the sizes of the populations of
Laos and Liberia?
Answer (a)
Sha Tin College Mathematics Department KS 4 CORE ASSIGNMENT Number II
[1]
4
(b)
Write the population of Mauritius in standard form.
Answer (b)
(c)
[1]
Which two countries are nearest in size, in terms of their populations?
Answer (c)
and
[1]
#4 (non calc) Convert these numbers to standard form:
a) 340
b) 0.006
c) 1.32
d) 7 million
[4]
#5 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
Total for Section C
[4]
/15
D: Speed, Distance, Time Calculations and Graphs
#1
The travel graph shows
Hassan’s daily run.
He runs 1 km from home,
rests, and then runs back
home.
(a)
For how many minutes does he rest?
Answer (a)
min [1]
Sha Tin College Mathematics Department KS 4 CORE ASSIGNMENT Number II
5
(b)
(i)
How long does it take him to run back home?
Answer (b)(i)
(ii)
Calculate the speed, in km/h, at which he runs back home.
Answer (b)(ii)
#2
min [1]
km/h [1]
The length of one lap of the track used for the Japanese Grand Prix car race
is 5 km 760 m. The race is 53 laps of the track.
(a)
Calculate the total length of the race.
Answer (a)
(b)
km [2]
The time that the winner of the race took was 1 hour 33 minutes.
(i)
The race started at 14 30. At what time did the winner finish?
Answer (b)(i)
(ii)
[2]
Write 1 hour 33 minutes in hours, giving your answer as a decimal.
Answer (b)(ii)
h [2]
Sha Tin College Mathematics Department KS 4 CORE ASSIGNMENT Number II
6
(c)
Each lap of the track is approximately 6 kilometres.
The race is about 50 laps of the track.
The winner’s time was about 1
1
2
hours.
Use these figures to estimate the winner’s average speed for the whole
race.
Answer (c)
km/h [2]
#3
Sha Tin College Mathematics Department KS 4 CORE ASSIGNMENT Number II
7
The graph shows the progress of two leading cars during the first two minutes of a
Grand Prix race.
(a)
Which car first goes into the lead?
Answer (a)
(b)
[1]
What happens about 38 seconds after the start?
Answer (b)
(c)
[1]
After 50 seconds,
(i)
what is the distance, in metres, between the cars,
Answer (c)(i)
(ii)
metres [1]
which car is in the lead?
Answer (c)(ii)
(d)
[1]
For the period of time between 50 seconds and 80 seconds, write a
comment on
(i)
the distance between the cars,
Answer (d)(i)
(ii)
[1]
the speed of the cars.
Answer (d)(ii)
(e)
[1]
How many seconds after the start of the race does car A regain the lead?
Answer (e)
(f)
[1]
Calculate, in kilometres per hour, the average speed of car A during the
first two minutes.
Answer (f)
km/h [2]
Sha Tin College Mathematics Department KS 4 CORE ASSIGNMENT Number II
8
#4
The table shows an extract from an airline’s flight plan.
Flight duration
(hours and minutes)
Distance
(km)
Dubai – Amman
3 h 00 min
2280
Dubai – Bangkok
5 h 50 min
5000
Dubai – Cairo
4 h 00 min
2714
Dubai – Istanbul
4 h 20 min
3003
Dubai – Dhaka
5 h 30 min
3581
Dubai – London
7 h 30 min
5428
From – To
(a)
Which of these distances appears to be given to one significant figure
only?
Answer (a) Dubai to
[1]
(b)
How much further is the Dubai – Dhaka flight than the Dubai – Cairo
flight?
Answer (b)
(c)
km [1]
One flight is exactly twice the distance of another.
Which two flights are these?
Answer (c)
Dubai to
is twice the distance of
Dubai to
[2]
#5
(a)
A businessman travels from Dhaka to Dubai on a flight which takes
5 h 40 min, and then on to London. What is his total flight time?
Answer (d)
h
min [1]
Sha Tin College Mathematics Department KS 4 CORE ASSIGNMENT Number II
9
(b)
Calculate the average speed, in kilometres per hour, of the flight.
(i)
from Dubai to Amman,
Answer (e)(i)
(ii)
km/h [2]
from Dubai to Istanbul.
Answer (e)(ii)
#6 non calc
km/h [2]
A family arrives home at 01 10 after a journey that took 7
1
2
hours.
At what time on the previous day did their journey start?
Answer
[2]
Total for Section D
CAN DO STATEMENTS
/31
TICK HERE
RECAP Calculate powers and roots without a calculator.
RECAP Indices. Simplify expressions using indices. Multiplying and
dividing eg 8x6 ÷ 2x2
NEW Know the laws of indices
NEW Know the zero index
Know the meaning of negative indices
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
standard form.
RECAP Standard Form. Convert from ordinary to standard form and
vice-versa using negative indices. Be able to manipulate numbers in
standard form.
RECAP(A) Calculations involving time: second(s), minutes (min)
hours (h) days, months, years, 1 year = 365 days including the relation
between consecutive units.
RECAP(A) Reading from timetables and doing practical work with
time.
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
Sha Tin College Mathematics Department KS 4 CORE ASSIGNMENT Number II
10