ICSE Class 10 Mathematics Previous Year Question Paper 2020 Download in PDF. This Old Question Paper also known as ICSE Specimen Paper 2020 Class 10 Mathematics included all Chapter of ICSE Syllabus GST, Banking, Shares and Dividend in two Variables, Linear Ineuations in One Variable, Quadratic Equations, Solving Simple Problems, Ratio and Proportion, Remainder and Factor Theorems, Matrices, Arithmetic Progressions, Geometric Progressions, Section and Mid – Point Formula, Equation of a Line, Similarity, Loci, Circles, Tangents and Intersecting Chords, Constructions, Cylinder,Cone And Sphere (Surface Area and Volume), Trigonometrical Identities,Heights and Distances, Graphical Representation, Measures of Central Tendency, Probabilty
ICSE Class 10 Mathematics Previous Year Question Paper 2020 from Chapter GST, Banking, Shares and Dividend in two Variables, Linear Ineuations in One Variable, Quadratic Equations, Solving Simple Problems, Ratio and Proportion, Remainder and Factor Theorems, Matrices, Arithmetic Progressions, Geometric Progressions, Section and Mid – Point Formula, Equation of a Line, Similarity, Loci, Circles, Tangents and Intersecting Chords, Constructions, Cylinder,Cone And Sphere (Surface Area and Volume), Trigonometrical Identities,Heights and Distances, Graphical Representation, Measures of Central Tendency, Probabilty
SECTION A (40 Marks)
Attempt all questions from this Section.
Question 1:
(a) Find the value of ‘k’ if 4x3 – 2x2 + kx + 5 leaves remainder -10 when divided by 2x + 1.
(b) Amit deposits ₹ 1600 per month in a recurring deposit account, If he gets ₹ 31,080 at the time of maturity, what is the rate of interest per annum?
(c) A shopkeeper bought an article with market price ₹ 1200 from the wholesaler at a discount of 10%. The shopkeeper sells this article to the customer on the market price printed on it. If the rate of GST is 6%, then find:
(i) GST paid by the wholesaler.
(ii) Amount paid by the customer to buy the item.
Question 2:
(a) Solve the following inequation and represent your solution on the real number line:
(b) Find the 16th term of the A.P. 7, 11, 15, 19…. Find the sum of the first 6 terms.
(c) In the given figure CE is a tangent to the circle at point C. ABCD is a cyclic quadrilateral. If ∠ ABC = 93o and ∠ DCE = 35o
Find
(i) ∠ ADC
(iI) ∠ CAD
(ii) ∠ACD
Question 3:
(a) Prove the following identity
(b) Find x and y if :
(c) For what value of ‘k’ will the following quadratic equation:
( k + 1 )x2 – 4kx + 9 = 0 have real and equal roots? Solve the equations.
Question 4:
(a) A box consists of 4 red, 5 black and 6 white balls. One ball is drawn out at random. Find the probability that the ball drawn is:
(i) black
(ii) red or white
(b) Calculate the median and mode for the following distribution:
Weight (in kg) | 35 | 47 | 52 | 56 | 60 |
No. of students | 4 | 3 | 5 | 3 | 2 |
(c) A solid cylinder of radius 7 cm and height 14 cm is melted and recast into solid spheres each of radius 3.5 cm. Find the number of spheres formed.
SECTION B (40 Marks)
Attempt any four questions from this Section
Question 5:
(a) The 2nd and 45th term of an arithmetic progression are 10 and 96 respectively. Find the first term and the common difference and hence find the sum of the first 15 terms.
(b) If A = [3/0 -1/2], find matrix B such that A2 – 2B = 3A + 5I where I is a 2 x 2 identity matrix.
(c) With the help of a graph paper, taking 1cm=1unit along both x and y axis:
(i) Plot points A (0, 3), B (2, 3), C (3, 0), D (2, -3), E (0, -3)
(ii) Reflect points B, C and D on the y axis and name them as B’, C’ and D’ respectively.
