8 chapters · 8 questions each · Click any chapter to expand
Plot the points A(3, 4), B(-2, 3), C(-4, -2) and D(5, -3) on the Cartesian plane and name the quadrant in which each lies.
Write the coordinates of the point which lies on the y-axis at a distance of 5 units from the origin in the positive direction.
In which quadrant or on which axis do the following points lie: (-3, 5), (4, -1), (2, 0), (-3, -6), (0, -7)?
If the coordinates of two points are P(2, 3) and Q(2, -1), are they in the same quadrant? Justify.
The point (a, b) lies in the third quadrant. What are the signs of a and b?
Plot the points (1, 1), (4, 1), (4, 4) and (1, 4). Name the figure formed and find its area.
Locate the points (0, 3), (0, -3), (3, 0) and (-3, 0) on a graph paper. Join them in order and name the figure.
State whether True or False: The point (-5, 0) lies on the negative side of the x-axis.
Find the zero of the polynomial p(x) = 3x - 9.
If p(x) = 2x + 5, find p(0), p(2) and p(-3).
Check whether x = -2 is a zero of the polynomial p(x) = 4x + 8.
Draw the graph of y = 2x - 3 and find the point where it cuts the x-axis.
Write a linear polynomial whose zero is 5.
Classify as monomial, binomial or trinomial: 3x, 2x + 1, x^2 + x + 1, 7.
The cost of one pen is Rs. x and one notebook is Rs. (x + 10). Write a linear polynomial for the total cost.
Find the value of k if x = 2 is a zero of p(x) = kx - 6.
Is zero a rational number? Justify with reasoning.
Find five rational numbers between 1 and 2.
Express 0.6̄ (recurring) in the form p/q.
Show that √2 is irrational.
Rationalise the denominator of 1/(√7 - √6).
Simplify: (2^3 × 2^4) / 2^5.
Find: (i) 64^(1/2) (ii) 32^(1/5) (iii) 125^(1/3).
Represent √5 on the number line.
Expand using identity: (3x + 2y)^2.
Find (102)^2 using a suitable identity.
Factorise: 9x^2 - 16y^2.
Factorise: x^3 + 8.
Without actually calculating, find (-12)^3 + (7)^3 + (5)^3.
If x + 1/x = 5, find x^2 + 1/x^2.
Evaluate (998)^3 using identity.
Expand: (2a - 3b + c)^2.
In a right triangle ABC, right-angled at B, if AB = 3 and BC = 4, find sin C, cos C and tan C.
Evaluate: sin 30° + cos 60°.
If sin A = 3/5, find cos A and tan A.
Show that sin²(45°) + cos²(45°) = 1.
A ladder 10 m long leans against a wall and reaches a height of 8 m. Find the angle and distance of foot from wall.
Find x if tan 60° = x/10.
Give two real-life examples of periodic motion.
If cos θ = 1/2, find the value of θ.
Find the area of a triangle with sides 13 cm, 14 cm and 15 cm using Heron's formula.
The perimeter of a rectangular field is 240 m and its length is 80 m. Find the breadth and area.
Find the area of a parallelogram with base 12 cm and height 8 cm.
A rhombus has diagonals of 16 cm and 12 cm. Find its area.
Find the area of a circle with radius 7 cm. (Take π = 22/7)
The area of an equilateral triangle is 25√3 cm². Find its side.
A trapezium has parallel sides 25 cm and 13 cm and height 10 cm. Find its area.
A wire bent as a square encloses 484 cm². The same wire is bent as a circle. Find the area enclosed.
A die is rolled once. Find the probability of getting (i) an even number (ii) a number greater than 4.
A coin is tossed 1000 times and head appears 540 times. Find the empirical probability of getting a tail.
A bag contains 5 red, 3 blue and 2 green balls. A ball is drawn at random. Find the probability that it is red.
Two coins are tossed simultaneously. Find the probability of getting at least one head.
From a well-shuffled pack of 52 cards, one card is drawn. Find P(king) and P(red card).
If P(E) = 0.65, find P(not E).
A die is rolled 200 times and 3 appears 40 times. Find the experimental probability of getting 3.
Give one example each of a sure event and an impossible event.
Find the 10th term of the AP: 2, 5, 8, 11, …
The first term of an AP is 5 and the common difference is 3. Find the sum of the first 20 terms.
Which term of the AP: 3, 8, 13, 18, … is 78?
Find the sum of all natural numbers between 1 and 100 which are divisible by 5.
The 5th term of an AP is 19 and the 9th term is 35. Find the AP.
Find the 6th term of the GP: 3, 6, 12, 24, …
How many terms of the AP: 9, 17, 25, … must be taken to give a sum of 636?
A man saves Rs. 100 in the first month and increases his savings by Rs. 50 every month. What will be his total savings after one year?
