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24 Hr Phone Helpline from 10 am 9 March (Thu) to 10 am 10 March (Fri) 1
th
ICSE Mathematics 2023 Board Exam
(All Types Covered)
Note: After every question I have mentioned PROBABILITY OF COMING IN BOARDS (P.O.C.I.B) Ch. 1 GST
1. M/s Ram Traders, Delhi, provided the following services to M/s Geeta Trading Company in Agra (UP). Find the amount of bill: Number of services
Cost of each service (in Rs.)
GST% 5 12 18 12
(P.O.C.I.B - 100%)
2. A is a manufacturer of T.V. sets in Delhi. He manufactures a particular brand of T.V. set and marks it at Rs.75,000. He then sells this T.V. set to a wholesaler B in Punjab at a discount of 30%. The wholesaler B raises the marked price of the T.V. set bought by 30% and then sells it to dealer C in Delhi. If the rate of GST = 5%, find tax (under GST) paid by wholesaler B to the government. (P.O.C.I.B - 70%) 3. Kritika, a manufacturer, sells binoculars for Rs. 3,750 to Aarushi, a wholesaler, who sells it to Vashu, a retailer, at a profit of 12%. Vashu, The retailer, sells it to a customer, Dhir, at a profit of Rs. 600. The GST charged is 18%, and all the sales are intra-state, find: (i) The GST paid by the wholesaler, Aarushi, to the Central Government. (ii) The price paid by the retailer, Vashu, inclusive of tax. (iii) The total GST received by State Government. (iv) The price paid by the customer, Dhir. (P.O.C.I.B - 70%) 4. A shopkeeper buys an article whose list price is Rs. 450 at some rate of discount from a wholesaler. He sells the article to a consumer at the list price and charges GST at the rate of 6%. If the shopkeeper has to pay GST of Rs. 2.70, find the rate of discount at which he bought the article from the wholesaler. (P.O.C.I.B - 1 %) Ch. 2 Banking 1. Vedik deposited Rs. 350 per month in a bank for 1 year and 3 months under the Recurring Deposit Scheme. If the maturity value of his deposits is Rs. 5,565; find the rate of interest per annum. (P.O.C.I.B - 100%) 2. Rishabh has a Recurring Deposit Account in a post office for 3 years at 8% p.a. simple interest. If he gets Rs. 9,990 as interest at the time of maturity, find : (i) the monthly instalment (ii) the amount of maturity. (P.O.C.I.B - 100%) 3. Sonia had a recurring deposit account in a bank and deposited Rs. 600 per month for 2½ years. If the rate of interest was 10% p.a., find the maturity value of this account. (P.O.C.I.B - 100%)
24 Hr Phone Helpline from 10 am 9 March (Thu) to 10 am 10 March (Fri) 2
4. Mr. Britto deposits a certain sum of money each month in a Recurring Deposit Account of a bank. If the rate of interest is of 8% per annum and Mr. Britto gets Rs. 8088 from the bank after 3 years, find the value of his monthly instalment. (P.O.C.I.B - 100%) 5. The maturity value of a R.D. Account is Rs. 16,176. If the monthly installment is Rs. 400 and the rate of interest is 8%; find the time (period) of this R.D. Account. (P.O.C.I.B - 10%) Ch. 4 Linear Inequations 1. Solve the following inequation and graph the solution set on the number line 2x – 3 < x + 2 3x + 5, x Z. (P.O.C.I.B - 100%) 2. (P.O.C.I.B - 100%) 3. (P.O.C.I.B - 100%) 4. (P.O.C.I.B - 100%) 5. P is the solution set of 7x – 2 > 4x + 1 and Q is the solution set of 9x – 45 ≥ 5(x – 5); where x ∈ R. Represent: (i) P ∩ Q (ii) P – Q (iii) P ∩ Q on different number lines. (P.O.C.I.B - 1 %) Ch. 5 Quadratic Equations 1. Solve the following question and give your answer correct to 2 decimal places: 5 x 2 - 3 x – 4 = 0 (P.O.C.I.B - 100%) 2. (P.O.C.I.B - 100%) 3. Solve for x using the quadratic formula. Write your answer correct to two significant figures: (x – 1)^2 – 3x + 4 = 0. (P.O.C.I.B - 100%) 4. Find the value of ‘k’ for which x = 3 is a solution of the quadratic equation, (k + 2)x^2 – kx + 6 = 0. Thus find the other root of the equation. (20%) 5. Find the value of k for which the following equation has equal roots. x^2 + 4kx + (k^2 – k + 2) = 0 (P.O.C.I.B - 80%) 6. Find the value of ‘m’ for which the given equation has real and equal roots. x^2 + 2 (m – 1)x + (m + 5) = 0. (P.O.C.I.B - 80%)
