ST.THOMAS SCHOOL, DHURWA Class X Mathematics ...

ST.THOMAS SCHOOL, DHURWA

Class X Mathematics Assignment

SL-(i) GST ( CH-1)

1- A person goes to a shop to buy a jacket having list price; Rs 1180. The rate

of GST is 18%. He tells the shopkeeper to reduce the price such an extent

that he has to pay Rs 1180 inclusive of GST. Find the reduction needed in

the price of the jacket.

2- Manufacturer Suresh sells a television to a dealer Anil for Rs 20000/. The

dealer Anil sells it to the customer at a profit of Rs 2000/. If the sales are

intra-state and the rate of GST is 12%, find

(i) the amount of tax (under GST) paid by the dealer Anil to the central

Government.

(ii) the amount of tax (under GST) received by the state Government.

(iii) the amount that the customer pays for the television.

3- A shopkeeper buys an item whose list price is Rs 3000/ from a wholesaler

at a discount of 15% and sells it to the customer at the printed price. If the

sales are intra-state and the rate of GST is 12%, find

(i) the price of the item inclusive of GST at which the shopkeeper bought it.

(ii) the amount of tax (under GST) paid by the shopkeeper to the state

Government.

(iii) the amount that the customer pays for the item.

4- A shopkeeper who lives in Rajasthan buys an article at the printed price of

Rs 35000/ from a wholesaler who lives in Gujrat. The shopkeeper sells the

article to a customer in Rajasthan at a profit of 22% on the basic cost price.

If the rate of GST is 12%, find;

(i) the price of the article inclusive tax (under GST) at which the shopkeeper

bought it.

(ii) how much amount of tax(under GST) paid by the shopkeeper to the

Governments?

(iii) the amount of tax (under GST) received by the Gujrat Government.

(iv) the amount of tax (under GST) received by the Central Government.

(v) the amount which customer pays for the article.

5- The printed price of a modular table is Rs 2000/. The wholesaler is in U.P.

buys the modular table from a manufacturer in Rajasthan at a discount of

10% on the printed price. The wholesaler sells the modular table to a

retailer in M.P. at 20% above the marked price. If rate of GST is 5%. Find;

(i) the price of modular table inclusive tax (under GST) at which the

wholesaler bought it.

(ii) the price of modular table inclusive tax (under GST) at which the retailer

bought it.

(iii) how much amount of tax(under GST) paid by the wholesaler to the

Central Governments?

(iv) total tax (under GST) collected by the central Government.

SL-(ii) LINEAR INEQUATIONS (CH-4)

1- Write the solution of following in equation in set notation form; 5x-10

2x+2 , x .

2- An integer is such that one third of the next integer is at least 2 more than

one fourth of the previous integer. Find the smallest value of the integer.

3- P is the solution set of 8x-1 and Q is the solution set of ; 7x-2

3(x+6), where x Find the set P

4- if x , and A is solution set of 2(x-1) and B is a solution set of 4x-

4 8+x then find A

5- Let A= {x: 11x - 5 7x+3, x } and

B= {x: 18x-9 15+12x, x }

then find the solution set of A

6- Find all pairs of consecutive even positive integers, both of which are larger

than 5, such that their sum is less than 23.

7- Solve the in-equation; 37-(3x+5) 9x – 8(x-3), x and represent the

solution set on the number line.

8- Solve the in- equation ; 2x-7 4, x {1,2,3,4,5,6,7} and represent the

solution set on the number line.

9- Solve the following in- equation and represent the solution set on the

number line.

-8

-

-4x 7

, x I.

10- Find the value of x, which satisfy the in-equation;

-2

x 2 ; x W and also represent the solution set on the number

line.

11- Solve;

, x

, x .

SL-(III) Ratio and Proportion (CH-7)

1- Find the ratio between 7.8 cm and 8 km.

2- Find the ratio of 65 min. and 1.2 hrs.

3- The current price of a box is Rs 300/. Find its price if the price is decreased

in the ratio of 15 to 9.

4- Arrange in increasing order of magnitude, 3:4, 7:8,10:12, 15:8.

5- Find the following;

(i) The sub-duplicate ratio of 9p2 q2 :16r2 s4.

(ii) The sub-triplicate ratio of 125a3 : 1000b6.

(iii) The reciprocal ratio of 13xyz : 14abc.

6- If (x-9) : (3x+6) is duplicate ratio of 4:9 , then find the value of x.

