Class X SA-II MATHEMATICS SAMPLE PAPER 2016

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Special Individual A�en�on :One on one classes or doubt classes apart from the regular classes give individual a�en�on to each student. The doubt clearing sessions which will give the student the right push to their goal.

Faculty :This is one of the most important considera�ons while deciding about a coaching centre. We believe good teachers have the ability to transform studentsen�rely from non‐thinkers to intense‐thinkers.It is your responsibility to find out whether the Ins�tute does have Strong Pool of Full �me Faculty Members or not. This is important in case a Faculty leaves the Ins�tute midway so that Ins�tute is capable of filling that vacancy with a Faculty of same Calibre & Exper�se, eventuallysafeguarding your future.

Result :So many coaching ins�tutes show their results but don’t tell about the selec�on ra�o, how many students were enrolled for a course, like, say IIT‐JEE or AIPMT, how many were successful, what percentage of students secured ranked.

Student Teacher Ra�o : Number of students per class is also a factor, the less number of students for class the more is the a�en�on by the teacher on the students and also by the students towards teaching. So check out for number of students the ins�tute divides for a single class.

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APEX ,panel of teaching staff comprises of IITians, NITians, Doctors . APEX follows a very Strong, Systema�c & Objec�ve Selec�on Process. Apex conduct demo classes and mock sessions for students to help in making correct and wise decisions.

At APEX the Student‐Teacher Ra�o is less than 25:1,even at the peak �me. This facilitates proper Student‐Faculty interac�on. Our faculty is always willing to clear doubts of Students even individually, if required.

Apex consider doubts as the stepping stones towards understanding. each �me a modules gets completed its is followed by a doubt class. A doubt classon any topic can be demanded by the student, throughout the year round.

Tes�ng & Feedback system The only parameter to judge one's posi�on in the race is by analyzing the performance in tests. If students are to benefit from feedback,itmust not only be �mely and frequent, but also useful for improving performance byaddressing three areas: what students did well, what students need to improve on,and how to make this improvement.

At Apex, aspirants are exposed through weekly test and all India test series.The weekly tests ensure that aspirants keep their pace with content coverageand keep iden�fying their week areas. Regular tests are conducted and resultsof tests are also sent to aspirants and parents through SMS.

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MOCK TEST PAPERMATHEMATICS

(class10th)

Boost your IIT-JEE / AIPMT Preparation

MATHS X TERM-II

MODEL TEST PAPER-1 (UNSOLVED)

[For Summative Assessment-2 (Term - II)]

[Based on the latest CBSE Sample Question Paper]

Time : 3 hours M.M. : 80

General Instructions : Same as in CBSE Sample Question Paper.

SECTION A

(Question numbers 1 to 10 carry 1 mark each. For each of the questions 1 to 10, four

alternative choices have been provided of which only one is correct. You have to select the

correct choice.)

1. If the quadratic equation 2x2 – kx + 3 = 0 has equal roots, then the value of k is :

(a) ± 5 (b) ± 6 (c) ± 2 6 (d) ± 3 2

2. 51 + 52 + 53 + . ...... + 100 is equal to :

(a) 3775 (b) 4025 (c) 4275 (d) 5050

3. In a circle of radius 7 cm, tangent PT is drawn from a point P such that PT = 24 cm.

If O is the centre of the circle, then length of OP is :

(a) 30 cm (b) 28 cm (c) 25 cm (d) 31 cm

4. If two tangents inclined at angle of 60° are drawn to a circle of radius 3 cm, then

length of each tangent is equal to :

(a) 3 cm (b) 2 3 cm (c)2

3cm (d) 3 3 cm

5. Two circles touch each other externally at C and AB is a common tangent to the

circles. Then, ∠ACB is :

(a) 60° (b) 45° (c) 90° (d) 180°

6. To divide a line segment AB in the ratio 4 : 7, a ray AX is drawn first such that

∠BAX is an acute angle and then points A1, A2, A3, . ....... are located at equal

distances on the ray AX and the point B is joined to :

(a) A12

(b) A11

(c) A10

(d) A9

7. The area of the sector which subtends an angle of 60° at the centre of a circle is

4.4 cm2, then area of the circle is :

(a) 36 cm2 (b) 26.4 cm2 (c) 36.6 cm2 (d) 30 cm2

8. Volume of the largest right circular cone that can be cut out from a cube of edge

4.2 cm is :

(a) 9.7 cm3 (b) 77.6 cm3 (c) 58.2 cm3 (d) 19.4 cm3

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9. The ratio of the length of a rod and its shadow is 1: 3 . The altitude of the sun is :

(a) 30° (b) 45° (c) 60° (d) 90°

10. If two dice are thrown simultaneously, then the probability of getting a doublet is :

(a)5

36(b)

1

18(c)

1

9(d)

1

6

SECTION B

(Question numbers 11 to 18 carry 2 marks each)

11. Using quadratic formula, solve the following quadratic equation for x :

x2 – 4ax + 4a2 – b2 = 0

12. Split 207 into three parts such that these are in A.P. and the product of the two

smaller parts is 4632.