(iii) Write the co-ordinates of B’, C’ and D’.
(iv) Write the equation of line B’ D’.
(v) Name the figure BCDD’C’B’B
Question 6:
(a) In ∆ ABC and ∆EDC, AB is parallel to ED. BD = 1 3 BC and AB = 12.3 cm.
(i) Prove that ∆ABC ~∆EDC.
(ii) Find DE
(iii) Find:
(b) Find the ratio in which the line joining (-2, 5) and (-5, -6) is divided by the line y = -3. Hence find the point of intersection.
(c) The given solid figure is a cylinder surmounted by a cone. The diameter of the base of the cylinder is 6 cm. The height of the cone is 4 cm and the total height of the solid is 25 cm. Take π = 22 7 .
Find the:
(i) Volume of the solid
(ii) Curved surface area of the solid
Give your answers correct to the nearest whole number.
Question 7:
(a) In the given figure, PAB is a secant and PT a tangent to the circle with centre O. If ∠ATP = 40o , PA = 9 cm and AB = 7 cm.
Find: (i) ∠APT
(ii) length of PT
(b) The 1st and the 8th term of a GP are 4 and 512 respectively. Find:
(i) the common ratio
(ii) the sum of its first 5 terms.
(c) The mean of the following distribution is 49. Find the missing frequency ‘a’.
Class | 0 – 20 | 20 – 40 | 40 – 60 | 60 – 80 | 80 – 100 |
Frequency | 15 | 20 | 30 | a | 10 |
Question 8:
(a) Prove the following identity
(sinA + cosecA)2 + (cosA + secA) 2 = 5 + sec2A . cosec2A
(b) Find the equation of the perpendicular bisector of line segment joining A(4, 2) and B(-3, -5)
(c) Using properties of proportion, find x : y if
3 + 12 6 2 + 8 = 3 + 27 9 2 + 27
Question 9:
(a) The difference of the squares of two natural numbers is 84. The square of the larger number is 25 times the smaller number. Find the numbers.
(b) The following table shows the distribution of marks in Mathematics:
Marks (less than) | No. of students |
10 | 7 |
20 | 28 |
30 | 54 |
40 | 71 |
50 | 84 |
60 | 105 |
70 | 147 |
80 | 180 |
With the help of a graph paper, taking 2 cm = 10 units along one axis and 2 cm = 20 units along the other axis, plot an ogive for the above distribution and use it to find the:
(i) median.
(ii) number of students who scored distinction marks (75% and above)
(iii) number of students, who passed the examination if pass marks is 35%.
Question 10:
(a) Prove that two tangents drawn from an external point to a circle are of equal length.
(b) From the given figure find the:
(i) Coordinates of points P, Q, R.
(ii) Equation of the line through P and parallel to QR.
(c) Ms. Roy went to a departmental store and bought the following items. The GST rates and the quantity of each items and market price of each are given below:
S.No. | Items | Price per item in ₹ | Quantity | GST rate | Amount |
1.
2. 3. |
Walnut
Potato Chips Coffee |
650
50 80 |
1
2 2 |
5%
0% 18%
|
Find the:
(i) The total amount of SGST paid.
(ii) The total amount of the bill.
Question 11:
(a) Mr. Sharma receives an annual income of ₹ 900 in buying ₹ 50 shares selling at ₹ 80. If the dividend declared is 20%, find the:
(i) Amount invested by Mr. Sharma.
(ii) Percentage return on his investment.
(b) Two poles AB and PQ are standing opposite each other on either side of a road 200 m wide. From a point R between them on the road, the angles of elevation of the top of the poles AB and PQ are 45o and 40o respectively. If height of AB = 80 m, find the height of PQ correct to the nearest metre.
(c) Construct a triangle PQR, given RQ = 10 cm, ∠PRQ = 75o and base RP = 8 cm. Find by construction:
(i) The locus of points which are equidistant from QR and QP.
(ii) The locus of points which are equidistant from P and Q.
(iii) Mark the point O which satisfies conditions (i) and (ii).