IGCSE Mathematics Model Paper P4

8/6/2019 IGCSE Mathematics Model Paper P4

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IGCSE MODEL PAPER/P4 Praveen

1. In March 2011, Mr.Corbin along with his 4 friends visited maldives for a week.

(a) He exchanged US $3500 into Maldivian rufiyaa when the exchange rate was

$1=12.85 MRf.

Calculate how much maldivian rufiyaa he received.

Ans(1)(a) MRf . [2]

(b) Mr.Corbin and his 4 friends wanted to hire a speed boat for 6 hours.

(i) Which package will be profitable for them?

Ans(1)(b) (i)Package . [1]

(ii) Calculate the profit percentage .

Ans(1)(b) (ii)% [4]


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(c) They started from the resort at 2340 hrs , travelling at a speed of 60 miles per hour

and stopped at 0110 hrs.

(i) For how long they have been travelling ?

Ans 1(c)(i) hrs.min [1]

(ii) Show that they have travelled 145 km to the nearest kilometre. [2]

[ 1 mile = 1.60934 km ]

(d) In April 2011, exchange rate was US $1 = 15.42 Mrf.

(i) Express as a ratio,

the exchange rate of maldivian rufiyaa in march 2011 to april 2011.

Ans 1(d) (i) : [2]

(ii) How many US dollars he could have saved if he had visited Maldives in April 2011 ?

(Assuming that he spent $3500 in march)

Ans 1(d)(ii) $. [2]


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2. The diagram below shows the distance between 3 towns.

The distance between Atown and Btown is is 105km, Atown and Ctown is 140km,

and Btown to Ctown is 105km.

a) Show that the angle made inside the triangle at Btown is

Ans 2 (a) [3]

C-town

A-town

B-town

140 km

90 km

105 km

Not to scale


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b) Find the angle made inside the triangle at Ctown.

Ans 2 (b) [2]

(c) Find the area enclosed by the 3 towns, to the nearest km.

Ans 2 (c).km [2]

(d) Bearing of Ctown from Btown is .Calculate the bearing of

(i) Btown from Ctown

Ans 2 (d) (i) ..... [2]

(ii) Btown from Atown

Ans 2 (d) (ii) .... [2]

(e) A private company planned to build a common water park for 3 towns in the region nearer to

B than A and also nearer to AC than BC.

By construcing accurately the neccesary lines on the triangle,

shade the region in which the water park can be constructed. [3]


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3. Mohammed purchases a basket of mangoes containing two varities kesar and alphonso.

He selects two mangoes from the basket randomly.

The tree diagram shows the probability of selecting Kesar mango and Alphonso mango.

(a) Find the value ofp, q and r.

Ans 3(a) = ..[1]= ..[1]

= ..[1]

(b) Calculate the probability of selecting

i) Both alphonso

Ans 3(b)(i) .[2]

ii) Exactly one alphonso

Ans 3(b)(ii).[2]

iii) No alphonso

Ans 3(b)(iii).[2]


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c) If there is an alphonso in the second attempt, the probability of selecting alphonso in third

attempt is. Calculate the probability of selecting

i. All three alphnso.

Ans 3 (c)(i).[2]

ii. At least one kesar in all three attempts.

Ans 3 (c)(ii)...[2]

4. (a) Make gas the subject of the formula 3 =

Ans 4(a) g = ..[3]

(b) Factorise completely

Ans 4(b).[2]

(c) Show that

can be written as

[4]


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(d) hence or otherwise solve the equation

= 1

Ans 4(d) = . [3]

(e) Solve the quadratic equation exactly.

Ans 4(e) =.., = [4]

5. (a) p= and q=

(i) Find ,as a single column vector, p+2q.

Answer 5 (a)(i) [2](ii) Calculate the value of

.

Answer 5 (a)(ii) ........................................[1]


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(b) In the diagram,PQRS is a parallelogram.

X is the midpoint of QR and SR :SY = 3:2

= a and = b.

write down, in terms ofa and b, the expressions for,

(i)

Answer 5 (b)(i)........................................[2]

(ii)

Answer 5 (b)(ii)........................................[2]

(iii)

Answer 5 (b)(iii)........................................[2]

(iv)Use a vector method to show that , is parallel to and that [3]


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(c) ABCD is a trapezium. BC is parallel to AD.

