Worksheet 29 Memorandum: Term 4 Revision Grade 9 Mathematics

Worksheet 29 Memorandum: Term 4 Revision Grade 9 Mathematics

1. A (-2, 4) A' (4, -2) = Reflected about the line y = x B (-4, -5) B' (-2; -1) = Translated 2 units right and 4 units up. C (7; 2) C' (7; -2) = Reflected about the x-axis. D (3; -4) D' (-3; -4) = Reflected about the y-axis E (-6; 8), F (-8; 4) and G (-4, 4) E' (-3; 4), F'(-4; 2) and G' (-2; 2) = Reduced by a factor of 2.

2. a) A (-3, 4) reflected about the x-axis A' (-3; -4) b) B (4; -12) reflected about the line y = x B' (-12; 4) c) C (-2; 4) translated 4 units down and 12 units left C' (0; -14) d) D (3; -1) reflected about the y-axis D' (-3; -1)

3. a) E' (16, 8) enlarged by a factor of 4 E (4; 2) b) F' (1; 5) translated 3 units up and 4 units to the right F (-3; 2) c) G' (-3; 1) reflected about the line y = x G (1; -3) d) H' (-6; 8) reflected about the x-axis H (-6; -8)

4. a) The coordinates of the vertices will move to a point three times larger than the original point

b) The perimeter of the triangle will also become three times larger c) The area of the triangle will become 9 times larger.

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5. a) cylinder c) triangular prism

b) square based pyramid d) rectangular prism

6. a) Cylinder no vertices, 2 edges and 3 faces b) Square based pyramid 5 vertices, 8 edges and 5 faces c) Triangular prism 6 vertices, 9 edges and 5 faces d) Rectangular prism 8 vertices, 12 edges and 6 faces

7. a) Cylinder Surface Area = 22 + 2 Volume = 2

b) Square based pyramid

Surface area = 2 + 1 ( )( )

2

Volume

=

1 3

2

?

c) Triangular prism Surface area = + + +

Volume = Area of the triangle base x length

d) Rectangular prism Surface area = 2( + + )

Volume = ? ?

8. A population looks at every single individual in a group, while a sample is a random selection of some of those individuals in the group, for example, rhinos are a population, while all the rhinos in the Kruger national park would be a sample of those rhinos.

9. These questions are opinion based, however the answers should be logical. Here are suggested answers (but other logical answers are also possible).

a) A person's favourite restaurant A survey or questionnaire, as this only needs the name of the restaurant.

b) Which is better, tea or coffee? Again, a survey of questionnaire would suffice; it is not an open-ended question

c) How a person feels about their favourite sports team. This could be an open-ended questionnaire as it is easier to describe their feelings in their own words.

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d) How to make coffee This could be any of the three, although for instructions, most often open-ended questions should be used.

e) When a person should buy a house. Again, this could be any of the three, depending on the purpose of the research.

f)

A student's favourite study method. This could be as a survey or open-ended

question as the student might have several methods or an explanation of how they like

to study.

10. a)

b) c) d)

Average Calories Average KJoules

= 300+670+360+406+1275+421 441

7

= 3873

7

= 553.29 Calories = 1254+2803+1506+1699+ 2164+1760+1845

7

= 13031

7

= 1 861.57 kJoules

1254 1506 1699 1760 1845 2164 2803

Median = 1760 kJ

Calories Range = 1275 ? 300

= 975

kJ Range = 2803 ? 1254

= 1549

Yes, the Spur burger has a large amount of calories while the Burger King burger seems to also have a very high number of kJ

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e)

Number of Calories per Burger

Calories per Burger at different Fast Food places

1400

1200

1000

800

600

400

200

0

MacDonalds Burger King Steers

Nandos

Spur

Wimpy

KFC

Restaurants

Calories

f)

3000

kJoules vs number of Calories per Burger

2500

Numbr of kJoules

2000

1500

1000

500

0

0

200

400

600

800

1000

1200

1400

Number of Calories

g) From the scatterplot answer the following questions:

i)

A strong positive relationship

ii) About 1000 kJoules of energy.

h) Yes, it is possible. Often there are things on the internet that aren't true.

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11. a)

1 2

1

H

1

2

2

1 2 1 2

T

1 2

1

2

H HHH

H

1

2

T

HHT

1

H HTH

2

T

1 2 1 2

H

T

HTT

H THH

1

T

THT

2

1

H TTH

2

T

1

T

TTT

2

b)

Probability

of

throwing

three

heads

in

a

row

=

1 2

?

1 2

?

1 2

=

1 8

c)

Probability of throwing two heads and one tails in any order = 1 + 1 + 1 = 3

888 8

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