Maths Online Test Class 8

A number is divisible by 3 if the sum of its digits is divisible by 3. Sum = 1+8+a+7+1 = 17+a. For 17+a to be divisible by 3, a must be 1 (18) or 4 (21) or 7 (24). Given options, 1 is correct.

A number is divisible by 9 if the sum of its digits is divisible by 9. Sum = 2+y+2+5 = 9+y. For 9+y to be divisible by 9, y must be 0 or 9. Given options, 0 is correct.

8A5 + 94A = 1A33. Looking at the units column: 5 + A = 3 or 13. If 5 + A = 13, then A = 8. Checking: 885 + 948 = 1833. This matches.

(10A + 1) + (10 + B) = 10B + 0. Simplifying: 10A + B + 11 = 10B. 10A + 11 = 9B. Testing A=7: 70 + 11 = 81, so 9B = 81, B = 9. This matches.

A number is divisible by 3 if the sum of its digits is divisible by 3. For 15267, sum = 1+5+2+6+7 = 21, which is divisible by 3.

The expression 64a^2 - 80ab + 25b^2 is of the form x^2 - 2xy + y^2, which factors to (x - y)^2. Here, x = 8a and y = 5b, so it is (8a - 5b)^2.

Option C is an identity (2/3x + 2 = 2/3x + 2). Option A is incorrect because (x+2)^2 = x^2 + 4x + 4. Option B is incorrect because a^2 + b^2 is not (a+b)^2.

Factoring the numerator: y^2 + 7y + 10 = (y + 5)(y + 2). Dividing by (y + 5) leaves (y + 2).

Expanding (x - 3)(x + a) = x^2 + ax - 3x - 3a = x^2 + (a - 3)x - 3a. Comparing to x^2 - x - 6, we have a - 3 = -1, so a = 2. Also -3a = -6, so a = 2.

Using the difference of squares formula, a^2 - b^2 = (a - b)(a + b). Here, (8.6 - 1.4)(8.6 + 1.4) = (7.2)(10) = 72.

Factor by grouping: 15pq + 25p + 9q + 15 = 5p(3q + 5) + 3(3q + 5). Factoring out the common binomial (3q + 5) yields (5p + 3)(3q + 5).

To factor x^2 - 7x + 12, find two numbers that multiply to 12 and add to -7. These numbers are -3 and -4, so the factors are (x - 3)(x - 4).

Option B states 4x + 5x = 8x², which is incorrect. When adding like terms 4x and 5x, we add the coefficients: 4x + 5x = 9x, not 8x². The other options A, C, and D all show correct algebraic expansions and simplifications.

92 * 93 = 92 * (90 + 3) = 8280 + 276 = 8556.

Substitute x = 2 and y = 3 into x^x + y^x: 2^2 + 3^2 = 4 + 9 = 13.

Given x + 1/x = 2, square both sides: (x + 1/x)^2 = 2^2, which is x^2 + 2(x)(1/x) + 1/x^2 = 4. This simplifies to x^2 + 2 + 1/x^2 = 4, so x^2 + 1/x^2 = 2.

Expand both squares: (a^2 + 2ab + b^2) + (a^2 - 2ab + b^2). The 2ab and -2ab cancel out, leaving 2a^2 + 2b^2, which is 2(a^2 + b^2).

The expression a^2 + 2ab + b^2 is the expansion of (a + b)^2. Since (a + b)^2 = 49, taking the square root gives a + b = 7 (assuming positive values).

The sum is 1/(x + y) + 1/(x - y). Find a common denominator: (x - y)/((x + y)(x - y)) + (x + y)/((x + y)(x - y)) = (x - y + x + y) / (x^2 - y^2) = 2x / (x^2 - y^2).

The area of a rectangle is length * breadth. 3x * 5y = 15xy.

(a + b - 3) - (b - a + 3) + (a - b + 3) = a + b - 3 - b + a - 3 + a - b + 3. Combining like terms: (a + a + a) + (b - b - b) + (-3 - 3 + 3) = 3a - b - 3.

Let the required expression be X. Then 3x + y + X = 2x + 3y, so X = 2x + 3y - 3x - y = -x + 2y. This gives us what must be added to transform the first expression into the second.

Substitute n = -2 into 5n - 2: 5(-2) - 2 = -10 - 2 = -12.

A monomial is an expression consisting of a single term. xyz is a single term, so it is a monomial.