Maharashtra SSC Algebra (Mathematics Part I) Board Paper July 2025

Written board papers, 40 marks and 2 hours each: Science & Technology Part 1 and 2, Algebra, Geometry and more.

2025, July 120 minutes 40 marks Save WhatsApp

Sections

Q.1 (A) Choose the correct alternative (4 marks)	4 questions
Q.1 (B) Solve the following subquestions (4 marks)	4 questions
Q.2 (A) Complete and write any two activities (4 marks)	3 questions
Q.2 (B) Solve any four subquestions (8 marks)	5 questions
Q.3 (A) Complete and write any one activity (3 marks)	2 questions
Q.3 (B) Solve any two subquestions (6 marks)	3 questions
Q.4 Solve any two subquestions (8 marks)	3 questions
Q.5 Solve any one subquestion (3 marks)	2 questions

About the July 2025 SSC Algebra board paper

This is the Mathematics Part I (Algebra) paper set by the Maharashtra State Board for the July 2025 Class 10 examination (English medium, Revised Course, paper code N 684). It is a 2-hour paper for 40 marks and calculators are not allowed.

The paper follows the usual board pattern: four MCQs and four one-mark questions in Q.1, activities to complete and short sums in Q.2, one activity plus 3-mark sums in Q.3, and 4-mark and 3-mark problems with internal choice in Q.4 and Q.5. All six chapters of the Algebra syllabus appear — determinants and Cramer's rule, simultaneous equations, quadratic equations solved by completing the square and by factorisation, an A.P. whose terms are 4, 9, 14, shares, brokerage and GST, probability with playing cards and two dice, and statistics (central angles, mean by the assumed-mean method and the median of grouped data).

Chapters covered

Instructions

Solve on paper with a timer, then check against the solutions.

Q.1 (A) Choose the correct alternative (4 marks)

Q.1 (A)(i) The value of determinant \(\begin{vmatrix} 5 & 3 \\ -7 & -4 \end{vmatrix}\) is ..........................
1. (A) –1
2. (B) –41
3. (C) 41
4. (D) 1
1 mark See answer →
Q.1 (A)(ii) Out of the following equations which one is not a quadratic equation ?
1. (A) \(x^2 + 4x = 11 + x^2\)
2. (B) \(x^2 = 4x\)
3. (C) \(5x^2 = 90\)
4. (D) \(2x - x^2 = x^2 + 5\)
1 mark See answer →
Q.1 (A)(iii) For given A.P. \(a = 3.5\), \(d = 0\), then \(t_2\) = .........................
1. (A) 0
2. (B) 3.5
3. (C) 7
4. (D) 10.5
1 mark See answer →
Q.1 (A)(iv) From the following numbers which number cannot represent a probability ?
1. (A) 0.6
2. (B) 2.0
3. (C) 0.15
4. (D) 0.75
1 mark See answer →

Q.1 (B) Solve the following subquestions (4 marks)

Q.1 (B)(i) For simultaneous equations in variables \(x\) and \(y\), \(D_x = 49\), \(D_y = -63\), \(D = 7\), then find the value of \(x\).

1 mark See answer →
Q.1 (B)(ii) Write the following quadratic equation in standard form : \(2y = 10 - y^2\)

1 mark See answer →
Q.1 (B)(iii) Face value of one share is ₹ 100 and premium is ₹ 10. Find the market value of the share.

1 mark See answer →
Q.1 (B)(iv) Find the class mark of the class 6–10.

1 mark See answer →

Q.2 (A) Complete and write any two activities (4 marks)

Q.2 (A)(i) Complete the following activity to solve the quadratic equation \(x^2 + 8x - 48 = 0\) by completing square method.
Activity :
\(\therefore\ x^2 + 8x - 48 = 0\)
\(\therefore\ x^2 + 8x + 16 -\) ____ \(- 48 = 0\)
\(\therefore\ (x + 4)^2 -\) ____ \(= 0\)
\(\therefore\ (x + 4)^2 = 64\)
\(\therefore\ x + 4 =\) ____ or \(x + 4 = -8\)
\(\therefore\ x = 4\) or \(x =\) ____

2 marks See answer →
Q.2 (A)(ii) Courier service agent charged total ₹ 590 to courier a parcel from Nashik to Nagpur. In the tax invoice taxable value is ₹ 500 on which CGST is ₹ 45 and SGST is ₹ 45. Complete the following activity to find the rate of GST charged for this service :
Activity :
Total GST = CGST + SGST
\(=\) ____ \(+ 45\)
\(=\) ₹ ____
Rate of GST \(= \dfrac{90}{500} \times\) ____
\(\therefore\) Rate of GST charged by agent is ____ %

2 marks See answer →

Q.2 (A)(iii) The monthly expenditure of a family on different items is shown in the following table. Complete the following activity to calculate the related central angles.

