SSC PUBLIC EXAMINATIONS - MATHS GUESS PAPER

 SSC PUBLIC EXAMINATIONS - MATHS GUESS PAPER

Total chapters in mathematics are - 14

Questions paper - PART - A

SECTION -I

Six, 2marks questions

6Q × 2marks = 12 marks ( no choice )

SECTION - II

6Q × 4marks = 24 marks ( no choice )

SECTION -III

Essay type questions 

4Q × 6 marks = 24 marks 

out of 6 questions you have to answer 4 questions.

👉 1.REAL NUMBERS

2 marks Questions 

1. Division algorithm 

Ex: 1. Use Euclid’s division algorithm to find the HCF of

(i) 500 and 150

(ii) 194 and 35890

Note : sometimes they asked the number is your choice.

2. Find the LCM and HCF of the following integers by the prime factorisation method.

(i) 10, 15 and 35

(ii) 13, 17 and 23

(iii) 7, 9 and 25

3. Determine the value of the following.

I. log3 base 27,  ii. Log 1/64 base 2

👉 4 marks Questions 

1. Show that 2–√3 is a irrational number. 

2. If x2 + y2 = 7xy then show that 2 log (x + y) = log x + log y + 2 log 3. 

3. Prove that 2√3 +√5 is an irrational number. ( It may be given for 4 or 6 marks also )

👉 6 MARKS QUESTIONS 

1. Prove that √2 + √ 3 is an rational number. 

2. Prove that √ 5 - √3 is an rational number 

3. Prove that 2√3 + 3√ 5 is an rational number. 

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👉2. SETS

Note: convert roaster farm to set builder farm  (Or)  Set builder farm to roster farm.

This conversions based on number system. 

2 marks.... 

Ex: 1. Write roster and builder form of “The set of all natural numbers which divide 42”. 

2. Write A = {1, 2, 3, 4} in set builder form. 

3. If A = {1, 2, 3, 4} and B = (1, 2, 3, 5, 6} then find

(i) A ∩ B

(ii) B ∩ A

(iii) A – B and

(iv) B – C then comment on the above. 

4. Represent the following through Venn- diagram.

i) A – B

ii) B – A

iii) A ∪ B

iv) A ∩ B

👉 4 MARKS

1.If A = {x / x is a prime number and x < 20} then B = {x / 2x + 1, x ∈ w and x < 9} then Find

(i) A ∩ B

(ii) B ∩ A

(iii) A – B

(iv) B – A. What do you observe ?

2. If x+y =10xy, then prove that 2 log(x + y)= log x + log y + 2 log 2+ log 3. 

3. From the given Venn diagram show that n(AUB)= n(A) +n(B) - n(A OB). 

➡️ Converting set builder farm into roster farm association with that find either AUB or A intersection B or  A - B, B - A. ( in this model )

👉 6 MARKS QUESTIONS 

1.If x is set of all factors of 24 and y is set all factors of 36 then find X ∪ Y and X ∩ Y using venn – diagrams. Comment. 

2. If A = {x / x ∈ N, x < 6 } and B = { x : x ∈ N, 3 < x < 8} then show that A – B ≠ B – A with the help of venn – diagram.

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👉3. POLYNOMIAL 

2 MARKS...

1. If p(t) = 3t3 + 4t – 5, find the values of p(1), p(-1), P(0), p(2), p(-2). 

2. Find the zeros, the sum of the zeros and the product of the zeros of the quadratic polynomial as follow: P(x) = 3x2 - x -4

3. Find a quadratic polynomial if the sum and product of zeros as follows :

The sum of zeros = −3; the product of zeros =−4.

👉 4 MARKS 

1. Find the zeroes of the given polynomials.

i) p(x) = 4x

ii) p(x) = x2 – 9x + 20

iii) p(x) = (x + 5) (x + 6)

iv) p(x) = x4 – 81

2. Verify the relationship between the zeroes and the coefficient of x2 – 25 by finding its zeroes. 

👉 6 MARKS

1.Draw the graph of the quadratic polynomial p(x)= x2-4x +3and find the zeroes of the polynomial from the graph. 

2. Draw the graph of polynomial

p(x) = x2 – 3x + 2 and find its zeros.

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👉 LINEAR EQUATIONS IN TWO VARIABLES 

1. The ratio of incomes of two persons is 9 : 7 and the ratio of their expenditures is 4 : 3. If each of them manages to save RS.2000 per month, find their monthly incomes

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👉 Quadratic Equations

2 Marks...

1. Find the roots of the following quadratic equation: 23–√x2 – 5x + 3–√ = 0 

2. Find the roots of the following quadratic equations by applying the quadratic formula.

i) 3x2 + 4x – 12 = 0

ii) 2x2 + 23–√x – 3 = 0

3. Find the value of k for the following quadratic equation so that they have equal roots.

i) x2 – kx + 25 = 0.

4. Solve the equation 3x = 5x + 2.

5. The product of two consecutive positive integers is 306. Find the integers.

💠 4 MARKS Questions 

1. Solve the given pair of linear equations by elimination method. ( They may ask Elimination method or graphical representation )

i) 2x + y – 5 = 0 and

ii) 3x – 2y – 4 = 0.

2. Find the roots of the following quadratic equations, If they exist, by the method of the completing the square.

i) x2 + 5x = 4

ii) 4x2 + 6x = 3

3. 1.Find the roots of the following quadratic equations by factorisation.

i) x2 – 6x + 5 = 0

ii) 2x2 – 7x + 6 = 0

iii) x(x + 7) = -12

iv) 3x2 + 7x – 6 = 0

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👉 Progressions - 

2 marks 

1. Find the

i) 25th term of the A.P.: 8, 11, 14,………

ii) 10th term of the A.P.: – 10, -6, -2,…….