13. In the figure, CP and CQ are tangents to a circle with centre O. ARB is another

tangent touching the circle at R. If CP = 11 cm and BC = 7 cm, then find the length

of BR.

14. Find the area of the shaded region in the figure below, if AB = 12 cm, BC = 5 cm.

(Take π = 3.14)

15. A solid metallic sphere of radius 10.5 cm is melted and recast into a number of

smaller cones, each of radius 3.5 cm and height 3 cm. Find the number of cones so

formed.

16. Find the point on the x-axis which is equidistant from (2, –5) and (–2, 9).

17. Find the ratio in which the line segment joining the points (–3, 10) and (6, –8) is

divided by (–1, 6).

18. A bag contains 5 red balls, 8 white balls, 4 green balls and 7 black balls. A ball is

drawn at random from the bag. Find the probability that it is not green.

OR

From a well-shuffled pack of cards, a card is drawn at random. Find the probability that

the card drawn is a black queen.

t

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SECTION C

(Question numbers 19 to 28 carry 3 marks each)

19. Solve for x :

1 3 13

2 4 3

x x

x x

− −+ =

− −; x ≠ 2, 4

OR

The sum of the squares of two consecutive odd numbers is 394. Find the numbers.

20. Find the 31st term of an A.P. whose 11th term is 38 and 16th term is 73.

21. In the given figure, there are two concentric circles with centre O and of the radii

5 cm and 3 cm. From an external point P, tangents PA and PB are drawn to these

circles.

If AP = 12 cm, find the length of BP?

OR

Prove that the lengths of the tangents drawn from an external point to a circle

are equal.

22. Construct a triangle with sides 5 cm, 6 cm and 7 cm and then construct another

triangle whose sides are 7

5of the corresponding sides of the first triangle.

23. In the figure, OACB is a quadrant of a circle with centre

O and radius 3.5 cm.

If OD = 2 cm, find the area of the

(i) quadrant OACB

(ii) shaded region

24. Two cones with the same base radius 8 cm and height 15 cm are joined together along

their bases. Find the surface area of the shape so formed.

OR

A solid is in the shape of a cone standing on a hemisphere with both their radii being

equal to 1 cm and the height of the cone is equal to its radius. Find the volume of

the solid in terms of π.

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3 = 1.732]

25. The angle of elevation of the top of a building from the foot of the tower is 30° and

the angle of elevation of the top of the tower from the foot of the building is 60°.

If the tower is 50 m high, find the height of the building.

26. Find the area of a rhombus if its vertices are (3, 0), (4, 5) (–1, 4) and (–2, –1) taken

in order.

27. If the vertices of a ∆ABC are A(1, m), B(4, –3) and C(–9, 7) and its area is

15 sq. units, find the value of m.

28. Cards, marked with numbers 5 to 50, are placed in a box and mixed throughly. A card

is drawn from the box at random.

Find the probability that number on the taken out card is

(i) a prime number less than 10.

(ii) a number which is a perfect square.

SECTION D

(Question numbers 29 to 34 carry 4 marks each)

29. Two years ago, a man’s age was three times the square of his son’s age. In three

years, his age will be four times his son’s age. Find their present ages.

OR

If –5 is a root of the quadratric equation 2x2 + px – 15 = 0 and the quadratic equation

p(x2 + x) + k = 0 has equal roots, find the value of k.

30. A sum of Rs 700 is to be used to give seven cash prizes to students to a school for

their overall academic performance. If each prize is Rs 20 less than its preceding

prize, find the value of each of the prizes.

31. A circle touches the sides of a quadrilateral ABCD at P, Q, R, S respectively. Show

that the angles subtended at the centre by a pair of opposite sides are supplementary.

32. In Radhika’s house there is a flower pot. The sum of radii of circular top and bottom

of the flower pot is 140 cm and the difference of their circumferences is 88 cm. Find

the diameters of the circular top and bottom.

33. A cone of radius 8 cm and height 12 cm is divided into two parts by a plane through

the mid-point of its axis parallel to its base, find the ratio of the volumes of two parts.

OR

A well of diameter 3 m, dug 14 m deep. The earth taken out of it has been spread

evenly all around it in the shape of a circular ring of width 4 m to form an

embankment. Find the height of the embankment.

34. The angle of elevation of a jet fighter from a point A on the ground is 60°. After a

flight of 10 seconds, the angle of elevation changes to 30°. If the jet is flying at a

speed of 432 km/hour, find the constant height at which the jet is flying.

[Use

APEX INSTITUTE FOR IIT-JEE / MEDICAL / NTSE Head office: 62 Nitikhand-III, Indirapuram; | Contact: 0120-4331180, 9990495952 |

Web: www.apexiit.co.in/

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One year classroom Program.

M-95, C-98, P-95 B-98, C-97, P-95

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