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3 A. 1 Model Paper Model Paper - 1 (Term -I) Find that the following pairs of sets are equivalent or non-equivalent. (Any five) B. If, L = {0, 1, 2,...12}, M = {5, 7, 9,... 15} and N = {6, 8, 10, 12, 14} then find: C. Convert the following decimal numbers into binary numbers. (Any two) 3. D. Solve the followings: (Any one) E. Solve the followings. F. Find the decimal values by using the following quinary number readers. G. Simplify the following.

4 2 Model Paper Identify each of the following property. (Any five) I. Write the following numbers as power of 10: J. Find the sum of the following quinary numbers. (Any one)

5 A. Model Paper - 2 (Term -I) 1. Write the power sets of the following set and also verify its cardinality. B. It, O = {1, 3, 5, 7,... }, E = {2, 4, 6, 8,...} And N = {1, 2, 3, 4,...} then prove that: 1. C. Express the following binary numbers as decimal numbers. D. Convert the following decimal numbers into quinary numbers. (Any one). E. Simplify the following expression. 3 Model Paper F. Prove that: (Any one) G Identify each of the following property.

6 Express the following numbers as base 10: 4 Model Paper I. Find the sum of the following quinary numbers. (Any one) J. Simplify.

7 A. Model Paper - 3 (Term -I) Write the power sets of the following set and also verify their cardinality. B. If X = {1, 3, 7}, Y = {2, 3, 5} and Z = {1, 4, 8} then prove that: C. Express the following numbers as base 10: (Any one) D. Express the following binary numbers as decimal numbers. (Any one) E. Solve the followings. F. Evaluate the followings. (Any one) G. Find the additive and multiplicative inverse of the following rational numbers. (Any one) 5 Model Paper Express the following numbers as base 10: I. Evaluate the followings. (Any one) J. Simplify.

8 Model Paper - 4 (Term -I) A. Solve: (Any one) 1. If, A = {a, e, i, o, u}, B = {a, b, c} and C = {a, c, e, g} then prove that: (i) (ii) B. Convert the following decimal numbers into binary numbers. (Any one) C. Express the following numbers as base 10: (Any one) D. Simplify the followings. 6 Model Paper E. F. Convert the following decimal numbers into quinary numbers. Simplify the following expression. G. 1. Prove that: (Any one) 2. Express the following numbers as base 10: I. Evaluate the followings. (Any one) J. Simplify.

9 Model Paper - 1 (Term -II) A. Find the square root of the following by division method. B. Solve: (Any one) 1. The cost for wooden flooring of a 18 feet long and 12 feet wide room is Rs , what will be the cost of 15 feet long and 10 feet wide room. 2. If 80 labourers construct a 200 metre long road in 25 days. In how many days, 100 labourers will construct a 150 metre long road. C. 7 Model Paper Ahmad got a life insurance policy of Rs. 1,40,000. Find the 1st premium that Ahmad has to pay. The rate of annual premium is 4.8% and policy fee is 0.1% D. Solve: (Any one) 1. Raza borrowed Rs for 3 months at the rate 3% per annum. Calculate the simple interest that Raza shall pay. 2. Khushi deposited Rs. 10,000 in a bank. After 2 years the bank returned her an amount Rs Calculate, what rate of simple interest she received from the bank? E. Farah deposited Rs. 6,250 for 2 years in a bank at the rate of 8% per annum. Calculate the compound interest that bank paid to Farah. F. Find the square root of the following decimal fractions by division method. G. Find the square roots of the following irrational numbers up to two decimal places. (Any one) Find the number that gives after multiplying itself. I. A group of 48 ants have food for 16 days but 12 ants died after 4 days due to rain. For how many days the remaining food will be enough. J. Sheikh got an insurance policy for his shop worth Rs. 7,50,000 at the rate 3.7% for 3 years. Find the benefit of policy if he had got a claim of Rs. 1,00,000. The rate of depreciation is 6%.