Activity :

Different items	Percentage of expenditure	Measure of central angle
Food	40	\(\dfrac{40}{100} \times 360^\circ =\) ____ \(^\circ\)
Clothing	20	\(\dfrac{20}{100} \times 360^\circ =\) ____ \(^\circ\)
Education	30	\(\dfrac{30}{100} \times 360^\circ =\) ____ \(^\circ\)
Other expenditure	10	\(\dfrac{10}{100} \times 360^\circ =\) ____ \(^\circ\)
Total	100	360°

2 marks See answer →

Q.2 (B) Solve any four subquestions (8 marks)

Q.2 (B)(i) Find the values of \((x + y)\) and \((x - y)\) of the following given simultaneous equations :
\(101x + 99y = 501\)
\(99x + 101y = 499\)

2 marks See answer →
Q.2 (B)(ii) Solve the following quadratic equation by factorisation method : \(x^2 - 15x + 54 = 0\)

2 marks See answer →
Q.2 (B)(iii) Which term of the following A.P. is 560 ?
2, 11, 20, 29, .......

2 marks See answer →
Q.2 (B)(iv) Market value of a share is ₹ 200. If the brokerage rate is 0.3%, then find the purchase value of the share.

2 marks See answer →
Q.2 (B)(v) If \(\sum f_i d_i = 10,000\), \(\sum f_i = 100\) and \(A = 2000\), then find mean \((\bar{x})\).

2 marks See answer →

Q.3 (A) Complete and write any one activity (3 marks)

Q.3 (A)(i) In an A.P. sum of three consecutive terms is 27 and their product is 504. Complete the following activity to find the terms.
Activity :
Let three consecutive terms be \(a - d\), \(a\), \(a + d\).
\(\therefore\ a - d + a + a + d =\) ____
\(\therefore\ a =\) ____
Similarly :
\((a - d) \times a \times (a + d) =\) ____
\(\therefore\ [(9)^2 - d^2] \times 9 = 504\)
\(\therefore\ (81 - d^2) \times 9 = 504\)
\(\therefore\ d^2 = 81 -\) ____
\(\therefore\ d = \pm 5\)
Thus by putting \(a = 9\) and \(d = 5\) we get three consecutive terms = ____
Or by putting \(a = 9\) and \(d = -5\) we get three consecutive terms = ____

3 marks See answer →
Q.3 (A)(ii) A card is drawn from a well shuffled pack of 52 playing cards. Complete the following activity to find the probability of the following events :
(a) A red card
(b) A face card.
Activity :
Let ‘S’ is the sample space
\(\therefore\ n(S) =\) ____
Event A : Card drawn is a red card.
Total red cards = ____
\(\therefore\ n(A) =\) ____
\(\therefore\ P(A) = \dfrac{n(A)}{n(S)}\) ................. Formula
\(\therefore\ P(A) = \dfrac{26}{52}\)
\(\therefore\ P(A) =\) ____
Event B : Card drawn is a face card.
Total face cards = 12
\(\therefore\ n(B) =\) ____
\(\therefore\ P(B) = \dfrac{n(B)}{n(S)}\) ................. Formula
\(\therefore\ P(B) = \dfrac{12}{52}\)
\(\therefore\ P(B) =\) ____

3 marks See answer →

Q.3 (B) Solve any two subquestions (6 marks)

Q.3 (B)(ii) Shri Shivajirao has purchased 150 shares of F.V. ₹ 100, for M.V. of ₹ 120. Company has paid 7% dividend. Find the rate of return on his investment.

3 marks See answer →
Q.3 (B)(iii) Product of Shraddha’s age 2 years ago and 3 years hence is 84. Find her present age.

3 marks See answer →
Q.3 (B)(iv) Solve the following simultaneous equations graphically : \(x + y = 6\), \(x - y = 4\)

3 marks See answer →

Q.4 Solve any two subquestions (8 marks)

Q.4 (i) In an agriculture field the ratio of salary of skilled and unskilled workers is 5 : 4. Total salary of one day of both of them is ₹ 900. Find daily wages of skilled and unskilled workers.

4 marks See answer →
Q.4 (ii) Two dice are thrown. Find the probability of the following events :
(a) Event A : The sum of the numbers on their upper faces is at least 9.
(b) Event B : The sum of the numbers on their upper faces is divisible by 5.
(c) Event C : The number on the upper face of the first die is greater than the number on the upper face of the second die.

4 marks See answer →
Q.4 (iii) In the following frequency distribution table ages of 300 patients and number of patients in a hospital is given. Find the median age of the patients :
Age (In years) Number of patients
10–20 60
20–30 42
30–40 55
40–50 70
50–60 53
60–70 20

4 marks See answer →

Age (In years)	Number of patients
10–20	60
20–30	42
30–40	55
40–50	70
50–60	53
60–70	20

Q.5 Solve any one subquestion (3 marks)

Q.5 (i) Three conditions are given below. Write the quadratic equation for each of them satisfy that condition :
(a) If discriminant \(\Delta = 0\)
(b) If discriminant \(\Delta > 0\)
(c) If discriminant \(\Delta < 0\)

3 marks See answer →
Q.5 (ii) If first term of an A.P. is ‘\(p\)’, second term is ‘\(q\)’ and last term is ‘\(r\)’, then show that the sum of all terms is \(\dfrac{(p + r)(q + r - 2p)}{2(q - p)}\).

3 marks See answer →