Year 10 - Homework Sheet 19
NUMBER CALCULATIONS
1.
John invests $610 into a bank account paying compound interest at a rate of
6.5% per annum. By completing the spaces below, calculate the total amount in
John’s account after 2 years. Round your final answer to 2 decimal places.
Starting Amount: $
×
= Year 1 Total Amount: $
Year 1 Amount: $
×
= Year 2 Total Amount: $
The heat setting of a gas oven is called its Gas Mark. A Gas Mark, G, can be converted
to a temperature, C° by using the formula: C = 15G + 120
2.
Factorise the expression 15G + 120.
3.
Make G the subject of the formula C = 15G + 120.
The distance from the Earth to the Moon is 400 000 kilometres.
4.
Write the number 400 000 in standard form.
5.
The distance from the Earth to the Sun is 1.5 × 108 kilometres.
Calculate the value of the expression: distance from the Earth to the Moon
distance from the Earth to the Sun
ISBN: 9781877489150
Give your answer in standard form.
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MEDICAL MATH
Chemists studying the use of aspirin have found that the amount of aspirin (in
milligrams) in your bloodstream after t hours is given by the function y = A(0.7)t
where A is the initial amount of aspirin in a given dose.
1.
A doctor prescribes 2 aspirin tablets every 4 hours. Each tablet has 200 mg of
aspirin. How much aspirin will still be in the bloodstream after 8 hours?
A car and an ambulance are traveling towards each other. They are 1 km (1000 metres)
apart. The car is traveling at a speed of 50 km / hr (13.9 metres / second). The
ambulance is traveling faster at 80 km / hr (22.2 metres / second). The ambulance is
racing to an accident and has its siren on. In ideal conditions, the siren can be heard
from 400 m.
If the conditions are ideal, in how many seconds will the driver of the car first hear
the siren?
Ambulance
22 m/s
Car
siren (400 m)
13.9 m/s
1000 metres
Year 10, Worksheet 19, Page 2 - www.mathscentre.co.nz
ISBN: 9781877489150
2.
MATHS IN SPACE
The book “Rocket Boys” was made into a movie called “October Sky”. It is
based on the true story of a coal miner’s son who takes up rocketry and
eventually becomes a NASA scientist. In the story he experiments with
different rocket designs.
He uses a formula R =
S+F+P
S+P
R is the mass ratio of a rocket.
S is the mass of the structure.
F is the mass of the fuel.
P is the mass of the payload (that part of the rocket such as satellites
etc that are being carried for a fee into space).
A more efficient rocket design requires less propellant to achieve a given goal,
and would therefore have a lower mass ratio. A higher mass ratio permits the
rocket to achieve a higher velocity. Typical rockets have mass ratios in the
range from 8 to 20. The Space Shuttle, for example, has a mass ratio of 16.
A small rocket is designed with a mass structure of 900 grams and a payload
of 1500 grams. How much fuel (in kilograms) should be loaded into the rocket
if it is to have a mass ratio of 8?
SICK MATHEMATICS
ISBN: 9781877489150
A nurse dispensing medication has to take into account the weight of the patient. In one
particular instant, a patient is taking 150 milligram blood pressure tablets. The dosage
is 5 milligrams per kilogram of body weight and the tablets should be taken 3 times a
day (every 8 hours). If the patient weighs 120 kg, how many tablets would be needed
for a 30 day supply?
Year 10, Homework Sheet 19, Page 3 - www.mathscentre.co.nz
MATHEMATICS IN DESIGN
A
The diagram represents the plan view of the corner of a
display cabinet. The corner is fitted with a concave piece of
glass (represented by the arc AB).
The arc AB is a quarter of a circle with the centre of the
circle at C. The circle radius is 46cm.
1.
Calculate the length of the arc AB.
Give your answer correct to 3 significant figures.
46cm
B
C
46cm
Note: diagram is not drawn to scale
In another design, the concave window in part 1. is replaced by 3 identical glass
panels. These panels are all straight and are represented in the diagram below by the
lines AP, PQ and QB.
2.
Calculate the length of each panel
(i.e. calculate the lengths of one of AP, PQ or QB).
Give your answer correct to 3 significant figures.
46 cm
P
Q
46cm
L
75
A
B
75
30
C
46 cm
46cm
Note: diagram is not drawn to scale
6.
The Pyramid Arena is a sports stadium in Memphis,
USA. It is the 6th largest pyramid in the world.
It has a 183 metre square base and is 98 metres tall.
Year 10, Homework Sheet 19, Page 4 - www.mathscentre.co.nz
ISBN: 9781877489150
What is the volume of this pyramid?