7- Divide Rs 1870 into three parts in such a way that half of the first part, one-

third of the second part and one-sixth of the third part are all equal.

8- What number must be added to each of the numbers 7, 16, 43, and 79 to

make them in proportion ?

9- If a, b, c and d are in proportion then prove that (ma+nb):b=(mc+nd):d.

10- What is mean proportional between 10+2 and 15-3

11- Find the third proportional of 9 and 21.

12- Find the forth proportional to 9, 16 and 63.

13- 13-If x, y and z are in continued proportion then prove that

=

.

14- If

=

, use the properties of proportion to find (i) m:n and

.

15- Using the properties of proportion solve for x;

.

SL-(iv) Remainder and Factor Theorem (CH-8)

1- Using remainder theorem, find the remainder when x3-5x2+3x+1 is divided

by (x-1/3).

2- Using remainder theorem, find the value of x, if on dividing 7y3+2y2-xy+14

by y+3 leaves a remainder -49.

3- If the polynomial ax3+3x2+5x-4 and x3-4x+a leave the same remainder,

when divided by (x-2), then find the value of a.

4- A function f is defined by f(x)=144-16x2, calculate f(2). Also, find the value of

x, when f(x)=0.

5- Find the remainder when f(x)=2x3-3x2-4x-5 is divided by g(x)=2x+1.

6- Find the remainder, when f(x)=12x3-13x2-5x+7 is divided by 3x+2.

7- What number should be subtracted from 2x3-5x2+5x, so that the resulting

polynomial has a factor 2x-3 ?

8- Using factor theorem, factorise the polynomial completely;

2x2+10x+12.

9- Using factor theorem, factorise the polynomial completely;

3x3+2x2-19x+6.

10- The polynomial px3+4x2-3x+q is completely divisible by x2-1,

find the values of p & q. Also, for these values of p and q factorise the given

polynomial completely.

SL-(v) Arithmetic Progression (CH-10)

1- How many terms are there in the given sequence 3,6,9,12,…111 ?

2- Which term of an AP 21,18,15,….is -81 ?

3- Determine the general term of an AP whose 7th term is -1 and 16th term is

17 ?

4- How many numbers of two digit are divisible by 7 ?

5- Determine the 10th term from the end of an AP 4,9,14,….,254 .

6- The sum of three numbers in an AP is 15 and their product is 105. Find the

numbers.

7- If (k-3), (2k+1), (4k+3) are three consecutive terms of an AP, find the value

of k.

8- Check 0 is a term of an AP: 31, 28, 25,…..

9- Find the value of p, if the given value of x is the pth term of an AP 25, 50,75,

100,…. ; x=1000.

10- The 11th term of an AP is 80 and the 16th term is 110. Find 31st term.

11- Find the sum of the first 22 terms of an AP 8, 3, -2,…. .

12- Find the sum of first 17 terms of an AP, where 4th and 9th terms are -

15 and -30 respectively.

13- If the sum of first p terms of an AP is q and the sum of first q terms is

p, then find the sum of first (p+q) terms.

14- If the sum of first n terms of an AP is given by Sn=n(4n+1), then find

nth term of AP. Also, find the AP.

15- The sum of first six terms of an AP is 42. The ratio of its 10th term and

30th term is 1:3, find the first and 13th terms of the AP.

SL-(VI) Geometric Progression (CH-11)

1- Find the nth term and 12th term of the sequence -6, 18, -54,…. .

2- Which term of the GP 5, 10, 20, 40, …..is 5120 ?

3- If the 4th and 9th terms of a GP 54 and 13122 respectively, then find the GP.

4- The 4th term of a GP is 16 and 7th term is 128, find the 1st term and the

common ratio of the series.

5- Find the GP whose 5th and 8th terms are 80 and 640, respectively.

6- If the 4th, 10th and 16th terms of a GP are x, y, z respectively. Prove that x, y,

z are in GP.

7- If 1st and nth terms of a GP are a and b respectively and P is the product of n

terms, then prove that P2=(ab)n.

8- Find the sum of the series; 2+6+18+54+…….+4374.

9- Find the sum of n terms of the sequence given by an = 2n +3n, n

10- A GP consists of an even number of terms. If the sum of all terms is 5

times the sum of the terms occupying odd places, then find its common

ratio.

11- The sum of the first three terms of a GP is 16 and the sum of next

three terms is 128. Determine the first term, the common ratio and sum to

n terms of the GP.

