Chapter 1 · Model TestAttempt first – solutions on the next page

Model Test Paper മാതൃകാ ചോദ്യപേപ്പർ

Set a timer for 1½ hours, keep the textbook closed, and write your answers in a notebook. Show every step – write the equations first, then solve them. Then check your work on the solved paper, which also shows how marks are given.

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Kerala State Syllabus · Standard IX · Mathematics Part 1

MATHEMATICS – Chapter 1: Pairs of Equations (സമവാക്യജോടികൾ)

Time: 1½ hoursMaximum marks: 40
Instructions: Read each question carefully. For word problems, say what each letter stands for and write the equations before solving. Marks are given for correct steps even when the final answer is wrong. Section A: 8 × 1 = 8, Section B: 5 × 2 = 10, Section C: 4 × 3 = 12, Section D: 2 × 5 = 10.
SECTION A – Answer all questions8 × 1 = 8 marks
1.
If x + y = 10 and x − y = 4, then x = and y = .
(1)
2.
Two numbers have sum 30 and difference 6. The larger number is .
(1)
3.
If 2x + 3y = 12 and 2x + y = 8, then 2y = .
(1)
4.
Which pair of equations has the solution x = 2, y = 3?
(a) x + y = 5, x − y = −1(b) x + y = 6, x − y = 1(c) 2x + y = 6, x + y = 5(d) x − y = 1, x + y = 5
(1)
5.
How many solutions does the single equation x + y = 10 have if x and y may be any numbers?
(a) one(b) two(c) none(d) infinitely many
(1)
6.
A two-digit number has tens digit a and units digit b. The number is .
(1)
7.
3 pens and 2 books cost ₹50; 3 pens and 4 books cost ₹70. One book costs ₹.
(1)
8.
For the pair x + y = 7 and 2x + 2y = 14, which statement is true?
(a) x = 3, y = 4 is the only solution(b) there is no solution(c) x and y cannot be found separately(d) x must equal y
(1)
SECTION B – Answer all questions5 × 2 = 10 marks
9.
The sum of two numbers is 40 and their difference is 10. Find the numbers.
(2)
10.
A table and a chair together cost ₹5000. A table and 3 chairs cost ₹7000. Find the price of each.
(2)
11.
Solve: 3x + 2y = 18, x + 2y = 10.
(2)
12.
Adding 2 to the numerator of a fraction and simplifying gives ½. Adding 1 to its denominator instead gives ⅓. Find the fraction.
(2)
13.
The perimeter of a rectangle is 30 cm and its length is 3 cm more than its breadth. Find its length and breadth.
(2)
SECTION C – Answer all questions4 × 3 = 12 marks
14.
2 kg of apples and 3 kg of oranges cost ₹420. 3 kg of apples and 2 kg of oranges cost ₹380. Find the price of 1 kg of each.
(3)
15.
Solve by making the coefficients of one letter equal: 4x + 3y = 24, 3x − 2y = 1.
(3)
16.
The digits of a two-digit number add up to 9. Reversing the digits gives a number 27 more than the original. Find the number.
(3)
17.
₹50000 is invested in two schemes, one at 8% and the other at 6% yearly interest. The total interest after one year is ₹3500. How much was invested in each scheme?
(3)
SECTION D – Answer all questions2 × 5 = 10 marks
18.
Five years ago a father was 3 times as old as his son. Five years from now he will be twice as old as his son.
  1. Write two equations for their present ages.
  2. Solve them.
  3. Check your answer with both facts.
  4. Explain why the difference of their ages is the same at every time.
(5)
19.
The speed of an object after t seconds is u + at metres per second. After 2 seconds its speed is 11 m/s; after 6 seconds it is 23 m/s.
  1. Write two equations in u and a.
  2. Find u and a.
  3. Find its speed after 10 seconds.
  4. The distance travelled in t seconds is ut + ½at². Find the distance travelled in the first 4 seconds.
  5. Explain why the pair x + y = 5, 2x + 2y = 12 has no solution.
(5)

— End of the paper —

📝 After the test

Check your answers on the next page and give yourself marks honestly using the marking hints there. Anything below 28/40 means the chapter needs one more round – the solved paper names the page to revisit for each question.

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