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GCSE الرياضيات10 أسئلة

GCSE Maths Foundation: Geometry practice questions

Ten free GCSE Maths Foundation tier questions on angles, area, volume, circles, Pythagoras, polygons and bearings, each with a worked solution. Suitable for AQA, Edexcel and OCR.

أسئلة أصلية كتبها مدرّسو Studoli بأسلوب امتحان GCSE. ليست أسئلة رسمية.

Timed mode

10 questions in 15 minutes, one question at a time. Your answers are marked when you submit or when the time runs out.

  1. الموضوع: Angles in a triangle

    1. Two angles in a triangle are 50° and 75°. Find the third angle.

    الحل

    C. 55°

    • Angles in a triangle add up to 180°.
    • 180 − 50 − 75 = 55°.

  2. الموضوع: Area

    2. Find the area of a rectangle 8 cm long and 5 cm wide.

    الحل

    B. 40 cm²

    • Area of a rectangle = length × width.
    • 8 × 5 = 40 cm².

  3. الموضوع: Area

    3. Find the area of a triangle with base 10 cm and perpendicular height 6 cm.

    الحل

    A. 30 cm²

    • Area of a triangle = ½ × base × height.
    • ½ × 10 × 6 = 30 cm².

  4. الموضوع: Polygons

    4. What is the sum of the interior angles of a pentagon?

    الحل

    D. 540°

    • Sum of interior angles = (n − 2) × 180°.
    • For a pentagon, n = 5: 3 × 180 = 540°.

  5. الموضوع: Circles

    5. Find the circumference of a circle with radius 5 cm. Use π = 3.14.

    الحل

    C. 31.4 cm

    • Circumference = 2πr.
    • 2 × 3.14 × 5 = 31.4 cm.

  6. الموضوع: Pythagoras

    6. The two shorter sides of a right-angled triangle are 6 cm and 8 cm. Find the longest side.

    الحل

    B. 10 cm

    • Pythagoras: c² = a² + b².
    • c² = 36 + 64 = 100, so c = 10 cm.

  7. الموضوع: Volume

    7. Find the volume of a cuboid 4 cm by 3 cm by 2 cm.

    الحل

    A. 24 cm³

    • Volume of a cuboid = length × width × height.
    • 4 × 3 × 2 = 24 cm³.

  8. الموضوع: Angles on a line

    8. Two angles lie on a straight line. One is 112°. Find the other.

    الحل

    D. 68°

    • Angles on a straight line add up to 180°.
    • 180 − 112 = 68°.

  9. الموضوع: Polygons

    9. Find the exterior angle of a regular hexagon.

    الحل

    C. 60°

    • Exterior angles of any polygon add up to 360°.
    • 360 ÷ 6 = 60°.

  10. الموضوع: Bearings

    10. What is the bearing of due east?

    الحل

    B. 090°

    • Bearings are measured clockwise from north and written with three figures.
    • East is a quarter turn clockwise from north: 090°.
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