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Quiz Chapter 2: Factorisation and Algebraic Fractions

10 questions · Form 2 Mathematics Bab 2: Factorisation and Algebraic Fractions

Question 1 of 10Score: 0

Simplify the expression: (2x3) + (x4).

Full Question List & Answer Key

Prefer reading to quizzing? All 10 questions are listed below with the answer and explanation under each one.

1. Simplify the expression: (2x3) + (x4).

  1. 3x7
  2. 11x12
  3. 3x12
  4. 8x12
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Answer: B

Find the LCM of 3 and 4, which is 12: (2x × 412) + (x × 312) = 8x12 + 3x12 = 11x12.

2. Simplify: 1 - x - 23.

  1. 5 - x3
  2. 1 - x3
  3. x + 13
  4. 5 + x3
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Answer: A

Combine under common denominator 3: 3 - (x - 2)3 = 3 - x + 23 = 5 - x3.

3. Factorise 5p + 5q - ap - aq completely.

  1. (5 - a)(p - q)
  2. (5 + a)(p + q)
  3. (5 - a)(p + q)
  4. (a - 5)(p + q)
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Answer: C

Group terms: 5(p + q) - a(p + q) = (5 - a)(p + q).

4. What is the expanded form of (3a - 2b)²?

  1. 9a² - 4b²
  2. 9a² + 4b²
  3. 9a² - 12ab + 4b²
  4. 9a² - 6ab + 4b²
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Answer: C

Using identity (x - y)² = x² - 2xy + y²: (3a)² - 2(3a)(2b) + (2b)² = 9a² - 12ab + 4b².

5. Factorise completely: 3x² - 12.

  1. 3(x - 2)²
  2. 3(x + 2)(x - 2)
  3. (3x + 6)(x - 2)
  4. 3(x² - 4)
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Answer: B

First factor out 3: 3(x² - 4). Then apply difference of squares: 3(x + 2)(x - 2).

6. Expand: 2(x - 3) - 3(2 - x).

  1. 5x - 12
  2. -x - 12
  3. 5x
  4. x - 12
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Answer: A

Expand each term: 2x - 6 - 6 + 3x = (2x + 3x) + (-6 - 6) = 5x - 12.

7. Factorise x² - 49.

  1. (x - 7)²
  2. (x + 7)(x - 7)
  3. (x + 49)(x - 1)
  4. (x - 7)(x - 7)
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Answer: B

Using difference of two squares a² - b² = (a + b)(a - b): x² - 7² = (x + 7)(x - 7).

8. Factorise the quadratic expression: x² - 7x + 12.

  1. (x - 3)(x + 4)
  2. (x + 3)(x + 4)
  3. (x - 3)(x - 4)
  4. (x - 2)(x - 6)
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Answer: C

Find two numbers that multiply to +12 and add up to -7. The numbers are -3 and -4. So, (x - 3)(x - 4).

9. Express x² - 9x + 3 in its simplest form.

  1. x + 3
  2. x - 3
  3. x - 9
  4. 1x + 3
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Answer: B

Factorise the numerator: (x + 3)x - 3x + 3 = x - 3.

10. If the area of a rectangle is (x² + 6x + 8) cm² and its length is (x + 4) cm, find its width.

  1. (x + 2) cm
  2. (x - 2) cm
  3. (x + 3) cm
  4. (x + 1) cm
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Answer: A

Width = Area ÷ Length = x² + 6x + 8x + 4 = (x + 4)(x + 2)x + 4 = x + 2 cm.

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