Chapter 2 · 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. You may use √2 ≈ 1.414, √3 ≈ 1.732, √5 ≈ 2.236, √6 ≈ 2.449 and √12 ≈ 3.464 wherever a decimal is asked for. Then check your work on the solved paper, which also shows how marks are given.

(the navigation bars are left out when printing)

Kerala State Syllabus · Standard IX · Mathematics Part 1

MATHEMATICS – Chapter 2: New Numbers (പുതിയ സംഖ്യകൾ)

Time: 1½ hoursMaximum marks: 40
Instructions: Read each question carefully. Show your working – marks are given for correct steps even when the final answer is wrong. Where a decimal answer is asked for, round to the number of places stated. 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.
The square drawn on the diagonal of a square of side 1 m has area sq m.
(1)
2.
√(2¼) =
(1)
3.
√10 lies between the natural numbers and .
(1)
4.
A right triangle has perpendicular sides 1 m and √2 m. Its hypotenuse is
(a) 2 m(b) √3 m(c) 3 m(d) (√2 + 1) m
(1)
5.
Which of these is NOT a fraction?
(a) 1.5(b) √9(c) √5(d) 2¼
(1)
6.
1.41² = 1.9881 and 1.42² = 2.0164. So √2 lies between and .
(1)
7.
The perimeter of a right triangle with perpendicular sides 1 m and 1 m is
(a) (2 + √2) m(b) 3 m(c) 2√2 m(d) (1 + √2) m
(1)
8.
For positive numbers x and y, √x + √y √(x + y). (Write >, < or =.)
(1)
SECTION B – Answer all questions5 × 2 = 10 marks
9.
Describe how to draw a square of area 2 sq cm and a square of area 3 sq cm using right triangles. Write the lengths of their sides.
(2)
10.
Show that (1⅓)² < 2 < (1½)². What does this tell you about √2?
(2)
11.
A right triangle has hypotenuse 3 cm and one perpendicular side 2 cm. Find the third side, and the perimeter correct to 2 decimal places.
(2)
12.
Using √2 ≈ 1.414 and √3 ≈ 1.732, find correct to 2 decimal places:
  1. 1 + √2 + √3
  2. (2 + √3) − (1 + √2)
(2)
13.
Write the decimal forms of ⅓, ⅙ and √2. Which of them have a repeating block of digits?
(2)
SECTION C – Answer all questions4 × 3 = 12 marks
14.
1.7² = 2.89, 1.8² = 3.24, 1.73² = 2.9929 and 1.74² = 3.0276.
  1. Between which tenths does √3 lie?
  2. Between which hundredths?
  3. Write √3 correct to 2 decimal places.
(3)
15.
A right triangle has perpendicular sides 1 m and 2 m.
  1. Find its hypotenuse.
  2. Find its perimeter correct to a centimetre.
  3. A second right triangle has perpendicular sides √5 m and 2 m. Find its hypotenuse, and how much longer its perimeter is than that of the first triangle.
(3)
16.
An equilateral triangle of side 4 m is cut along its height into two halves.
  1. Find the height.
  2. Find the perimeter of one half, correct to 2 decimal places.
  3. How much less is this than the perimeter of the whole triangle?
(3)
17.
Right triangles are drawn one after another as in the figure: each has one perpendicular side 1 m, the hypotenuse of each becomes a perpendicular side of the next, and the first has both perpendicular sides 1 m.
  1. Write the sides of the 5th triangle.
  2. How much longer is the perimeter of the 5th triangle than that of the 4th?
  3. After the 3rd triangle, which is the next triangle whose hypotenuse is a natural number?
(3)
SECTION D – Answer all questions2 × 5 = 10 marks
18.
Prove that the square of no fraction is 2.
(5)
19.
Two squares of areas x and y are placed corner to corner as in the figure, and the triangle between them is completed.
  1. Explain why the square drawn on the third side of this triangle has area x + y.
  2. Write the lengths of the three sides of the triangle.
  3. Why is √x + √y > √(x + y)?
  4. Check this with x = 9 and y = 16.
  5. For x = 3 and y = 6, compute √x + √y − √(x + y) correct to 3 decimal places.
(5)

— End of the paper —

📝 After the test

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

Next: Model Test Paper – Solved ▶