(English Medium) ICSE Class 10 - CISCE Important Questions for Mathematics

The sum of first 15 terms of an A.P. is 750 and its first term is 15. Find its 20^th term.

The 5^th term and the 9^th term of an Arithmetic Progression are 4 and – 12 respectively.

Find:

1. the first term
2. common difference
3. sum of 16 terms of the AP.

Which term of the Arithmetic Progression (A.P.) 15, 30, 45, 60...... is 300?

Hence find the sum of all the terms of the Arithmetic Progression (A.P.)

The n^th term of an Arithmetic Progression (A.P.) is given by the relation T_n = 6(7 – n)..

Find:

1. its first term and common difference
2. sum of its first 25 terms

The point (3, 0) is invariant under reflection in:

Use graph sheet to Solution this question. Take 2 cm = 1 unit alogn both the axes.

1. Plot A, B, C where A(0, 4), B(1, 1) and C(4, 0)
2. Reflect A and B on the x-axis and name them as E and D respectively.
3. Reflect B through the origion and name it F. Write down the coordinates of F.
4. Reflect B and C on the y-axis and name them as H and G respectively.
5. Join points A, B, C, D, E, F, G, H and A in order and name the closed figure formed.

Use graph sheet for this question. Take 2 cm = 1 unit along the axes.

1. Plot A(0, 3), B(2, 1) and C(4, –1).
2. Reflect point B and C in y-axis and name their images as B' and C' respectively. Plot and write coordinates of the points B' and C'.
3. Reflect point A in the line BB' and name its images as A'.
4. Plot and write coordinates of point A'.
5. Join the points ABA'B' and give the geometrical name of the closed figure so formed.

Study the graph and answer each of the following:

1. Write the coordinates of points A, B, C and D.
2. Given that, point C is the image of point A. Name and write the equation of the line of reflection.
3. Write the coordinates of the image of the point D under reflection in y-axis.
4. Whats the name given to a point whose image is the point itself?
5. On joining the points A, B, C, D and A in order, a figure is formed. Name the closed figure.

The coordinates of the vertices of ΔABC are respectively (–4, –2), (6, 2), and (4, 6). The centroid G of ΔABC is ______.

In the given diagram, ABC is a triangle, where B(4, – 4) and C(– 4, –2). D is a point on AC.

1. Write down the coordinates of A and D.
2. Find the coordinates of the centroid of ΔABC.
3. If D divides AC in the ratio k : 1, find the value of k.
4. Find the equation of the line BD.

In the given figure ∠BAP = ∠DCP = 70°, PC = 6 cm and CA = 4 cm, then PD : DB is ______.

In the given figure, AC || DE || BF. If AC = 24 cm, EG = 8 cm, GB = 16 cm, BF = 30 cm.

1. Prove ΔGED ∼ ΔGBF
2. Find DE
3. DB : AB

In the given diagram, ΔABC ∼ ΔPQR. If AD and PS are bisectors of ∠BAC and ∠QPR respectively then ______.

In the given diagram ΔADB and ΔACB are two right angled triangles with ∠ADB = ∠BCA = 90°. If AB = 10 cm, AD = 6 cm, BC = 2.4 cm and DP = 4.5 cm.

1. Prove that ΔAPD ∼ ΔBPC
2. Find the length of BD and PB
3. Hence, find the length of PA
4. Find area ΔAPD : area ΔBPC.

Use ruler and compasses only for the following questions. All constructions lines and arcs must be clearly shown.

Construct the locus of points at a distance of 3.5 cm from A.

Use ruler and compasses only for the following questions. All constructions lines and arcs must be clearly shown

Construct the locus of points equidistant from AC and BC.

Use ruler and compasses only for the following questions. All constructions lines and arcs must be clearly shown

Mark 2 points X and Y which are a distance of 3.5 cm from A and also equidistant from AC and BC. Measure XY.

Construct a triangle ABC with AB = 5.5 cm, AC = 6 cm and ∠BAC = 105°

Hence:

1) Construct the locus of points equidistant from BA and BC

2) Construct the locus of points equidistant from B and C.

3) Mark the point which satisfies the above two loci as P. Measure and write the length of PC.

Use ruler and compasses only for this question:

I. Construct  ABC, where AB = 3.5 cm, BC = 6 cm and ABC = 60o.
II. Construct the locus of points inside the triangle which are equidistant from BA and BC.
III. Construct the locus of points inside the triangle which are equidistant from B and C.
IV. Mark the point P which is equidistant from AB, BC and also equidistant from B and C. Measure and records the length of PB.

Use ruler and compass to answer this question. Construct ∠ABC = 90°, where AB = 6 cm, BC = 8 cm.

1. Construct the locus of points equidistant from B and C.
2. Construct the locus of points equidistant from A and B.
3. Mark the point which satisfies both the conditions (a) and (b) as 0. Construct the locus of points keeping a fixed distance OA from the fixed point 0.
4. Construct the locus of points which are equidistant from BA and BC.