12- Find the least value of n for which the sum 1+3+32+…..to n terms is

greater than 7000.

13- Solve the equation -4+(-1)+2+…….+x = 437.

14- A student decided to solve 2 questions of Mathematics first day and

doubles the number everyday . In how many days will he be able to solve

the total questions 2046 in the book ?

15- 150 workers were engaged to finish a job in certain number of days,

4 workers dropped out on the second day, 4 more workers dropped out on

the third day and so on. It took 8 more days to finish the work. Find the

number of days in which the work was completed.

SL-(VII) Reflection (CH-12)

1. State the co-ordinate of the following points under reflection in x- axis.

(a) (3,2) (b) (-5,4) (c) (0,0)

2. State the co-ordinate of the following points under reflection in y axis.

(a) (6,-3) (b) (-1,0) (c) (-8,-2)

3. State the co-ordinate of the following points under reflection in origin.

(a) (-2,-4) (b) (-2,7) (c) (0,0)

4. The point A(-3,2) is reflected in the x axis to the point A’ .Point A’ is then

reflected in the origin to point A’’.

a. Write down the co-ordinates of A’’

b. Write down the single transformation that maps A onto A’’

5. Point A (4,-1) is reflected as A’ in the y axis. Point B on reflection in the x

axis is mapped as B’

(-2,5) . Write the co-ordinates of A’ and B.

6. The point P(4,1) and Q(-2,4) are reflected in line y=3. Find the co-

ordinates of P’, the image of P and Q’, the Image of Q.

7. A point P(-2,3) is reflected in the line x=2 to point P’. Find the co-

ordinates of P’.

8. P and Q have co-ordinates (0,5) and (-2,4).

(a) P is invariant when reflected in an axis .Name the axis.

(b) Find image of Q on reflection in the axis found in (a)

(c) (0,k) on reflection in the origin is invariant . write the value of k.

(d) Write down the co-ordinate of the image of Q, obtained by reflecting

it in the origin followed by reflection in x-axis.

9. (a) The point P(2,-4) is reflected about the line x=0 to get the image Q.

Find the co-ordinates of Q,

(b) the point Q is reflected about the line y=0 to get the image R. Find the

co-ordinates of R.

(c) Name the figure PQR.

(d) Find the area of PQR

10. Using a graph paper, plot the points A(6,4) and B(0,4).

(a) Reflect A and B in the origin to get the images A’ and B’.

(b) Write the co-ordinates of A’ and B’.

(c) State the geometrical name of the figure ABA’B’.

(d) Find its perimeter.

SL-(VIII) Section and mid point formula (CH-13)

1. In what ratio is the line joining (2,-3) and (5,6) divided by the x-axis.

2. P is a point on the line joining A(4,3) and B(-2,6) such that 5AP=2BP. Find

the co-ordinate of P.

3. The point P (5,-4) divides the line segment AB , As shown in the figure in

the ratio 2:5.Find the co-ordinates of the points A and B.

4. Show that the line segment joining the points (-5.8) and (10,-4) is trisected

by the co-ordinate axes.

5. A(5,3), B(1.0) and C(7,-3) are the vertices of triangle ABC .If L is the mid-

point of AB and M is the mid-point of AC Show that LM = ½ BC.

6. A(-1,0), B(1.3) and D(3,5) are the vertices of a parallelogram ABCD. Find the

co-ordinates of vertex C.

7. Calculate the co-ordinates of the centroid of the triangle ABC, if A(7,-2),

B(0,1) and C(-1,4)

8. Find the co-ordinates of points of trisection of the line segment joining the

point (6,-9) and the origin.

9. The mid- point of the line segment joining (4a,2b-3) and (-4,3b) is (2,-2a)

find the values of a and b

10. Find the ratio in which the line 2x+y=4 divides the line segment joining the

points P(2,-2) and Q(3,7).

SL-(IX) Equation of line (CH-14)

1. Find the slope of a line whose inclination is (a) 30: (b)72:30’

2. Find the inclination of the line whose slope is (a) √3 (b)1.0875

3. The line given by the equation 2x-(y/3)=7 passes through the point (k,6);

Calculate the value of k.

4. The line passing through (-4,-2) and (2,-3) is perpendicular to the line

passing through (a,5) and (2,-1). Find a.

5. Show that the lines 2x – 5y = 1 , x -3y = 6 and x + 5y + 2 = 0 are

concurrent.