10 Model Paper - 2 (Term -II) A. Find the square root of the following by division method. B. Solve: (Any one) 1. If 16 girls uses 48 lipsticks in 30 days, then how many lipsticks 20 girls will use in 25 days girls knit 100 sweaters by working 6 hours daily, how many sweaters 150 girls will knit by working 8 hours daily. C. 8 Model Paper Tuba got a life insurance policy whose annual premium is Rs. 8,640. Calculate the half yearly, quarterly and monthly premiums which are 51%, 26% and 9% of annual premium. D. Solve: (Any one) 1. Khushi deposited Rs. 10,000 in a bank. After 2 years the bank returned her an amount Rs Calculate, what rate of simple interest she received from the bank? 2. Imran deposited Rs in a bank at the rate of simple interest 20%. Calculate, in how many years can he get the amount to the double? (Hint: Amount = = Rs. 4800) E. Nosheen invested Rs. 51,200 at the rate of 25% per annum for 5 years. Find the compound interest for the given investment. F. Find the square root of the following decimal fractions by division method. G. Find the square roots of the following irrational numbers up to two decimal places. A mason took Rs for repairing the floor of a circular mosque at the rate of Rs /m. Find the radius of the circular floor the mosque. I. If 18 fat girls of a hostel can eat 240 loaves of bread in a meal then how many fat girls can eat the 160 in a meal? J. Rana bought a vehicle for Rs. 5,00,000 and got it insured at the rate of 4.5% yearly for ten years. But after 3 years his vehicle damaged completely in an accident. Calculate the benefit of policy that Rana got. The rate of depreciation is 10%.

11 Model Paper - 3 (Term -II) A. Find the square root of the following by division method. B. Find the square roots of the following irrational numbers up to one decimal place? C. 9 Model Paper A cargo company takes Rs. 500 for 80kg of goods to carry up to the distance of 12km, how much the cargo company will take for 60kg of goods for a distance of 20km. D. Solve: (Any one) 1. Find the simple interest on Rs for 146 days at the rate of 5% per annum. 2. Imran deposited Rs in a bank at the rate of simple interest 20%. Calculate, in how many years can he get the amount to the double? (Hint: Amount = = Rs. 4800) E. Ali borrowed Rs. 45,000 for 4 years at the rate of 20% per annum. Find the compound interest that Ali has to pay. F. Find the square root of the following decimal fractions by division method. G. I. Which smallest number can be subtracted from to get a perfect square? A fairy wants to help an innocent princess who is at the distance of 816km from the fairyland. Tell in what time the fairy will reach the princess where the fairy can travel 1020km in one hour. Haris got an insurance of his bike worth Rs. 75,000 at the rate of 3.5% for 3 years. Calculate the benefit of policy if Haris had a claim of Rs. 12,000. The rate of depreciation is 10%.

12 J. Fill in the blanks. (Any four) 10 Model Paper

13 Model Paper - 4 (Term -II) A. Find the square root of the following by division method. B. Find the square roots of the following irrational numbers up to two decimal places. C. If 80 labourers construct a 200 metre long road in 25 days. In how many days, 100 labourers will construct a 150 metre long road. D. Solve: (Any one) 1. Sheikh got an insurance policy for his shop worth Rs. 7,50,000 at the rate 3.7% for 3 years. Find the benefit of policy if he had got a claim of Rs. 1,00,000. The rate of depreciation is 6%. 2. Rana bought a vehicle for Rs. 5,00,000 and got it insured at the rate of 4.5% yearly for ten years. But after 3 years his vehicle damaged completely in an accident. Calculate the benefit of policy that Rana got. The rate of depreciation is 10%. E. Haider invested Rs. 1,00,000 for 3 years at the rate of 10% per annum. Find the compound interest that Haider earned. F. 11 Model Paper Find the square root of the following decimal fractions by division method. G. I. Which smallest number can be subtracted from to get a perfect square? Find mean proportional of 4 and 16. Fill in the blanks. (Any four)

14 12 Model Paper J. Usma got an insurance of his property at the rate of 2.4% yearly for 4 years. Calculate the premium he paid in 4 years. The rate of depreciation is 10% and worth of the property is Rs. 20,00,000.

15 13 Model Paper Model Paper - 1 (Term -III) A. Simplify the following polynomials. B. Find the square of the following by using a formula. (Any one) C. Simplify: D. Construct the square PQRS, whose diagonals are: E. Draw the following triangles and construct the bisectors of their angles. MN = 4.2cm 3. M = 80 F. Simplify. G. I. J. Solve the following by using the formulae. Evaluate: Factorize by using the formula. Resolve into factors.