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6. (P.O.C.I.B - 100%)
Ch. 8 Remainder Factor Theorem
1. Find the value of a and b if x 1 and x 2 are factors of x^3 ax + b. Hence, factorise completely. (P.O.C.I.B - 100%) 2. Using the Remainder Theorem, factorise the following completely: 4x^3 + 7x^2 – 36x – 63. (P.O.C.I.B - 100%) 3. Find the values of constants a and b when (x^2 + x – 6) is a factor of expression x^3 + ax^2 + bx – 12. Hence factorise completely. (P.O.C.I.B - 10%) 4. The polynomials 2x^3 – 7x^2 + ax – 6 and x^3 – 8x^2 + (2a + 1) x – 16 leave the same remainder when divided by x – 2. Find the value of ‘a’. (P.O.C.I.B - 70%) Ch. 9 Matrices 1. **(P.O.C.I.B - 100%)
- (P.O.C.I.B - 100%) 3.** **(P.O.C.I.B - 70%)
- (P.O.C.I.B - 70%)** Ch. 10 A.P. 1. Which term of the arithmetic progression 1 + 4 + 7 + 10 + ……. is 52? (P.O.C.I.B - 100%) 2. Find the 31st^ term of an arithmetic progression whose 1 0 th^ term is 38 and 16 th^ term is 74. (P.O.C.I.B - 100%) 3. Find the sum of all natural numbers between 250 and 1000 which are divisible by 9. (P.O.C.I.B - 100%) 4. The sum of the first three terms of an Arithmetic Progression is 42 and the product of the first and third term is 52. Find the first term and the common difference. (P.O.C.I.B - 30%)
24 Hr Phone Helpline from 10 am 9 March (Thu) to 10 am 10 March (Fri) 5
5. If (k – 3), (2k + 1) and (4k + 3) are three consecutive terms of an A. P., find the value of k. (P.O.C.I.B - 30%) 6. How many terms of the A.P. 24, 21, 18, … must be taken so that their sum is 78? (P.O.C.I.B - 80%) Ch. 12 Reflection 1. Use a graph paper for this question. (Take 2 cm = 1 unit on both axes) (i) Plot the following points: A (0, 4), B (2, 3), C (1, 1) and D (2, 0). (ii) Reflect points B, C, D on the y-axis and write down their co-ordinates. Name the images as B, C, D respectively. (iii) Join the points A, B, C, D, D, C, B and A in order, so as to form a closed figure. Find its area and perimeter. (iv) Name two invariant points under reflection in y-axis. (P.O.C.I.B - 100%) 2. The points P (5, 1) and Q (2, 2) are reflected in line x = 2. Use graph paper to find the images P and Q of points P and Q in line x = 2. Take 2 cm = 2 units. (i) Name the figure PPQQ. (ii) Find the area of PPQQ. (P.O.C.I.B - 100%) Ch. 13 Section Midpoint Formula 1. In what ratio is the line joining (2, – 3) and (5, 6) divided by the x-axis? Also find the co-ordinates of the point. (P.O.C.I.B - 100%) 2. Calculate the ratio in which the line joining A(6, 5) and B(4, – 3) is divided by the line y = 2. (P.O.C.I.B - 80%) 3. The mid-point of the line segment joining (4a, 2b – 3) and (–4 , 3b) is (2, – 2a). Find the values of a and b. (P.O.C.I.B - 50%) 4. The co-ordinates of the centroid of a triangle PQR are (2, – 5). (P.O.C.I.B - 10%) If Q (–6, 5) and R (11, 8); calculate the co-ordinates of vertex P. Ch. 14 Equation of Line 1. The line passing through (–4, – 2) and (2, – 3) is perpendicular to the line passing through (a, 5) and (2, – 1) find a. (P.O.C.I.B - 100%) 2. ABCD is a parallelogram where A( x , y ), B(5, 8), C(4, 7) and D(2, – 4). Find: (i) Co-ordinates of A. (ii) the equation of a line, through the centroid and parallel to AB. (P.O.C.I.B - 100%) 3.