2. Which term of the A.P 5, 8, 11, 14, ….. is 47?

3. Find the sum of the following APs.

i) 4, 9, 14, …… to 14 terms.

4. Write the terms of the G.P. When the first term ‘a’ and the common ratio ‘r’ are given.

i) a = 5, r = 2

5. Which term of the G.P. 3,9,27, …… is 729.

➡️ 4 MARKS QUESTIONS 

1. Find the sum of the following APs.

i) 4, 9, 14, …… to 14 terms

ii) – 32, – 28, – 24, …… to 12 terms.

2. Which term of the A.P. 21, 18, 15, .... is -81 ? Also find the term which becomes zero. 

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👉 7. Coordinate Geometry

➡️ 2 MARKS QUESTIONS 

1. Show that the points A = (4, 2), B (7, 5) and C (9, 7) are collinear.

2. Find the mid point of the line segment formed by the points (-5, 5) and (5, -5) 

3. Find the distance between the following pairs of points. (Each 1 Mark)

i) (3, 4) and (6, 2)

ii) (-4, 6) and (0, 2)

4. Find the slope of the line joining the points.

i) (7, -5) and (8, 1)

5. Find the centroid of the triangle whose vertices are (2, 3), (-4, 7) and (2, -4). 

6. The Sdes of a triangle measure 2/2. 4 and 2/6 units. Is it a right-angled triangle? Justify. 

👉 6 MARKS

1. In an acute angled triangle ABC, if sin(A+B-C) = and cos(B + C-A) = , 2 then find <A, <B and <C. 

2. Construct triangle ABC with BC =7 cm, <B= 45° and <C= 60°. Then construct another triangle similar to  ∆ABC, whose sides are the 3/5 times of the corresponding sides of ∆ ABC.

3. Find the trisection points of the line segment joined by the points (-3, 3) and (3, -3).

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👉  8. Similar Triangles

1. State and prove basic proportionality theorem

S.A.S similarity 

A.A.A similarity 

A.S.A similarity 

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👉  9 Tangents and Secants to a Circle

1. Calculate the length of Tangent from a point 13 cm away from the centre of a circle of radius 5 cm.

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👉  10 Mensuration

2 marks 

💠 In this topic questions based on hemisphere cylinder, cone.

1. Find the volume and total surface area of a hemisphere whose radius is 35 cm ?

2. Find the volume and surface area of a sphere of radius 42 cm.

3. The shape of solid iron rod is a cylindrical. Its height is 20cm and base diameter is 14 cm. Then find the total volume of 60 such rods.

👉 4 MARKS QUESTIONS 

1.Three metal cubes with edges 15 cm., 12 cm. and 9 cm. respectively are melted together and formed into a single cube. Find the diagonal of this cube.

👉 6 MARKS QUESTIONS 

1. The diameter and height of a cylinder are equal, and its volume is 2156 cm3 . The cylinder is cut into two equal cylinders. Find the total surface area of each cylinder.

2. A cylindrical bucket, 36 cm high and with radius of base 16 cm is filled with rice. This bucket is emptied out on the ground and a conical heap of rice is formed. If the height of the comical heap is 27 cm. find the radius d slant height of the heap.

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👉  11. Trigonometry

2 MARKS..

1. All trigonometric values and ratios must be memorized.

Based on these values, a two-mark question will be asked.

2. Find the value of

i) Sin 75° – Cos 15°

ii) Sec 23° – Cosec 67°

2. Express tan 0' in terms of 'sin 0'. 

💠 4 marks Questions 

1. Show that TanA+CotB/TanB+CotA = Tan A . Cot B. ( Not: prove LHS = RHS )

👉 6 MARKS QUESTIONS 

1. Show that Tan2q/1+Secq=1−Cosq/Cosq

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👉  12. Applications of Trigonometry

2 MARKS

🔶 In rare ,one question will be asked for two mark. 

Q: They gave a statement you have to represent a diagram

1. An observer standing at a distance of 10m from the foot of a tower, observe its top with an angle of elevation of 60 ". Draw a suitable diagram for this situation. 

👉 6 MARKS QUESTIONS 

1. From a point P on the ground the angle of elevation of the top of a 10 m tall buildingis 30°. A flag is hoisted at the top of the building and the angle of elevation of the top of the flagstaff from P is 45°. Find the length of the flagstaff and the distanceof the building from the point P. (You may take √3 = 1.732)

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👉  13. Probability.

2 MARKS

1. Find the probability of getting a sum of the numbers on dice is 7, when two dice are rolled at a time. 

2. red and 8 white balls are present in a bag. If a ball is taken randomly from the bag then find the probability of it to be

i) white ball

ii) not to be a white ball 

3. Find the probability of getting a vowel' if a letter is chosen randomly from the word "INNOVATION". 

👉 4 MARKS QUESTIONS 

There are 25 cards of same size in a bag on which number 1 to 25 are written one card is taken out of the bag at random. Find the probability that the number on the selected card is not divisible by 5.

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👉  14. Statistics - 

2 MARKS

In this topic you will get a question on ungrouped data. 

( Note: You won't get any question on grouped data in section 1 )

👉 4 MARKS

1. Write the formula for Median of a grouped data and explain each term of it. 

👉 6 MARKS QUESTIONS 

Q: they will give you group data and ask to find mean, median and mode.

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Note: Graph question from: polynomials, paraff linear equations, statistics

 

PART - B : 30 minutes duration 

20 Q × 1M = 20 marks

👉 One question from each chapter Sometimes two questions are asked from some chapters.

👉 Most of the questions asked on fundamentals.

                 All the best 💐 💐 💐