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Exam-Style Questions.

Problems adapted from questions set for previous Mathematics exams.

1.

GCSE Higher

The diagram shows an isosceles triangle (not drawn to scale).

Isosceles Triangle

Angle ABC = angle ACB, AB = \(3x+8\) and AC = \(5x-7\).

Use an algebraic method to find the value of \(x\).


2.

GCSE Higher

Multiply out and simplify:

$$(x-6)^2$$

3.

GCSE Higher

Two rectangles, not drawn to scale, are shown below. All measurements are in centimetres. Both rectangles have the same areas. Work out the perimeter of the rectangle on the left.

Two Rectangles

4.

GCSE Higher

(a) Simplify \( \left(\dfrac{3a}{a^3 - 3}\right)^0 \)

 

(b) Simplify \( \dfrac{9(2b-1)}{(2b-1)^2}\)

 

(c) Simplify \( (2c^3d^4)^5 \)


5.

GCSE Higher

Expand and simplify the following expression:

$$ (2x^2 + 3)(4x - 5) - 8x(x^2 - 7) $$

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The exam-style questions appearing on this site are based on those set in previous examinations (or sample assessment papers for future examinations) by the major examination boards. The wording, diagrams and figures used in these questions have been changed from the originals so that students can have fresh, relevant problem solving practice even if they have previously worked through the related exam paper.

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