Plus One Maths Improvement Question Paper 2018

Kerala Plus One Maths Improvement Question Paper 2018

Time Allowed: 2 1/2 hours
Cool off time: 15 Minutes
Maximum Marks: 80

General Instructions to Candidates :

  • There is a ‘cool off time’ of 15 minutes in addition to the writing time .
  • Use the ‘cool off time’ to get familiar with the questions and to plan your answers.
  • Read instructions carefully .
  • Read questions carefully before you answering.
  • Calculations, figures and graphs should be shown in the answer sheet itself.
  • Malayalam version of the questions is also provided.
  • .Give equations wherever necessary.
  • Electronic devices except non programmable calculators are not allowed in the Examination Hall.

Plus One Maths Previous Year Question Papers and Answers

Answer any 6 questions from question numbers 1 to 7. Each carries 3 scores
Plus One Maths Improvement Question Papers 2018A

Question 1.
a. If A= {2, 3, 4, 5} and B = {4, 5, 6, 7}, then write :
i. A ∪ B ii. A ∩ B
b. Which one of the following is equal to {x : x∈ R, ∂< x ≤ 4 }?
i. {2,3,4}
ii. {3,4}
iii. [2, 4]
iv.(2, 4]
Plus One Maths Improvement Question Papers 2018Q1

Question 2.
Consider the set
A = {x : x is an integer, 0 ≤ x < 4}
a. Write A in Roser form
b. If B = {5, 6}, then write A x B
c. Write the number of possible relations from A to B
Plus One Maths Improvement Question Papers 2018Q2
Plus One Maths Improvement Question Papers 2018Q2.1

Question 3.
Prove that
Plus One Maths Improvement Question Papers 2018Q3

Question 4.
Plus One Maths Improvement Question Papers 2018Q4

Question 5.
Find the polar from of the complex number
Plus One Maths Improvement Question Papers 2018Q5

Question 6.
How many terms of the GP, 3, 3/2, 3/4,…………………..are needed to give the sum
\(\frac { 3069 }{ 512 } \) ?
Plus One Maths Improvement Question Papers 2018Q6

Question 7.
Consider the real valued function
Plus One Maths Improvement Question Papers 2018Q7
a. Find the domain of f(x).
Plus One Maths Improvement Question Papers 2018Q7.1

Question 8.
a. If U = {1, 2, 3,4, 5, 6, 7, 8, 9}
A = {2, 4, 6, 8}
B = {2, 3, 5, 7}
Verify (A ∪B) = A’ ∩ B’
b. If A and B are two disjoint sets with n(A) = 4 and n(B) = 2, then n (A-B) = …………
Plus One Maths Improvement Question Papers 2018Q8

Question 9.
Consider the statement P(n) : 1-3 + 32 +……….. \({ 3 }^{ n-1 }=\frac { { 3 }^{ n-1 } }{ 2 } \)
a. Show that P(1) is TRUE
b. Prove by principle of Mathematical induction, that P(n) is TRUE for all n ∈ N
Plus One Maths Improvement Question Papers 2018Q9
Plus One Maths Improvement Question Papers 2018Q9.1

Question 10.
Solve the following inequalities graphically
2x + y ≥ 4
x + y ≤ 3 and
2x – 3y ≤ 6
Plus One Maths Improvement Question Papers 2018Q10

Question 11.
Find the square roots of the complex number 3 – 4i.
Plus One Maths Improvement Question Papers 2018Q11

Question 12.
a. Insert five numbers between 8 and 26 such that the resulting sequence is an AP. b. Find the sum to n terms of the series
1 x 2 + 2 x 3 + 3 x 4+…………..
Plus One Maths Improvement Question Papers 2018Q12

Question 13.
a. Find the equation of the perpendicular bisector of the line joining the points (0, 0) and (-3, 4).
b. Find the coordinates of the point on the line y = 3x-2 that is equidistant from (0,0) and (-3 -4)
Plus One Maths Improvement Question Papers 2018Q13

Question 14.
a. Reduce the equation x – y = 4 into normal form.
b. Write the distance of this line from origin
Plus One Maths Improvement Question Papers 2018Q14

Question 15.
a. Find the derivative of f(x) = x Sin x with respect to x.
b. Find the derivative of the function y = √x with respect to x by using first principles.
Plus One Maths Improvement Question Papers 2018Q15

Question 16.
Consider the points A (3, 8, 10) and B (6, 10, -8).
a. Find the ratio in which the line segment joining A and B is divided by the YZ coordinate plane.
b. Find the coordinates of the point of division.
c. Which coordinate plane divides the line segment AB internally? Justify your answer.
Plus One Maths Improvement Question Papers 2018Q16