6. The points (-3,2), (2,-1) and (a,4) are collinear .Find a.

7. Find the equation of lines passing through point (-2,0) are equally inclined

to the co-ordinate axes.

8. Find the equation of line which is perpendicular to the line (x/a) –(y/b) = 1

at the point where this line meets y axis.

9. Find the value of k such that the line (k-2)x + (k+3)y -5 = 0 is :

(1) Perpendicular to the line 2x –y +7 =0

(2) Parallel to it .

10. ABCD is a parallelogram where A(x, y) , B(5,8) , C(4,7) and D(2,-4) Find:

(1) The co-ordinate of A

(2) Equation of diagonal BD

11. Find the equation of line through the intersection of lines 2x –y = 1 and 3x

+2y = -9 and making an angle of 30: with positive direction of x- axis.

12. A line AB meets X axis at A and Y axis at B. P(4,-1) divides AB in the ratio 1:2.

(1) Find the co-ordinates of A and B.

(2) Find the equation of line through P and perpendicular to AB

SL-(X) Similarity (CH-15)

1. In the given figure ,straight line AB and CD intersect at P; and AC is parallel

to BD .Prove that:

(1) ∆ APC and ∆BPD are similar.

(2) If BD =2.4 cm , AC=3.6 cm PD =4.0cm and PB = 3.2 cm ; find the lengths

of PA and

PC

2. In quadrilateral ABCD, the diagonal AC and BD intersect each other at point

O.

If AO=2CO and BO=2DO show that

(1) ∆ AOB and ∆COD are similar.

(2) OA x OD = OB x OC

3. In the given figure AB ǁ DC , BO = 6cm and DQ = 8 cm find :BP x DO

4. In the given figure QR ǁ AB and DR ǁ QB Prove that : PQ² = PD x PA

5. A line PQ is drawn parallel to the side BC of a ∆ ABC Which cuts side AB at P

and AC at Q . If AB = 9.0 cm , CA = 6.0 cm and AQ = 4.2 cm , Find the length

of AP.

6. In the figure given below , AB CD and EF are parallel lines . Given AB = 7.5

cm , DC= y cm , EF =4.5 cm , BC = x cm and CE =3 cm . calculate the value of

x and y.

7. In the following figure M is mid-point of BC of a parallelogram ABCD. DM

intersect the diagonal AC at P and AB produced at E . Prove that : PE = 2 PD

8. The given figure shows a parallelogram ABCD .E is a point in AD and CE

produced meets BA produced at point F . If AE = 4 cm, AF = 8 cm and AB =

12 cm . Find the perimeter of the parallelogram ABCD.

9. In the given triangle PQR , LM ǁ QR and PM:MR=3:4

Calculate the value of the ratio

(1) PL/PQ and then LM/QR

(2) Area of ∆LMN/Area of ∆MNR

(3) Area of ∆LQM/Area of ∆LQN

10. In the figure given below , ABCD is a parallelogram, P is a point on BC such

that BP:PC=1:2 . DP produced meets AB produced at Q . Given the area of

triangle CPQ=20cm²

Calculate :

(1) Area of triangle CDP.

(2) Area of parallelogram ABCD.

11. The scale of a map is 1 : 50,000 . In the map , a triangular plot ABC of land

has the following dimensions:

AB=2 cm , BC =3.5 cm and angle ABC = 90 :

Calculate:

(1) The actual length of side BC , In km, of the land.

(2) The area of the plot in sq. km.

12. A model of a ship is made to a scale 1 : 300.

(1) The length of the model of the ship is 2m calculate the length of the

ship.

(2) The area of the deck of the ship is 180,000 m² . Calculate the area of the

deck of the model.

(3) The volume of the model is 6.5 m³. Calculate the volume of the ship.

13. In the given figure AB and DE are perpendicular to BC .

(1) Prove that : ∆ABC ~ ∆DEC

(2) If AB = 6 cm, DE = 4 cm. and AC = 15 cm. Calculate CD.

(3) Find the ratio of the area of a ∆ABC : area of ∆DEC

SL-(XI) Loci (CH-16)

1. Given CP is the bisector of angle C of the ∆ABC

Prove that P is equidistant from AC and BC

2. Describe the locus of the mid-points of all chords parallel to a given chord of a circle.

3. In triangle LMN , bisectors of the interior angles at L and N intersect each other at point A. Prove that (1) Point A is equidistant from all the three sides of the triangle . (2) AM bisects angle LMN.

