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New Millennium Academy

Birauta, Pokhara-17, Kaski  |  nripendraswaracharya.com.np

Class 8  ·  Mathematics
Indices & Algebra
Model Question Sets · 2083 B.S.
📊 Specification Grid – Marks Distribution
Level K
(Knowledge)		 U
(Understanding)		 A
(Application)		 HA
(Higher Ability)		 Total
Questions 2 1 2 1 6
Marks 1 + 1 = 2 2 2 + 2 = 4 2 10

Indices & Algebra — Model Question Sets

Class 8 Mathematics  ·  10 Sets  ·  10 Marks Each

SET – 1 Indices & Algebra ▲ Top
1.a. What must be in box of \((4x)^{\square}\) so that its value will be 1? [1K]
1.b. Simplify: \[\frac{x^{p-q+1} \times x^{q-r+1} \times x^{r-p+1}}{x^3}\] [2A]
2.a. Write the factors of \(a^2 - b^2\). [1K]
2.b. Factorize: \((a+b)^2 - 7(a+b) + 12\) [2U]
3.a. The area of rectangular playground is \(3x^2 + 10x + 8 \text{ m}^2\). Find the length and breadth of playground. [2A]
3.b. For what value of '\(a\)' the value of algebraic expression \(a^2 - 3a + 2\) will be zero? [2HA]
SET – 2 Indices & Algebra ▲ Top
1.a. Write the value of \(2^{-3}\). [1K]
1.b. Simplify using law of indices: \[\frac{4^4 \times 5^5}{25^3 \times 16^2}\] [2A]
2.a. What must be filled in blank space to make expression \((x)^2 + \cdots + (4)^2\) a perfect square? [1K]
2.b. Factorize: \(2x^2\) - \(\dfrac{18}{z^2}\) [2U]
3.a. The volume of a rectangular room is \(4c^3 - 8c^2 - 12c \text{ m}^3\). Calculate its dimensions. [2A]
3.b. For what value of '\(y\)' the value of algebraic expression \(9y^2 - 6y + 1\) will be zero? [2HA]
SET – 3 Indices & Algebra ▲ Top
1.a. What is the value of \(2^x \times 2^{-x}\)? [1K]
1.b. Prove that: \[\frac{x^{m+n+2} \times x^{m+n+2}}{x^{2(m+n+1)}} = x^2\] [2A]
2. Sita wrote two algebraic expressions as,
1st: \(2x^2 - x - 15\)
2nd: \(x^2 + 10x + 9\)
a. Write two numbers whose sum is 10 and product is 9. [1K]
2.b. Factorize 1st expression. [2U]
3.a. Show \(x^2 + 3x + 2\) represent a rectangle geometrically, write its length and breadth. [2A]
3.b. For what value of '\(a\)' the value of algebraic expression \(2a^3 - 18a\) will be zero? [2HA]
SET – 4 Indices & Algebra ▲ Top
1.a. Write the value of \((x^a \times x^{-a})^5\). [1K]
1.b. Simplify: \[\frac{3^{n+1} + 3^n}{4 \times 3^n}\] [2A]
2.a. Write the factors of \((a^2 - 1)\). [1K]
2.b. Factorize: \(x^2 + 7x + 12\) [2U]
3.a. The area of a rectangular garden is \(2x^2 + 7x + 6 \text{ m}^2\). Find its length and breadth. [2A]
3.b. For what value of '\(x\)', the value of the algebraic expression \(x^2 - 5x + 6\) is zero? [2HA]
SET – 5 Indices & Algebra ▲ Top
1.a. Express \(\dfrac{1}{x^{-3}}\) in positive index form. [1K]
1.b. Simplify: \[\left(\frac{x^a}{x^b}\right)^{a+b} \times \left(\frac{x^b}{x^c}\right)^{b+c} \times \left(\frac{x^c}{x^a}\right)^{c+a}\] [2A]