Question 17.
a. Write the contrapositive of the statement: “If the integer n is odd, then n2 is odd”,
b. Prove by the method of contradiction ‘ √7 is irrational’
Plus One Maths Improvement Question Papers 2018Q17

Answer any 5 questions from question numbers 18 to 24. Each carries 6 scores

Question 18.
Plus One Maths Improvement Question Papers 2018A18
find the valueof x and y.
b. Consider the function f (x) = |x| = 3, draw the graph of f (x)
c. Write the domain and range of (x)
Plus One Maths Improvement Question Papers 2018Q18.1

Question 19.
a. Find the value of Sin (75°)
Plus One Maths Improvement Question Papers 2018Q19
b. In the given figure. ∠AOB = 30° and radius of the circle is d units. Find the length of are APB.
c. Find the length of chord AB
Plus One Maths Improvement Question Papers 2018Q19.1
Plus One Maths Improvement Question Papers 2018Q19.2

Question 20.
a. Find the number words with or without meaning, which can be made by using all the letters of the word GANGA.
b. If these words are written as in a dictionary, what will be the 26th word?
c. A group consists of 4 girls and 7 boys. In how many ways, can a team of 5 members be selected if the team should have at least 3 girls?
Plus One Maths Improvement Question Papers 2018Q20

Question 21.
a. Write the expansion of (a + b)n.
b. Find the coefficient of xy7in the expansion of (x-2y)12
c. Show that 9n-1 – 8n – 9 is divisible by 64.
Plus One Maths Improvement Question Papers 2018Q21
Plus One Maths Improvement Question Papers 2018Q21.1

Question 22.
Focii of the ellipse in the given figure are (± √12,0) and vertices are (± 4, 0).
a. Find the equation of the ellipse.
b. Write the equation of a circle with centre (0, k) and radius r.
c. The circle in the figure passes through the points A, B and C on ellipse. Find the equation of a circle.
Plus One Maths Improvement Question Papers 2018Q22

Question 23.
Consider the following table
Plus One Maths Improvement Question Papers 2018Q23
a. Find the arithmatic mean of marks given in the above data
Plus One Maths Improvement Question Papers 2018Q23.1
b. Find the standard deviation of marks in the above data.
Plus One Maths Improvement Question Papers 2018Q23.2
c. Find the coefficient of variation.
Plus One Maths Improvement Question Papers 2018Q23.3

Question 24.
a. Consider the experiment in which a coin is tossed repeatedly until a head comes up. Write the sample space.
b. If A and B are two events of a sample space with P (A) = 0.54, (P(B) = 0.69 and P (A ∩ B) = 0.35. Find P (A’ ∩ B’).
c. 3 cards are drawn from a well shuffled pack of 52 cards. Find the prohibility that
i. all the 3 cards are diamond.
ii. at least one of the cards is non diamond
iii. one card is king and two are jacks.
Plus One Maths Improvement Question Papers 2018Q24

Answers

Answer 1.
a. A ∪ B = {2, 3, 4, 5, 6, 7}
A∩B = {4, 5}
b. iv) (2, 4]

Answer 2.
a. A = {0, 1,2,3}
b. A x B = {(0, 5),(0, 6),(1, 5),(1, 6),(2, 5), (2, 6),(3, 5),(3, 6)}
c. No. of possible relations from A to B
= 2mn = 24 x 2 = 256

Answer 3.
Plus One Maths Improvement Question Papers 2018A3

Answer 4.
Plus One Maths Improvement Question Papers 2018A4
Plus One Maths Improvement Question Papers 2018A4.1

Answer 5.
Plus One Maths Improvement Question Papers 2018A5

Answer 6.
Plus One Maths Improvement Question Papers 2018A6
∴ n = 10

Answer 7.
Plus One Maths Improvement Question Papers 2018A7

Answer 8.
a. A ∪ B = {2, 3, 4, 5, 6, 7, 8}
(A ∩ B)’ = {1, 9}………….(1)
A’= {1, 3, 5, 7, 9}, B’={1, 4, 6, 8, 9} A’∩B’= {1, 9}…………….(2)
From (1) and (2), we have (A + B)’ = A’ ∩ B’
b. n (A – B) = n (A) = 4

Answer 9.
Plus One Maths Improvement Question Papers 2018A9

Answer 10.
Plus One Maths Improvement Question Papers 2018A10
Plus One Maths Improvement Question Papers 2018A10.1

