# ICSE Specimen Question Paper

Topics: Triangle, Pythagorean theorem, Nine-point circle Pages: 9 (1580 words) Published: December 11, 2012
MATHEMATICS
(Two hours and a half) Answers to this Paper must be written on the paper provided separately. You will not be allowed to write during the first 15 minutes. This time is to be spent in reading the question paper. The time given at the head of this Paper is the time allowed for writing the answers. Attempt all questions from Section A and any four questions from Section B. All working, including rough work, must be clearly shown and must be done on the same sheet as the rest of the answer. Omission of essential working will result in loss of marks. The intended marks for questions or parts of questions are given in brackets [ ]. Mathematical tables are provided.

SECTION A (40 Marks) Attempt all questions from this Section Question 1 (a) (b) Find the value of a and b if x 1 and x 2 are factors of x 3 ax b .

[3]

In the figure given below, ABCD is a parallelogram. E is a point on AB. CE intersects the diagonal BD at G and EF is parallel to BC. If AE : EB = 1 : 2 find (i) (ii) EF : AD area of triangle BEF : area of triangle ABD D F C

[3]

G A E B

57

ICSE Specimen Question Paper

(c)

On a certain sum of money, the difference between the compound interest for a year, payable half yearly, and the simple interest for a year is Rs 16. Find the sum lent out, if the rate of interest in both cases is 8 % . [4]

Question 2 (a) Plot the points A(9,6) and B(5,9) on the graph paper. These two points are the vertices of a figure ABCD which is symmetrical about x = 5 and y = 6. Complete the figure on the graph. Write down the geometrical name of the figure. (b) In the diagram given below EDC. The tangent drawn to the circle at C ACB. [3] [3]

makes an angle of 500 with AB produced. Find the measure of
E

D C

G A B

(c) PQRS is a square piece of land of side 56 m. Two semicircular grass covered lawns are made on two of its opposite sides as shown in the figure. Calculate the area of the uncovered portion. S R

[4]

P

Q

58

ICSE Specimen Question Paper

Question 3 (a) If A
4 4 -2 6

and B =

2

1

3 -2

find the matrix D such that [3]

3A – 2B + 2D = 0 (b) A point P(a, b) is reflected in the Y-axis to P1 (-3, 1) Write down the values of a and b. P11 is the image of P when reflected in the X axis. Write down the coordinates of P 11. P111 is the image of P when reflected in the line X = 5. Write down the coordinates of P 111. (c) Given : A { x : 3 2 x 1 9, x R} , B { x :11 3 x 2 23, x R}

[3]

where R is the set of real numbers. (i) (ii) Question 4 (a) Without using a trigonometric table calculate: 4 sin 32 cos58 5 tan 48 cot 42 8 sec 72 cosec18

Represent A and B on number lines On the number line also mark A

B.

[4]

[3]

(b)

Mr. Jacob has a two years recurring deposit account in State Bank of India and deposits Rs.1500 per month. If he receives Rs.37,875 at the time of maturity, find the rate of interest. [3]

(c)

Calculate the arithmetic mean, correct to one decimal place, for the following frequency distribution of marks obtained in a Geometry test. Marks No of students 0-10 7 10-20 13 20-30 15 30-40 12 40-50 3 [4] SECTION B (40 Marks) Attempt any four questions from this Section

Question 5 (a) If
2 4 6 2 3x 2 +2 3 4 =5 4 y

find the values of x and y. 59

[3]

ICSE Specimen Question Paper

(b)

In the diagram given below if AF = 21 cm, CE = 30 cm and FB = 7 cm. Find the volume of the figure. C
21 cm 30 cm

[3]
E 0 0 D

A

F
7 cm

B

(c)

A man bought 200 shares each of face value Rs.10 at Rs. 12 per share. At the end of the year, the company from which he bought the shares declares a dividend of 15%. Calculate: (i) (ii) (iii) the amount of money invested by the man the amount of dividend he received the percentage return on his outlay. [4]

Question 6 (a) Solve the following quadratic equation for x and give your answer correct to three significant figures: 2 x2
(b)

4x 3

0

[3]

An integer is...