Chapter 5 · 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. Then check them on the solved paper, which also shows how marks are given. You may use √2 ≈ 1.414, √3 ≈ 1.732 and √5 ≈ 2.236 where a decimal is asked for.

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Kerala State Syllabus · Standard IX · Mathematics Part 1

MATHEMATICS – Chapter 5: Irrational Numbers (അഭിന്നകഗുണനം)

Time: 1½ hoursMaximum marks: 40
Instructions: Read each question carefully. Give exact answers using √ unless a decimal is asked for. Show your working – 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.
Written in its simplest form, √72 = .
(1)
2.
√3 × √27 =
(a) √30(b) 9(c) 3√3(d) 81
(1)
3.
The height of an equilateral triangle of side 6 cm is cm.
(1)
4.
Which of these is a natural number?
(a) √5 × √10(b) √2 × √8(c) √3 × √5(d) √6 ÷ √2
(1)
5.
Written without a square root in the denominator, 1√5 = .
(1)
6.
(√5 + 2)(√5 − 2) =
(a) 1(b) 3(c) 5 − 2√5(d) 9
(1)
7.
√50 ÷ √2 = .
(1)
8.
In Heron's formula for the area of a triangle with sides a, b, c, the number s stands for
(a) a + b + c(b) ½(a + b + c)(c) ⅓(a + b + c)(d) abc
(1)
SECTION B – Answer all questions5 × 2 = 10 marks
9.
Using √2 ≈ 1.414 and √3 ≈ 1.732, find √6 correct to three decimal places. Explain which rule you used.
(2)
10.
Find the perimeter and the area of an equilateral triangle of side 6 cm.
(2)
11.
Two squares of areas 48 sq cm and 27 sq cm are placed side by side on a line as in the figure. Find the exact length of the bottom line.
(2)
12.
Write 1√5 − 2 in a form that has no square root in the denominator. (Use question 6.)
(2)
13.
For each of the following, find whether the result is a natural number, a fraction, or an irrational number, and write its value in simplest form:
  1. √8 × √18
  2. √12 ÷ √3
  3. √7 × √14
  4. √(2/3) × √(3/8)
(2)
SECTION C – Answer all questions4 × 3 = 12 marks
14.
The height of an equilateral triangle is 6√3 cm.
  1. Find the length of its side.
  2. Find its perimeter.
  3. Find its area.
(3)
15.
The sides of a triangle are 10 cm, 10 cm and 12 cm (figure).
  1. Find the height of the triangle, measured to the 12 cm side.
  2. Find its area.
  3. Check your area using Heron's formula.
(3)
16.
A regular hexagon has side 4 cm. Find its area, exactly and correct to one decimal place. (Hint: split it into equilateral triangles.)
(3)
17.
Use Heron's formula to find the area of a triangle with sides 7 cm, 8 cm and 9 cm. Write the answer in simplest form and also as a decimal correct to one place.
(3)
SECTION D – Answer all questions2 × 5 = 10 marks
18.
In the figure, squares are drawn on the two perpendicular sides of a right triangle. Their areas are 32 sq cm and 18 sq cm.
  1. Write the lengths of the two perpendicular sides in simplest form.
  2. Find the length of the hypotenuse in simplest form.
  3. Find the perimeter of the triangle, exactly and correct to one decimal place.
  4. Find the area of the triangle.
(5)
19.
A plot of land has the shape of the quadrilateral ABCD in the figure, with AB = 5 m, BC = 12 m, CD = 15 m, DA = 14 m and the diagonal AC = 13 m.
  1. Show that the angle at B is a right angle, and find the area of triangle ABC.
  2. Find the area of triangle ACD using Heron's formula.
  3. Find the total area of the plot.
(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 ▶