Answer 11.
Plus One Maths Improvement Question Papers 2018A11

Answer 12.
Plus One Maths Improvement Question Papers 2018A12
Plus One Maths Improvement Question Papers 2018A12.1

Answer 13.
a. Let the required line l is perpendicular bisector of the line joining A(0,0) and B (-3, 4).
Plus One Maths Improvement Question Papers 2018A13
Since l is perpendicular bisector of AB, it passes through the midpoint of AB.
Plus One Maths Improvement Question Papers 2018A13.1

Answer 14.
Plus One Maths Improvement Question Papers 2018A14

Answer 15.
Plus One Maths Improvement Question Papers 2018A15

Answer 16.
a. Since the line joining A and Bis divided by the YZ plane, x = 0
Plus One Maths Improvement Question Papers 2018A16
∴ the points divides the YZ plane in the ratio 1 : 2 externally.
b. R divides AB in the ratio 1:2 externally,
Plus One Maths Improvement Question Papers 2018A16.1
Since m:n = – z1 : z2 = -10 : -8 = 5:4
XY plane divides the line segment internally.

Answer 17.
a. If n2 is not even, then the integer n is not even.
b. Let us assu,e that √7 is a rational number.
√7 =a/b, where a and b are co-prime, i.e., a and b have no common factors. Squaring we have,
7b2 = a2 ⇒ 7 divides a.
∴ Let a = lk
∴a2= 49k2  ⇒ 7b2= 49k2 ⇒ b= 7k⇒7  divides b.
i.e., 7 divides both a and b, which is contradition to our assumption that a and b have no common factor. our supposition is wrong.
∴ √7 is an irrational number.

Answer 18.
Plus One Maths Improvement Question Papers 2018A18

Answer 19.
a. sin 75 = sin (45 + 30) = sin 45 cos 30 + cos 45 sin 30
Plus One Maths Improvement Question Papers 2018A19
=1.05 units
The radius of the circle is not given
properly. Type mismatching happened,
c. OA = OB = 2 units.
Plus One Maths Improvement Question Papers 2018A19.1

Answer 20.
a. Number of words = \(\frac { 5! }{ 2!2! } \)
= 30
b. If A is fixed, the remaining 4 letters can 4!
be permuted in \(\frac { 4! }{ 2! } \) = 12 ways.
If G is fixed, the ramaining 4 letters
can be permuted in \(\frac { 4! }{ 2! } \) = 12 ways.
∴ the 25th word is NAAGG.
∴ the 26th word is NAGAG
c. No. of selections
= 4C7C4C7C4 = 4 x 21 + 1 x 7 = 84 + 7 = 91

Answer 21.
Plus One Maths Improvement Question Papers 2018A21

Answer 22.
a. (± c ,0) = (±√2 , 0) ; (± a, 0) = (± 4, 0)
c= a– b2 ⇒ b2 = a2– c= 16 – 12 = 4
Equation of the ellipse is \(\frac { { x }^{ 2 } }{ 16 } +\frac { { y }^{ 2 } }{ 4 } \) = 1
b.. (x – 0)2+(y – k)2= r2 ⇒ x+ y– 2ky + k– r= 0
c. The co-ordinates of the points are :
A(-4,0), B(4,0) and C(0, -2).
Equation of the circle is
x+ y+ 2gx + 2fy + c = 0 ………….. (1)
(1) passes through A(-4, 0)
: 16 + 0 – 8g + c = 0 …………… (2)
(1) passes through B (4, 0)
: 16 + 0 + 8g + c = 0…………. (3)
passes through C (0, -2)
: 4 + 0-4f + c = 0 ……………… (4)
(2) + (3) ⇒ 32+2c=0
⇒ 2c = -32
⇒ c = -16 when c= -16
⇒ 16 + 0-8g – 16 = 0
⇒- 8g=0 ⇒ g=0
when c=-16 ⇒ 4 + 0-4f – 16 = 0
⇒- 4f = 12 ⇒ f = -3
Equation of the circle is
x+ y+ 2 (0) x + 2(-3) y+ – 16 = 0
⇒ x2 + y2-6y – 16 = 0

Answer 23.
Plus One Maths Improvement Question Papers 2018A23
Plus One Maths Improvement Question Papers 2018A23.1

24.
a. Sample space = {H, TH, TTH, TTTH, …………………… }
b. P(A’∩B’)= 1-P(A ∪ B)=1 -[P(A) + P(B)-P(A ∩ B)]
=1 – [0.54 + 0.69-0.35] =1-0.88=0.12
c. i. P(all cards are diamond)
Plus One Maths Improvement Question Papers 2018A24

Plus One Maths Previous Year Question Papers and Answers

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