MathematicsP2/Year10/2018-2019 Page 2 of 11

[Pages:7]01.

The

variables

x

and

y

are

connected

by

the

equation

!

=

# (%-3)2

+

%

-

2.

The table below shows some values of x and the corresponding values of y.

x ?1 0 1 2 2.5 3 3.5 4 5 6 y -2.9 -1.9 -0.8 a 4.5 c 5.5 b 3.5 4.11

(a) Find the values of a, b, and c.

Answer: ....................................................................... [2]

(b) Using a scale of 2 cm to 1 unit on each axis, draw the graph of the equation

!

=

# (,-.)/

+

%

-

2

for

?1

<

x

<

6,

on

the

grid

provided

in

the

next

page.

[3]

(c) Use your graph in (b) to find the value/s of x when y = 4. Answer: ....................................................................... [2]

(d) By drawing a suitable tangent line, determine the gradient of the curve at x = 2.

Answer: ....................................................................... [3]

(e) Determine the equation of the straight line that must be drawn to solve the equation (4 ? x) (x ? 3)2 = 1. Construct this line on your graph in (b) and solve (4 ? x) (x ? 3)2 = 1. [3]

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MathematicsP2/Year10/2018-2019

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02. The age, x years, of each elderly in a certain old folk home was recorded. The data is shown in the distribution table below.

Age (x years) 55 < x < 60 60 < x < 65 65 < x < 70 70 < x < 75 75 < x < 80 80 < x < 85 85 < x < 90

Number of people 10 m 48 47 27 15 7

(a) The estimated mean age of the elders is 71, find the value of m, correct to the nearest whole number.

Answer: ....................................................................... [3]

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(b) (i) Using the grid below, create a histogram for the following classes:

[4]

Age (x years) 55 < x < 65 65 < x < 70 70 < x < 75 75 < x < 80 80 < x < 90

Number of people

(ii) Estimate the number of elders with ages greater than 77 years.

Answer: ....................................................................... [1]

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03. Mrs Tan will either cook food or bake a cake for her family during a weekend. The probability that she cooks food is 4/5. If she cooks food for her family, the probability that she will overcook her food is 3/8. If she bakes a cake, the probability that she will burn the cake is 1/10.

(a) Create a tree diagram using the information described above.

[3]

(b) Find the probability that she will not burn the cake nor overcook the food during her weekend.

Answer: ....................................................................... [2]

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06. A ferry has a deck area of 3600 m2 for parking cars and trucks. Each car takes up 20 m2 of deck area and each truck takes up 80 m2.

On one trip, the ferry carries x cars and y trucks.

(a) Show that his information leads to the inequality x + 4y < 180.

[2]

(b) The charge for the trip is $25 for a car and $50 for a truck. The total amount of money taken is $3000. Write down an equation to represent this information and simplify it.

Answer: ....................................................................... [2]

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(c) The line x + 4y = 180 is drawn on the grid below.

(i) Draw, on the grid, the graph of the your equation in part (b).

[1]

(ii) Write down a possible number of cars and a possible number of trucks on the trip, which together satisfy both conditions.

Answer: ....................................................................... [2]

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