16 14 Model Paper Model Paper - 2 (Term -III) A. Prove that: B. Factorize. (Any one) C. Solve the following system of linear equations. D E. Construct the parallelogram ABCD, when. Draw the following triangles and construct the right bisectors of their sides. F. G. I. J. Simplify. Solve the following by using the formulae. Find the cube of the following by using a formula. Find the value of a + b + c when a + b + c = 36, and ab + bc + ca = 32 Factorize by using the formula.

17 15 Model Paper Model Paper - 3 (Term -III) A. Simplify the following by using the formulae. B. Evaluate the following by using the formula a b. (Any one) C. Simplify: D E. F. G. I. Divide the line segment: (Any one) Draw a pentagon of 2.9 cm long sides. Simplify. Solve the following by using the formulae. Find the cube of the following by using a formula. Prove that: J. Find the value of a + b + c when a + b + c = 14, and ab + bc + ca = 88.

18 16 Model Paper Model Paper - 4 (Term -III) A. Factorize: B C. Simplify: (Any one) Find the solution set of the following linear equation. D. Solve: (Any one) 1. Divide a line segment of length 10 cm into 5 congruent parts. 2. Draw a 9.8 cm ling line and divide it into 7 congruent parts. E Answer the following questions. 5. F. Simplify. G. I. J. Solve the following by using the formulae. Prove that: Simplify. Evaluate:

19 Model Paper - 1 (Term -IV) A. A 12.5 metre long steel pipe is placed against a wall at the height of 12 metre. Calculate the distance between the lower end of the pipe and the wall. B. Solve: (Any one) 1. The lengths of the sides of a quadrilateral PQRS are PQ = 11cm, QR = 13cm, RS = 16cm ans SP = 20cm. Where the diagonal is PR = 22cm. Find the area of the quadrilateral. 2. Calculate the area of a quadrilateral ABCD whose sides are AB = 3cm, BC = 4cm, CD = 3.5cm and AD = 2.5cm. Where AC = 5cm is the diagonal of the quadrilateral. C. D. 17 Model Paper The surface area of a sphere is 484 cm. Find the volume of the sphere. Roha bought the following kind of meat from the meat market. E F G. Calculate the mean price of the meat. Calculate the median and mode for each set of data below. Find the area of the triangle with the help of the given elements. (Any one) Find the surface area of an iron sphere whose radius is 7.7cm. Also calculate the cost of polishing the sphere at the rat of Rs. 10/cm. The radius of a cone s base is 5.5cm and slant height is 8.5cm. Find the surface area of the cone.

20 18 Model Paper I. I. A conical glass is full of juice. The height of the glass is 14cm and radius is 3.6cm. Find the quantity of the juice in the glass. (Hint: 1cm = 1ml) Tick (4) the correct answer.

21 Model Paper - 2 (Term -IV) A. A cylindrical blood tank in Vampire Estate is 350cm high and its inner radius is 140m. Find the capacity of the blood tank in liters and also calculate the price of the marble used in the inner side of the marble used in the inner side of the tank at the rate of Rs. 8/cm. B. Solve: (Any one) 1. Find the area os the triangle ABC whose sides are 13cm, 14cm and 15cm long respectively. 2. Three sides of a triangle are 2.5cm, 3.5cm and 5cm long respectively. Find the area of the triangle. C. D. 19 Model Paper Calculate the polishing cost of a wooden sphere at the rate of Rs. 275m where the radius of the shpere is 1.4m. Find the means of the following frequency tables. (Any one) E. F Find the mean, median and mode of the following data which is showing the number of doctors in 18 hospitals of a city. 49, 13, 12, 59, 12, 21, 10, 21, 13, 11, 32, 15, 26, 35, 45, 51, 14, 56. Solve: (Ane one) Calculate the area of a quadrilateral ABCD whose sides area AB = 3cm, BC = 4cm, CD = 3.5cm and AD = 2.5cm. Where AC = 5cm is the diagonal of the quadrilateral. A quadrilateral shaped field has lengths of sides 15m, 11m, 9m and 13m respectively. Find the area of the quadrilateral shaped field when the length of the diagonal is 18m.

