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GCSE Mathematics Flashcards

6 cards from real GCSE practice questions. Tap to flip, then mark Knew It or Still Learning — missed cards come back until you master them.

Read the first 6 GCSE Mathematics flashcards as text

  1. What is the gradient of a line segment from (1, 2) to (4, 8)?

    Answer: 2

    Gradient = (change in y) ÷ (change in x) = (8 − 2) ÷ (4 − 1) = 6 ÷ 3 = 2.

  2. What is a vector in mathematics?

    Answer: A quantity with both magnitude and direction

    A vector has both magnitude (size) and direction. Velocity is a vector (e.g., 60 km/h north) whereas speed is a scalar (just magnitude, no direction). Vectors are written as arrows or column vectors.

  3. Solve: x² − 9 = 0

    Answer: x = 3 or x = −3

    x² = 9, so x = ±√9 = ±3. Both x = 3 and x = −3 satisfy the equation because both squared give 9.

  4. What does the discriminant (b² − 4ac) tell you about a quadratic equation ax² + bx + c = 0?

    Answer: The number of real solutions the equation has

    If b² − 4ac > 0, there are two distinct real solutions; if = 0, one repeated solution; if < 0, no real solutions. The discriminant determines the nature of the roots without solving fully.

  5. A shape is enlarged by scale factor 3. The original area is 12 cm². What is the new area?

    Answer: 108 cm²

    When a shape is enlarged by scale factor k, areas scale by k². Scale factor 3 means area scales by 3² = 9. New area = 12 × 9 = 108 cm².

  6. What is sin 30°?

    Answer: 1/2

    sin 30° = 1/2 = 0.5. This is one of the standard exact trigonometric values: sin 30° = 0.5, cos 30° = √3/2, tan 30° = 1/√3. These are worth memorising.