Practicing with Class 8 Maths Question Paper Pdf Kerala Syllabus and Model Question Paper Set 2 will help students prepare effectively for their upcoming exams.
Class 8 Maths Model Question Paper Set 2 Kerala Syllabus
Time : 1½ Hours
Score : 40
Answer any 4 each carries 2 mark. (4 × 2 = 8)
Question 1.
In ∆ABC AB = AC, ∠A = 100°, find ∠B, ∠C.
Answer:
AB = AC
∠A = 100°
∠B = ∠C = \(\frac{180-100}{2} = 40\) = 40°
Question 2.
Find the sum of inner angles of a polygone with 6 sides.
Answer:
(n – 2)180° = (6 – 2)180°
= 4 × 180°
= 720°
Question 3.
The length of diagonal of a square is 8 cm. Find the area of that square.
Answer:
Area = \(\frac{1}{2}\)d²
= \(\frac{1}{2}\) × 8²
= 32 cm²
Question 4.
Draw a square of diagonal 7 cm.
Answer:
Question 5.
Match the following.
Answer:
Answer any 4 Each carries 3 mark. (4 × 3 = 12)
Question 6.
Total price of one pen and one pencil is 18 rupees. Price of one pen is 5 times the price of one pencil find he price of each.
Answer:
Cost of a Pencil = x
Cost of a pen = 5x
5x + x = 18
6x = 18
x = \(\frac{18}{6}\) = Rs. 3
Cost of a pencil, x = Rs. 3
Cost of a pen, 5x = 5 × 3 = Rs. 15
Question 7.
In the figure a square, regular pentagon and a regular Hexagon is combined together. Find ∠BAC?
Answer:
∠BAC = 360 – (90 + 120 + 108)
= 360 – 318
= 42°
Question 8.
Draw a circle of diameter 5.5 cm.
Answer:
Question 9.
The price of a smart phone decreases by 4% each year. Now the price is 12000 rupees. What will be price after 3 years?
Answer:
12000 × \(\left(\frac{100-4}{100}\right)^3\)
= 12000 × \(\left(\frac{96}{100}\right)^3\)
= 1200 × \(\frac{96}{100} \times \frac{96}{100} \times \frac{96}{100}\)
= Rs. 10616.832
Question 10.
In a trapezium ABCD, the parallel sides are 8 cm, 6 cm. The angles in the largest side is 60°, 75°.
(a) Draw a rough figure.
Answer:
(b) Draw trapezium ABCD in actual measures.
Answer:
Question 11.
The ratio of breadth and length of a rectangle is 4:5. By decreasing the breadth by 2 cm and increasing the length by 1 cm the ratio of breadth and length become 2:3. Find the breadth and length of the first rectangle.
Answer:
Breadth: length = 4:5
Lenght: 5x
Breadth: 4x
4x – 2 : 5x + 1 = 2 : 3
3 (4x – 2) = 2 (5x + 1)
12x – 6 = 10x + 2
2x = 8
Breadth = 4 × 4 = 16 cm
Length = 5 × 4 = 20 cm
Answer any 5, each carries 4 mark. (5 × 4 = 20)
Question 12.
3² – 1² = 4 × 2
4² – 2² = 4 × 3
5² – 3² = 4 × 4
6² – 4² = 4 × 5
____________
____________
(i) Write the next two lines of this pattern.
Answer:
7² – 5² = 4 × 6
8² – 6² = 4 × 7
(ii) What is the principle behind this pattern.
Answer:
The difference in the squares of alternate natural numbers always be a multiple of 4.
(iii) Explain it using algebra.
Answer:
(n + 2)² – n² = 4 (n + 1)
Question 13.
If x = -3, y = 6. Find the value of z = \(\frac{x}{y}+\frac{y}{x}\)
Answer:
z = \(\frac{-3}{6}+\frac{6}{-3}\)
= \(\frac{1}{2}\) + (-2)
= -2\(\frac{1}{2}\)
Question 14.
Marks of 40 students got in a maths examination is given below. Prepare a frequency table.
Answer:
Question 15.
(a) (100 + 2)² = 100² + 2 × 100 × 2 + 22
= ______ + ______ + ______
= ______
(203)² = ______
Answer:
(100 + 2)² = 100² + (2 × 100 × 2) + 2²
= 10000 + 400 + 4
= 10404
(203)² = (200 + 3)²
= 200² + (2 × 200 × 3) + 3²
= 40000 + 1200 + 9
= 41209
(b) 98 × 102 = (100 – 2) (______)
57 × 63 = ______
Answer:
98 × 102 = (100 – 2) (100 + 2)
= 1002 – 22
57 × 63 = (60 – 3) (60 + 3)
= 602 – 32
= 3600 – 9
= 3591
Question 16.
M is the midpoint of AB. AP as BQ are perpendicular to AB. Prove tat AP = BQ.
Answer:
AM = BM
∠A = ∠B
∠PMA – ∠QMB
∴ APAM = AQBM
∴ AP = BQ
Question 17.
Draw the quadrilateral, taking actual measurements.
Answer:
Question 18.
Sum of innerangles ofa polygon with ‘n’ sides is (n – 2) 180°. The sum of outer angles will be always 360°.
(i) What is the sum of innerangles of a polygon with 20 sides?
Answer:
(20 – 2) 180 = 18 × 180° = 3240°
(ii) What is the sum of outer angles of a polygon with 100 sides.
Answer:
360°
(iii) Which is the polygon having sum of inner angles and outer angles equal.
Answer:
Rectangle
(iv) Can 1080° be the sum of inner angles of a polygon?
Answer:
Yes, because 1080° is a multiple of 180.