22 G. The surface area of a sphere is 1764 cm. Find its volume and if we melt its volume then how many spheres of 1cm radius could be made out. I. J. 20 Model Paper The height of a cone is 11.2cm and slant height of the cone is 14cm. Calculate the surface are of the cone. A conical oil tank is 11m high whose base radius is 6.3m. Find the capacity of the tank in litres and cost of polishing the tank at the rate of Rs. 80/m. Answer the following questions. (Any four)

23 Model Paper - 3 (Term -IV) A. 120m, 160m and 200m are the lengths of the sides of a triangular shaped park. Find the area of the park and cost of repairing the park at the rate of Rs. 25/m. B. (Any one) 1. Calculate the surface are of a hemispherical tomb of a mosque whose radius is 4.2 metre. Also find the cost of painting the tomb at the rate of Rs. 120/m. 2. Find the cost of tiles used on a hemispherical shaped tomb at the rate of Rs. 4400/m where the radius of the tomb is 9.1m. C. D. 21 Model Paper The circumference of the base of a cone is 39.6cm and height is 8.4cm. Find the surface area of the cone. Find the means of the following frequency tables. (Any one) E. F Calculate the mean, median and mode of a data given below. The data represents the distance in kilometer that 25 workers of a factory travel daily. 7, 11, 10, 8, 7, 10, 9, 11, 9, 8, 9, 11, 10, 8, 6, 7, 9, 11, 8, 10, 11, 9, 10, 11. Solve: (Ane one) The lengths of the sides of a quadrilateral PQRS are PQ = 11cm, QR = 13cm, RS = 16cm and SP = 20cm. Where the diagonal is PR = 22cm. Find the area of the quadrilateral. Calculate the area of a quadrilateral ABCD whose sides area AB = 3cm, BC = 4cm, CD = 3.5cm and AD = 2.5cm. Where AC = 5cm is the diagonal of the quadrilateral.

24 G. I. 22 Model Paper Find the capacity of a hemispherical bowl in litres whose diameter is 21cm. (Hint: 1000cm = 1 litre) A metal cone with base radius 2.9cm melted and recasted into a sphere. Calculate the height of the cone if radius of the sphere is the same as the base radius of the cone. Fill in the blanks. J. Use the following frequency table to draw the histograms.

25 23 Model Paper Model Paper - 4 (Term -IV) A. Three sides of a triangle are 2.5cm, 3.5cm and 5cm long respectively. Find the area of the triangle. B. Find the radius of the following spheres. (Any one) C. D. The slant height of a cone is 13.8cm and circumference of its base is Find the lateral area of the right circular cone. Find the means of the following frequency tables. (Any one) E. The data below shows the daily wages of 30 labourers of a city. 200, 150, 125, 110, 175, 150, 225, 200, 125, 150, 200, 150, 110, 200, 150, 225, 175, 200, 125, 200, 200, 250, 150, 175, 225, 200, 200, 125, 150, 200. Calculate the mean, median and mode of the given data. F. Solve: (Ane one) 1. Find the area of a quadrilateral ABCD whose sides are AB = 18cm, BC = 10cm, CD = 15cm and AB = 17cm. Where the diagonal of the quadrilateral is AC = 20cm. 2. The lengths of the sides of a quadrilateral PQRS are PQ = 11cm, QR = 13cm, RS = 16cm and SP = 20cm. Where the diagonal is PR = 22cm. Find the area of the quadrilateral. G. Find the capacity of a spherical tank in litres whose radius is 2.1m. (Hint: 1m = 1000 litre)

26 I. 24 Model Paper A conical tent is 12 metres high and radius of its base is 9 metres. Calculate the volume of the air in the tent and cost of canvas that used to make the tent at the rate of Rs. 350/m. [Hint: canvas used for tent = lateral area of tent ( rl)] Use the following frequency table to draw the histograms. J. Roha bought the following kind of meat from the meat market. Calculate the mean price of the meat.

The City School PAF Chapter Prep Section. Mathematics. Class 8. First Term. Workbook for Intervention Classes

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