ICSE Class 10 Mathematics Previous Year Question Paper 2012

Mathematics is one of the crucial and most scoring subjects in ICSE Class 10TopperLearning presents ICSE Class 10 Mathematics study materials, enabling students to score well in the board examination. The ICSE Class 10 Maths syllabus is diverse and includes challenging concepts like Value Added Tax, Ratio and Proportion, Quadric Equations, and others that require effective study materials. 

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Question 1

If (x + 2) is a factor of the polynomial x3 - kx2 - 5x + 6 then the value of k is:                             [1]

  1. 1
  2. 2
  3. -2 

 

Question 2

The solution set of the inequation x - 3 ≥ - 5, x ∊ R is:                                                                       [1]

  1. {x : x > - 2, x ∊ R}
  2. {x : x ≤ -2, x ∊ R}
  3. {x : x  ≥ -2, x ∊ R}
  4. {-2, -1, 0, 1, 2}

 

Question 3

The product AB of two matrices A and B is possible if:                                   [1]

  1. A and B have the same number of rows. 
  2. The number of columns of A is equal to the number of rows of B.
  3. The number of rows of A is equal to the number of columns of B. 
  4. A and B have the same number of columns.

 

Question 4 

 If 70, 75, 80, 85 are the first four terms of an Arithmetic Progression. Then the 10th term is:       [1]

  1. 35
  2. 25 
  3. 115
  4. 105

 

Question 5

The selling price of a shirt excluding GST is Rs. 800. If the rate of GST is 12% then the total price of the shirt is:        [1]

  1. Rs. 704
  2. Rs. 96 
  3. Rs. 896 
  4. Rs. 848 

 

Question 6

Which of the following quadratic equations has 2 end 3 as its roots?                [1]

  1. x2 - 5x + 6 = 0
  2. x2 + 5x + 6 = 0
  3. x2 - 5x - 6 = 0
  4. x2 + 5x -6 = 0 

 

Question 7 

If x, 5.4, 5, 9 are in proportion then x is:               [1]

  1. 9.72 
  2. 25 
  3. 25/3

 

Question 8 

Mohit opened a Recurring deposit account in a bank for 2 years. He deposits Rs. 1000 every month and receives Rs. 25500 on maturity. The interest he earned in 2 years is:    [1]

  1. Rs. 13500
  2. Rs. 3000 
  3. Rs. 24000 
  4. Rs. 1500 

 

Question 9 

In the given figure AB = 24 cm, AC = 18 cm, DE = 12cm, DF = 9 cm and ∠BAC = ∠EDF. Then ΔABC ~ ΔDEF by the condition:          [1]

 

  1. AAA
  2. SAS
  3. SSS
  4. AAS

 

Question 10

 begin mathsize 12px style If space straight A equals open square brackets table row 5 10 row 3 cell negative 4 end cell end table close square brackets space and space straight I space equals open square brackets table row 1 0 row 0 1 end table close square brackets space then space AI space is space equal space to end style             [1]

  1. begin mathsize 12px style open square brackets table row 1 0 row 0 1 end table close square brackets end style
  2. begin mathsize 12px style open square brackets table row 5 10 row cell negative 3 end cell 4 end table close square brackets end style
  3. begin mathsize 12px style open square brackets table row 5 10 row cell negative 3 end cell 4 end table close square brackets end style
  4. begin mathsize 12px style open square brackets table row 15 15 row cell negative 1 end cell cell negative 1 end cell end table close square brackets end style

 

Question 11 

The polynomial x3 - 2x2 + ax + 12 when divided by (x + 1) leaves a remainder 20, then 'a' is equal to:[1]

  1. - 31 
  2. 11
  3. - 11 

 

Question 12 

In an Arithmetic Progression (A.P.) if, first term is 5, common difference is - 3 and then nth term is - 7, then n is equal to:[1]

  1. 17 
  2. - 13
  3. 7

 

