Home / iGCSE Mathematics (0580) : C2.2 Manipulate directed numbers. iGCSE Style Questions Paper 1

iGCSE Mathematics (0580) : C2.2 Manipulate directed numbers. iGCSE Style Questions Paper 1

Question

(a) Factorise completely.
18x² – 12x

(b) Expand and simplify.
(x + 5)(x – 3)

▶️ Answer/Explanation
Solution

Ans:

(a) 6x(3x – 2) (take out common factor 6x)

(b) x² + 2x – 15 (use FOIL method: x×x + x×(-3) + 5×x + 5×(-3))

Question

The diagram shows a rectangle with length \(3x-12\) and width \(x+7\).

Find an expression for the perimeter of the rectangle.

Give your answer in its simplest form.

▶️ Answer/Explanation
Solution

Ans: \(8x-10\) or \(2(4x-5)\)

The perimeter \( P \) of a rectangle is calculated using the formula:

\[ P = 2(\text{Length} + \text{Width}) \]

Substitute the given expressions for length (\(3x – 12\)) and width (\(x + 7\)):

\[ P = 2((3x – 12) + (x + 7)) \]

Simplify the expression inside the parentheses:

\[ P = 2(4x – 5) \]

Finally, expand to get the simplest form:

\[ P = 8x – 10 \]

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