Model Test Paper മാതൃകാ ചോദ്യപേപ്പർ
A full paper in the Kerala pattern. Work on paper, with a timer, before you look at the solutions.
Standard IX · Mathematics
Chapter 9 · രേഖീയസംഖ്യകൾ · Real Numbers
Instructions: Answer all questions. Show your working. Draw number lines where they help. Marks for each question are shown on the right.
SECTION A8 × 1 = 8 marks
1.
|−7| = .
(1)2.
The distance between −3 and 5 on the number line is .
(1)3.
The midpoint of −6 and 2 on the number line is .
(1)4.
Which of these is a rational number?
(1)(a) √2(b) π(c) −3/4(d) √3
5.
If |x| = 4, then x = or .
(1)6.
Which is bigger, −5 or −2?
(1)7.
On the number line, |x − y| is the between the numbers x and y.
(1)8.
For any number x, |−x| = .
(1)SECTION B5 × 2 = 10 marks
9.
Solve |x − 4| = 6.
(2)10.
Solve |x + 3| = 2.
(2)11.
Find all integers x with |x + 2| < 3.
(2)12.
Find the midpoint of (i) −3½ and 1½ (ii) −3 and 7.
(2)13.
Find the distance between (i) 4½ and −6¼ (ii) −2.5 and −0.7.
(2)SECTION C4 × 3 = 12 marks
14.
Complete the table and explain why |xy| = |x| |y| for any numbers x, y.
(3)| x | y | xy | |xy| | |x| |y| |
|---|---|---|---|---|
| −5 | 4 | |||
| 5 | −4 | |||
| −5 | −4 |
15.
Compare |x + y| and |x| + |y| when (i) x = 6, y = −2 (ii) x = −6, y = −2. When are they equal?
(3)16.
Solve (i) |x − 2| = |x − 8| (ii) |x + 1| = |x − 5|.
(3)17.
Find the numbers that divide the part of the number line from −2 to 4 into four equal parts.
(3)SECTION D2 × 5 = 10 marks
18.
(i) Explain what |x| means, in words and as cases. (ii) Solve |x − 1| < 3 and show the answer on the number line. (iii) Solve |x − 3| > 5. (iv) Write all integers x with |x − 1| < 3.
(5)19.
(i) Find the midpoint of 1 and 2. (ii) Using midpoints, find two more numbers between 1 and 2. (iii) Explain why there are infinitely many numbers between any two numbers. (iv) Find three numbers between −½ and −⅓.
(5)