Question 13

In the given figure PQ is parallel to TR, then by using condition of similarity:          [1]

 

  1. begin mathsize 12px style PQ over RT equals OP over OT equals OQ over OR end style
  2. begin mathsize 12px style PQ over RT equals OP over OR equals OQ over OT end style
  3. begin mathsize 12px style PQ over RT equals OR over OP equals OQ over OT end style
  4. begin mathsize 12px style PQ over RT equals OP over OR equals OT over OQ end style  

 

Question 14

If a, b, c, and d are proportional then begin mathsize 12px style fraction numerator straight a space plus space straight b over denominator straight a space minus space straight b end fraction end style is equal to:                           [1]

  1. begin mathsize 12px style straight c over straight d end style 
  2.  begin mathsize 12px style fraction numerator straight c space minus space straight d over denominator straight c space plus space straight d end fraction end style
  3. begin mathsize 12px style straight d over straight c end style
  4. begin mathsize 12px style fraction numerator straight c space plus space straight d over denominator straight c space minus space straight d end fraction end style 

 

Question 15

The first four terms of an Arithmetic Progression (A. P.), whose first term is 4 and common difference is -6, are:            [1]

  1. 4, -10, -16, -22  
  2. 4, 10, 16, 22
  3. 4, -2, -8, -14 
  4. 4, 2, 8, 14

 

Question 16 

 One of the roots of the quadratic equation x2 – 8x + 5 = 0 is 7.3166. The root of the equation correct to 4 significant figures is:       [1]

  1. 7.3166
  2. 7.317
  3. 7.316
  4. 7.32

 

Question 17

(x + 2) and (x + 3) are two factors of the polynomial x3 + 6x2 + 11x + 6. If this polynomial is completely factorised the result is:             [2]

  1. (x – 2)(x + 3)(x + 1)
  2. (x + 2)(x – 3)(x – 1)
  3. (x + 2)(x + 3)(x – 1)
  4. (x + 2)(x + 3)(x + 1)

 

Question 18

The sum of the first 20 terms of the Arithmetic Progression 2, 4, 6, 8,....is :                                                      [2]

  1. 400
  2. 840
  3. 420
  4. 800 

 

Question 19

The solution set on the number line of the linear inequation:                                                [2]

2y – 6 < y + 2 ≤ 2y, y ∈ N is 

  1.  

 

Question 20 

If x, y, z are in continued proportion then (y2 + z2): (x2 + y2) is equal to:                             [2]

  1. z : x
  2. x : z
  3. zx
  4. (y + z) : (x + y)

 
Question 21
 
The marked price of an article is Rs. 5,000. The shopkeeper gives a discount of 10%. If the rate of GST is 12%, then the amount paid by the customer including GST is:    [2]
  1. Rs. 5040
  2. Rs. 6100
  3. Rs. 6272
  4. Rs. 6160
 
Question 22

If A = begin mathsize 12px style open square brackets table row 3 5 row 1 4 end table close square brackets comma space straight B space equals space open square brackets table row 2 4 row 0 3 end table close square brackets space and space straight C space equals space open square brackets table row 1 cell negative 1 end cell row 2 1 end table close square brackets end style  then 5A – BC is equal to:                        [2]
 
  1. begin mathsize 12px style open square brackets table row cell negative 5 end cell cell negative 23 end cell row 1 17 end table close square brackets end style
  2. begin mathsize 12px style open square brackets table row 5 23 row 1 17 end table close square brackets end style
  3. begin mathsize 12px style open square brackets table row cell negative 2 end cell 8 row cell negative 3 end cell 3 end table close square brackets end style
  4. begin mathsize 12px style open square brackets table row 5 23 row cell negative 1 end cell 17 end table close square brackets end style
 
Question 23
 
In the given figure ABCD is a trapezium in which DC is parallel to AB.
AB = 16 cm and DC = 8 cm. OD = 5 cm, OB = (y + 3) cm, OA = 11 cm and OC = (x – 1) cm.
Using the given information answer the following questions.
 