2.a. What must be added to \(a^2 + b^2\) to make it a perfect square \((a - b)^2\)? [1K]
2.b. Factorize: \((x - y)^2 - 5(x - y) + 6\) [2U]
3.a. The area of a rectangular room is \(x^2 + 8x + 15 \text{ m}^2\). Find its length and breadth. [2A]
3.b. For what value of '\(m\)', the value of \(m^2 - 4m - 5\) will be zero? [2HA]
SET – 6 Indices & Algebra ▲ Top
1.a. What is the base and power in the expression \((-5x)^3\)? [1K]
1.b. Simplify: \[\frac{8^2 \times 2^4}{4^5}\] [2A]
2.a. Write the formula for \(a^2 - b^2\). [1K]
2.b. Factorize: \(x^2 - 2x - 15\) [2U]
3.a. The area of a rectangular field is \(4x^2 - 9 \text{ m}^2\). Write its possible length and breadth. [2A]
3.b. For what value of '\(p\)', the algebraic expression \(p^2 - 8p + 16\) equals zero? [2HA]
SET – 7 Indices & Algebra ▲ Top
1.a. Write the value of \(100^0 + 20^0\). [1K]
1.b. Prove that: \[\frac{x^{2a} \times x^{2b}}{x^{2(a+b)}} = 1\] [2A]
2. Ram has two algebraic expressions: \(3x^2 + 5x - 2\) and \(x^2 - 4\).
a. Write the factors of \(x^2 - 4\). [1K]
2.b. Factorize the first expression. [2U]
3.a. Show that \(x^2 + 5x + 6\) represents a rectangle geometrically and find its dimensions. [2A]
3.b. For what value of '\(k\)', is the value of \(k^3 - 4k\) equal to zero? [2HA]
SET – 8 Indices & Algebra ▲ Top
1.a. Express \(\sqrt[3]{x^2}\) in index form. [1K]
1.b. Simplify using laws of indices: \[\frac{6^4 \times 3^2}{2^4 \times 9^3}\] [2A]
2.a. What is the common factor in the expression \(4x^3y^2 - 8x^2y^3\)? [1K]
2.b. Factorize: \(3x^2 - 12\) [2U]
3.a. The area of a square room is \(9x^2 + 24x + 16 \text{ m}^2\). Find the length of its side. [2A]
3.b. For what values of '\(y\)', the expression \(y^2 - 7y + 12\) will be zero? [2HA]
SET – 9 Indices & Algebra ▲ Top
1.a. What must be the value of '\(m\)' if \(2^m = 1\)? [1K]
1.b. Simplify: \[\frac{3^4 \times 2^3}{6^2}\] [2A]
2.a. What is the common factor of \(2x^2\) and \(4x\)? [1K]
2.b. Factorize: \(x^2 + \dfrac{1}{x^2} - 2\) [2U]
3.a. The volume of a rectangular water tank is \(5x^3 - 20x\). Find its dimensions. [2A]
3.b. For what value of '\(z\)', will the expression \(2z^2 - 5z - 3\) be zero? [2HA]
SET – 10 Indices & Algebra ▲ Top
1.a. Write the value of \((5x^0)^2\). [1K]
1.b. Simplify: \[\frac{x^{a-b} \times x^{b-c}}{x^{a-c}}\] [2A]
2.a. What term must be subtracted from \(a^2 + b^2\) to make it \((a - b)^2\)? [1K]
2.b. Factorize: \(x^2 + 8x + 16\) [2U]
3.a. The area of a rectangular carpet is \(6x^2 - x - 2\) sq. units. Find its length and breadth. [2A]
3.b. For what value of '\(t\)', the expression \(t^2 - t - 20\) will be zero? [2HA]
New Millennium Academy
Birauta, Pokhara-17, Kaski  ·  nripendraswaracharya.com.np
Class 8 Mathematics  ·  Indices & Algebra — Model Question Sets  ·  2083 B.S.