Everything Maths Grade 10

30.After a ball is dropped, the rebound height of each bounce decreases. The equationy= 5(0,8)xshows
the relationship between the number of bouncesxand the height of the bounceyfor a certain ball.
What is the approximate height of the fifth bounce of this ball to the nearest tenth of a unit?

31.Mark had 15 coins in R 5 and R 2 pieces. He had 3 more R 2 coins than R 5 coins. He wrote a system
of equations to represent this situation, lettingxrepresent the number of R 5 coins andyrepresent the
number of R 2 coins. Then he solved the system by graphing.

a)Write down the system of equations.

b)Draw their graphs on the same set of axes.

c)Use your sketch to determine how many R 5 and R 2 pieces Mark had.

32.Shown the following graph of the following form:y=asin+qwherePoint Ais at(90◦;4,5), andPoint
Bis at(180◦; 3), determine the values ofaandq.

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 1

1

2

3

4

5

B

A

x

y

33.The graph below shows a trigonometric equation of the following form:y=acos+q. Two points
are shown on the graph: Point Aat(90◦; 0), andPoint B:(180◦; 3 ). Calculate the values ofa(the
amplitude of the graph) andq(the vertical shift of the graph).

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 4

 3

 2

 1

1

2

3

4

A

B

x

y

34.On the graph below you see a tangent curve of the following form: y=atan+q. Two points are
labelled on the curve:Point Ais at(0◦;3), andPoint Bis at(45◦;2).
Calculate, or otherwise determine, the values ofaandq.

222 6.8. Chapter summary