 
i. From the given figure name the pair of similar triangles:                   [1]
  1. ∆OAB, ∆OBC
  2. ∆COD, ∆AOB
  3. ∆ADB, ∆ACB
  4. ∆COD, ∆COB
 
ii. The corresponding proportional sides with respect to the pair of similar triangles obtained in (i):        [1]
  1. begin mathsize 12px style CD over AB equals OC over OA equals OD over OB end style
  2. begin mathsize 12px style AD over BC equals OC over OA equals OD over OB end style
  3. begin mathsize 12px style AD over BC equals BD over AC equals AB over DC end style
  4. begin mathsize 12px style OD over OB equals CD over CB equals OC over OA end style
 
iii. The ratio of the sides of the pair of similar triangles is:                    [1]
  1. 1 : 3
  2. 1 : 2 
  3. 2 : 3
  4. 3 : 1
 
iv. Using the ratio of sides of the pair of similar triangles the values of x and y are respectively:                   [1]
  1. x = 4.6, y = 7
  2. x = 7, y = 7 
  3. x = 6.5, y = 7
  4. x = 6.5, y = 2
 
Question 24 

Two cars X and Y use 1 litre of diesel to travel x km and (x + 3) km respectively. If both the cars covered a distance of 72 km, then:
 
i. The number of litres of diesel used by car X is :         [1]
  1. begin mathsize 12px style fraction numerator 72 over denominator straight x minus 3 end fraction space litres end style
  2. begin mathsize 12px style fraction numerator 72 over denominator straight x plus 3 end fraction space litres end style
  3. begin mathsize 12px style 72 over straight x space litres end style
  4. begin mathsize 12px style 12 over straight x space litres end style
 
ii. The number of litres of diesel used by car Y is:                                [1]
  1. begin mathsize 12px style fraction numerator 72 over denominator straight x minus 3 end fraction space litres end style
  2. begin mathsize 12px style fraction numerator 72 over denominator straight x plus 3 end fraction space litres end style
  3. begin mathsize 12px style 72 over straight x space litres end style
  4. begin mathsize 12px style fraction numerator 12 over denominator straight x space plus space 3 end fraction space litres end style
 
iii. If car X used 4 litres of diesel more than car Y in the journey, then:              [1]
  1. begin mathsize 12px style fraction numerator 72 over denominator straight x minus 3 end fraction minus 12 over straight x space equals 4 end style
  2. begin mathsize 12px style fraction numerator 72 over denominator straight x minus 3 end fraction minus 12 over straight x space equals 4 end style
  3. begin mathsize 12px style 72 over straight x minus fraction numerator 12 over denominator straight x plus 3 end fraction space equals 4 end style
  4. begin mathsize 12px style fraction numerator 72 over denominator straight x minus 3 end fraction minus 12 over straight x space equals 4 end style
 
iv. The amount of diesel used by the car X is:                 [1]
  1. 6 litres
  2. 12 litres 
  3. 18 litres
  4. 24 litres
 

Question 25 

Joseph has a recurring deposit account in a bank for two years at the rate of 8% per annum simple interest  
 
i. If at the time of maturity Joseph receives Rs. 2000 as interest then the mostly instalment is:        [1]
  1. Rs. 1200
  2. Rs. 600 
  3. Rs. 1000
  4. Rs. 1600
 
ii. The total amount deposited in the bank:                         [1]
  1. Rs. 25000
  2. Rs. 24000 
  3. Rs. 26000
  4. Rs. 23000
 
iii. The amount Joseph receives on maturity is:               [1]
  1. Rs. 27000
  2. Rs. 25000
  3. Rs. 26000
  4. Rs. 28000
 
iv. If the monthly instalment is Rs. 100 and the rate of interest is 8%, in how many months Joseph will receive Rs. 52 as interest?    [1]
  1. 18
  2. 30 
  3. 12
  4. 6

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