Find the value of

(i) k

Ans 5(c)(i) k= [1]

(ii) p and q

Ans 5(c)(ii)p =. , q = [2]

6.(a) A cyclindrical can has a volume of 475

The height of the can is 11cm.

Calculate the radius, r, of the circular base of the can.

Ans 6 (a) r = (3)

B

A D

C

2b

4a + kb

Pa + Qb

7a

4a + 2b

11 cm


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(b) The diagram shows a plastic cup.

The cup is part of a cone, the rest of which is

shown by broken lines.

The top and bottom of the cup are horizontal

circles, with radii 4cm and 3cm.

The cup is 10cm tall.

Use similarity to show that depth of the whole cone is 40cm.

[3]

(c) Calculate the capacity of the cup.

Ans 6 (c) ..[3]

10 cm

3 cm

4 cm


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7.

Use one of the letters B, C, D, E or F to answer the following questions.

a) (i) Which triangle is A mapped onto by a translation ?

Ans 7 (a) (i) Triangle [1]

(ii) Write down the translation vector.

Ans 7 (a) (ii). [2]

(b) (i) Which triangle is A mapped onto by a rotation ?

Ans 7 (b) (i) Triangle . [1]


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(ii) Describe the rotation completely.

Ans 6 (b) (ii) ....[2]

(c) (i) Which triangle is A mapped onto by an enlargement ?

Ans 7 (c)(i) Triangle ..[1]

(ii) Write down the centre and the scale factor of enlargement ?

Ans 7 (c) (ii) centre Scale factor = ..[2]

(d) (i) Which triangle is A mapped onto by the matrix ?

Ans 7 (d) (i) Triangle [1]

(ii) Describe the transformation completely ?

Ans 7 (d) (ii) ..[3]

(e) Write down the 22 matrix which represents the transformation that maps

triangle A onto triangle F .

Ans 7 (e) ...[2](f) State which shapes have an equal area to that of triangle E.

Ans 7 (f) , , .[3]

8. Distribution of ages of 100 members of a chess club are shown in the table below.

Ages(years) 20


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c) Complete the cumulative frequency table. [3]

Ages(years) A 30 A 40 A 50 A 60 A 70 A 80Cumulativefrequencies

25 75 100

Using a scale of 1 cm to represent 10 years on the horizontal axis and 1 cm to represent 10

players on the vertical axis, draw a cumulative frequency curve. [4]


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d) Use your graph to estimate

(i) the median age.

Ans 8 (d) (i) [1]

(ii) the inter quartile range.

Ans 8 (d) (ii) .[3]

e) Find the number of chess players whose age is atleast 45 years.

Ans 8(e)..years [1]


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9. Answer the whole of this question on a sheet of graph paper

The table below shows some values of x and their corresponding f(x) values,

where f(x) = 30-18x + x3

x -4 -3 -2 -1 0 1 2 3 4f(x) 38 57 p 47 30 q 2 3 22

a) Find the values ofp and q

Ans 9 (a) p = .., q = (2)

b) Using a scale of 2cm to represent 1 unit on the horizontal axis, for -4 x 5, and

2cm to represent 10 units on the vertical axis, for 0 y 60, plot the points from

your table to form a smooth curve. (4)

c) Estimate from your graph

i) the value of) Ans 9 (c) (i) y =.......(1)ii) the values of Ans 9 (c) (ii) x =...(1)iii) the values of =15 Ans 9 (c) (iii) x =.....(2)

d) Estimate from your graph the coordinates of the points where the gradient of the

curve f(x) is 0. Ans 9 (d) ............................................(2)

e) On the same grid draw the passing through the points (-3,60) and (3,0) (1)f) Use your graph to solve f(x) = g(x)

Ans 9 (f) ..(3)

g) For

, state the range of values of for which

Ans 9 (g) ...(1)

(h)For , has only one solution.

Express as an inequality, the range of k.

Ans 9 (h) ..(1)


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IGCSE Mathematics Model Paper P4

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