4. Construct a triangle ABC, with AB = 7cm , BC = 8cm , and angle ABC = 60: . Locate by the construction the point P such that : 1. P is equidistant from B and C 2. P is equidistant from AB and BC

Measure and record the length of PB. 5. On a graph paper , draw the lines x =3 and y = -5 . Now on the same graph

paper , draw The locus of the point which is equidistant from the given lines.

6. State the locus of a point in a rhombus ABCD, Which is equidistant (1) From AB and AD (2) From the vertices A and C .

7. Construct a triangle BCP, with BC= 5cm , BP = 4cm , and angle PBC = 45: . Complete the rectangle ABCD such that : (1) (a) P is equidistant from AB and BC

(b) P is equidistant from C and D (2) Measure and record the length of PB.

8. Construct a △ ABC with AB =6 cm and BC=4.5cm and AC=5cm Draw and lebel (1) The locus of the centre of all the circles which touch AB and AC (2) The locus of centre of all the circle s of radius 2 cm which touch AB. Hence construct the circle of radius 2 cm which touches AB and AC.

9. A straight line AB is 8 cm long . Draw and describe the locus of a point

which is : (1) always 4 cm from the line AB

(2) equidistant from A and B.

Mark the two points X and Y which are 4 cm from AB and equidistant from A and B . Describe the figure AXBY.

10. Draw an angle ABC =75: find a point p such that p is at a distance 2 cm from AB and 1.5 cm from BC.

SL-(XII) Cylinder Cone and Sphere (CH-20)

1. The inner radius of a pipe is 2.1 cm. How much water can 12m of this pipe

hold?

2. A metal pipe has a bore (inner diameter ) of 5 cm . the pipe is 5 mm thick all

round. Find the weight , in kilogram, of 2 metres of the pipe if 1 cm³ of the

metal weight 7.7g.

3. Find the total surface area of an open pipe of length 50cm , external

diameter 20cm and in internal diameter 6 cm.

4. The total surface area of hollow cylinder, which is open from both the sides

is 3575 cm², area of its base ring is 357.5cm² and its height is 14cm. Find

the thickness of the cylinder.

5. A closed cylindrical tank ,made of thin iron –sheet , has diameter =8.4m and

height 5.4m. how much metal sheet , to the nearest m²,is used in making

the tank, if (1/15) of the sheet actually used was wasted in making the tank.

6. Find the volume of a cone whose slant height is 17 cm and radius of base is

8 cm.

7. Eight metallic spheres ; each of radius 2mm are melted and cast into a

single sphere. Calculate the radius of the new sphere.

8. Find what length of canvas,1.5m in width , is required to make a conical

tent 48m in diameter and 7m in height ? Given that 10% of the canvas is

used in folds and stitching, Also, find the cost of the canvas at the rate of

Rs. 24 per meter.

9. A hemispherical bawl of diameter 7.2 cm is filled completely with chocolate

sauce. This sauce is poured into an inverted cone of radius 4.8 cm. Find the

height of the cone if it is completely filled.

10. A solid cone of radius 5 cm and height 8cm is melted and made into small

spheres of radius 0.5 cm . Find the number of spheres formed.

11. A cubical block of side 7cm is surmounted by a hemisphere of the largest

size. Find the surface area of resulting solid.

12. A solid metallic hemisphere of diameter 28cm is melted and recast into a

number of identical solid cones .each of diameter 14 cm and height 8 cm .

find the number of cones so formed.

13. Two solid spheres of radii 2 cm and 4 cm are melted and recast into a cone

of height 8 cm Find the radius of the cone so formed.

14. A certain number of metallic cones , each of radius 2 cm and height 3 cm ,

are melted and recast into a solid sphere of radius 6 cm. Find the number

of cones used.

15. Form a solid cylinder of height 36 cm and radius 14 cm , a conical cavity of

radius 7 cm and height 24 cm drilled is drilled out . Find the volume and the

total surface area of the remaining solid.

Details to prepare assignment

Month Chapter Name

April GST

April A.P.

April G.P.

May Section and Mid-Point Formula

May Equation of line

May Similarity

June Loci

June Cylinder Cone and Sphere

June Ratio proportion

June Linear Inequation

July Remainder and factor theorem

July Reflection

Note------------ Linear Inequation, Ratio proportion, Remainder and factor

theorem, Reflection were taught in STD 9.