24 Hr Phone Helpline from 10 am 9 March (Thu) to 10 am 10 March (Fri) 7
(P.O.C.I.B - 100%)
(P.O.C.I.B - 100%)
(P.O.C.I.B - 40%)
(P.O.C.I.B - 70%)
7. ABC is a triangle with AB = 10 cm, BC = 8 cm and AC = 6 cm. Three circles are drawn touching each Other with the vertices as their centres. Find the radii of the three circles. (P.O.C.I.B - 10%) Ch. 19 Constructions 1. Draw a circle of radius 4.5 cm. Draw two tangents to this circle so that the angle between the tangents is 45º. (P.O.C.I.B - 30%) 2. Draw a circle of radius 3 cm. Mark a point P at a distance of 5 cm from the centre of the circle drawn. Draw 2 tangents PA and PB to the given circle and measure the length of each tangent. (P.O.C.I.B - 30%) 3. Construct a triangle ABC in which BC = 5.5 cm, AB = 6 cm and ABC = 120º. Construct a circle circumscribing the ABC. (P.O.C.I.B - 100%) 4. Construct the incircle of an equilateral XYZ with side 6.3 cm. (100%) 5. Construct regular hexagon of side 4 cm. Draw its circumcircle. (100%) 6. Construct regular hexagon of side 5 cm. Draw its incircle. (P.O.C.I.B - 100%)
24 Hr Phone Helpline from 10 am 9 March (Thu) to 10 am 10 March (Fri) 8 Ch. 20 Cylinder, Cone & Sphere
1. A solid cone of height 8 cm and base radius 6 cm is melted and recast into identical cones, each of height 2 cm and diameter 1 cm. Find the number of cones formed. (P.O.C.I.B - 100%) 2. Two solid cylinders, one with diameter 60 cm and height 30 cm and the other with radius 30 cm and height 60 cm, are metled and recasted into a third solid cylinder of height 10 cm. Find the diameter of the cylinder formed. (P.O.C.I.B - 100%) 3. Eight metallic spheres each of radius 2mm, are melted and cast into a single sphere. Calculate the radius of the new sphere. (P.O.C.I.B - 100%) 4. From a rectangular solid of metal 42 cm by 20 cm by 30 cm, a conical cavity of diameter 14 cm and depth 24 cm is drilled out. (P.O.C.I.B - 70%) Find:(i) the volume of remaining solid, (ii) the surface area of remaining solid, (iii) the weight of the material drilled out if it weighs 7 gm per cm^3. Link for the concept of surface area: https://www.instagram.com/reel/Cl8-TSZvG3C/?igshid=YmMyMTA2M2Y= 5. A wooden toy is in the shape of a cone mounted on a cylinder as shown alongside. If the height of the cone is 24 cm, the total height of the toy is 60 cm and the radius of the base of the cone is twice the radius of the base of the cylinder is 10 cm; find the total surface area of the toy. [Take = 3.14] (P.O.C.I.B - 70%) 6. A vessel, in the form of an inverted cone, is filled with water to the brim. Its height is 32 cm and diameter of the base is 25.2 cm. Six equal solid cones are dropped in it, so that they are fully submerged. As a result, one-fourth of water in the original cone overflows. What is the volume of each of the solid cones submerged? (P.O.C.I.B - 1 %) 7. The internal and external diameters of a hollow hemispherical vessel are 21 cm and 28 cm respectively. Find its total surface area. (P.O.C.I.B - 50%) 8. A circular tank of diameter 2 m is dug and the earth removed is spread uniformly all around the tank to form an embankment 2 m in width and 1.6 m in height. Find the depth of the circular tank. (P.O.C.I.B - 1 %) 9. A circus tent is cylindrical to a height of 8m surmounted by a conical part. If total height of the tent is 13m and the diameter of its base is 24m; calculate: (i) total surface area of the tent (ii) Area of canvas, required to make this tent allowing 10% of the canvas used for folds and stitching. (P.O.C.I.B - 1 %)
24 Hr Phone Helpline from 10 am 9 March (Thu) to 10 am 10 March (Fri) 10
5. An aeroplane flying horizontally 1 km above the ground and going away from the observer is observed at an elevation of 60. After 10 seconds, its elevation is observed to be 30; find the uniform speed of the aeroplane in km per hour. (P.O.C.I.B - 1 %) 6. The angle of elevation of a cloud from a point 60m above a lake is 30 and the angle of depression of the reflection of cloud in the lake is 60. Find the height of the cloud from lake surface. (P.O.C.I.B - 1 %) Ch. 24 Measures of Central Tendency 1. (P.O.C.I.B - 100%) 2. (P.O.C.I.B - 100%) 3. (P.O.C.I.B - 100%) YouTube Link: https://youtu.be/Bx_gb26XvOw
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(P.O.C.I.B - 100%)
(P.O.C.I.B - 100%)
Ch. 25 Probability
1. Cards bearing numbers 2, 4, 6, 8, 10, 12, 14, 16, 18 and 20 are kept in a bag. A card is drawn at random from the bag. Find the probability of getting a card which is: (i) A prime number (ii) A number divisible by 4 (iii) A number that is multiple of 6 (iv) An odd number. (P.O.C.I.B - 100%) 2. Sixteen cards are labelled as a, b, c ......... m, n, o, p. They are put in a box and shuffled. A boy is asked to draw a card from the box. What is the probability that the card drawn is: (i) a vowel. (ii) a consonant (iii) none of the letters of the word median. (P.O.C.I.B - 100%) 3. From a pack of 52 playing cards all cards whose numbers are multiples of 3 are removed. A card is now drawn at random What is the probability that the card drawn is: (i) a face card (King, Jack or Queen) (ii) an even numbered red card? (P.O.C.I.B - 20%) 4. Two coins are tossed once. Find the probability of getting: (i) 2 heads (ii) at least 1 tail (P.O.C.I.B - 20%) 5. When 3 coins are tossed simultaneously, what is the probability of finding: (i) At most1 tail? (ii) At least 2 tails? (iii) Not less than 2 heads? (P.O.C.I.B - 20%) 6. A box contains some black balls and 30 white balls. If the probability of drawing a black ball is two-fifth of a white ball, find the number of black balls in the box. (P.O.C.I.B - 10%)
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