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SECTION A1.Solve the following simultaneous equations

y 2x + 1 = 0,

x2 2y2 3y + 2 = 0.

Give the answers correct to three decimal places.

(5 marks / SPM 2014) 2.Calculate the coordinates of the points of intersection of the curve x2 + xy + y2 = 7 and the

straight line 2x + 3y = 73.Given that (5, h) is a solution of the simultaneous equations h(x y) = x + y 1 = hx2 11y2.

Find

a.the value of h

b.the other solution of the equations.

4.Diagram shows a farm in the shape of adjoining squares owned by En. Rosli. If he has 250 m

of fence to enclose 3125 m2 of his farm, find the values of x and of y.

5.Balqis travels to her hometown Malacca which is 210 km away with an uniform speed of x km/h. If she increases her speed by 14 km/h, she would have arrived half an hour earlier.

a.Form an equation in x and show it reduces to x2 + 14 x 5880 = 0

b.Solve this equation to find Balqis original speed.

6.The ratio of the sum of the second and third term of a geometric progression to its fourth term is

3 : 4.

a.Show that 3r2 4r 4 = 0, where r is the common ratio.

b.If r > 0 and the fifth term of this progression is 48, find the first term.

7.Sketch the graph y = 3 cos 2x + 2 for the domain 0 x 2.

a.Hence, use your graph to determine

i.the range of y corresponding to the given domain.

ii.the number of complete cycle and the period of the graph.

b.Using the same axes, draw a suitable straight line to find the number of solutions to the equation

for .

State the number of solutions.

8.a. i.Sketch the graph of

ii.Determine the period of the curve.

b. Hence, using the same axes, draw a suitable graph to find the number of solution to the equation

State the number of solution.

SECTION B9.Table shows the values of two variables, x and y, obtained from an experiment. It is known that x and y are related by the equation y = Ceax, where a, C and e are constants.

x123456

y6.5910.8717.9029.5648.7380.34

a.Plot log 10 y against x, using a scale of 2 cm to 1 unit on the x-axes and 2 cm to 0.2 unit

on the log 10 y-axes. Hence, draw the line of best fit.

b.Given that log10 e = 0.4343, use your graph in (a) to find the value of

i.a

ii.C

10.Table shows the values of two variables, x and y, obtained from an experiment. It is known that x and y are related by the equation where p and q are constants.

x12491625

y1.00.120.501.01.251.40

a.Plot y against, using a scale of 2 cm to 0.1 unit on the -axes and 2 cm to 0.5 unit on the y-axes. Hence, draw the line of best fit.

b.Use your graph in (a) to find the value of

i.p

ii.q11.A decaying radioactive substance has an initial mass of 200 milligrams (mg). At time t days later, the mass of the radioactive substance has been reduced to y mg, which is given by the formula

y = y0ekt . Show that y0 = 200.Table shows the values of y measured at difference subsequent

times t.t (days)012467

y (mg)20073.5827.13.660.500.18

a.Plot log 10 y against t, using a scale of 2 cm to 1 unit on the t-axes and 2 cm to 0.5

unit on the log 10 y-axes. Hence, draw the line of best fit.

b.Given that log10 e = 0.4343, use your graph in (a) to find the value of

i.k

ii.the number of days taken for the radioactive substance to reduce by half.12.The gradient of a curve at any point P(x, y) is given by (5x 4)3. If the curve passes through the point .

a.Show that the curve is

b.Find the coordinates of the turning point of the curve.

13.The gradient of a curve at any point (x, y) is given by x2 + k. The tangent to the curve at the point (3, 5) is parallel to the line y = 11x 5

.

a.Show that k = 2

b.Find the equation of the curve.14. Diagram shows the curve y = x3 and the straight line meet at three different points. Find the area of region bounded by the curve y = x3 and the straight line .

15.The diagram show that the line y = x 1 pass through the curve y = 4x x2 3 at points (1, 0) and point A. Find

a.the coordinates of point A

b.the area enclosed between the curve y = 4x x2 3 and the straight line y = x 1

c.the area of region bounded the curve y = 4x x2 3, the straight line y = x 1 and the x-axis.

16.a.A Quality Controller of a factory producing electric fans is aware that 3% of its electric fans

are defective. On average, the factory produces 500 fans daily.

i.Determine the expected number of defective fans in each day.

ii.If a sample of 5 fans is taken at random, find the probability that not more than

1 is defective.

b.X is a normal random variable such that X ~ . Find

i.

ii. the value of and , given that P(X > 8.4) = 0.70 and P(X > 13.2) = 0.25

17.a.The normal variable X and Y measure the marks obtained by the Form 5 students of a

school for the Biology and Chemistry paper respectively. The table shows the marks of two students Majid and Shila for two subject.Biology; X ~ N(78.6, 16)Chemistry; Y ~ N(60.1, 36)

Majid77 marks73 marks

Shila90 marks58 marks

Find

i.the probability that Majid obtained more than 77 marks for Biology paper.

ii.the total standardized marks,z, of the two students for two subjects.

iii.hence, which one of the two students has performed better in the two subjects.

b.Silva bought 10 oranges. The probability that an orange bought by Silva is sour is 0.15.

Find the probability that of these oranges there is

i.exactly one orange that is sour.

ii.not more than two oranges that are sour.

SECTION C

18.a.The diagram shows a pyramid of height 9 cm and stands on a square base of 12 cm. The

vertex V is vertically above the point D and M is the midpoint of BC.

Calculate

i.

ii.the area of MAV

b.The diagram shows a cuboid PQRSTUVW which stands on its horizontal base. M is the

midpoint of PQ.

Find

i.the length WM

ii.

iii.the area of WRM

Q

y m

V

P

9 cm

12 cm

12 cm

R

3 cm

8 cm

V

6 cm

W

U

T

A

B

C

D

M

y = x 1

A

(1, 0)

y m

y

0

S

y = 4x x2 3

x

x m

x m

x

M

y

0

EMBED Equation.3

y = x3

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