BGCSE Mathematics 0563 flashcards
BGCSE Mathematics 0563 · Build recall with a focused review session.
32 cards. Read the term and the definition here. The deck at the top of this page is optional.
- HCF
- The highest common factor is the largest integer that divides each of two or more given integers exactly without a remainder.
- LCM
- The lowest common multiple is the smallest positive integer that is a multiple of each of two or more given integers.
- Standard form
- A number is in standard form when written as a × 10ⁿ, where 1 ≤ a < 10 and n is an integer.
- Prime number
- A prime number is an integer greater than 1 whose only positive factors are 1 and itself.
- Direct proportion
- Two quantities are in direct proportion when one is a constant multiple of the other, so doubling one doubles the other.
- Inverse proportion
- Two quantities are inversely proportional when their product is constant, so doubling one quantity halves the other.
- Percentage profit
- Percentage profit equals profit divided by cost price multiplied by 100, where profit is selling price minus cost price.
- Simple interest
- Simple interest is calculated as principal × rate × time ÷ 100, with time in years and rate as a percentage per year.
- Quadratic formula
- For ax² + bx + c = 0 with a ≠ 0, the solutions are x = [−b ± √(b² − 4ac)] ÷ (2a).
- Difference of squares
- The identity a² − b² = (a + b)(a − b) factorises a difference of two perfect squares into two binomial factors.
- Index law for products
- When multiplying powers with the same base, add the indices; for example, aᵐ × aⁿ = aᵐ⁺ⁿ and x³ × x⁴ = x⁷.
- Inequality reversal
- Multiplying or dividing both sides of an inequality by a negative number reverses the inequality sign.
- Gradient formula
- The gradient of a straight line through points (x₁, y₁) and (x₂, y₂) is (y₂ − y₁) ÷ (x₂ − x₁).
- Perpendicular gradients
- Two straight lines are perpendicular when the product of their gradients equals −1, so one gradient is the negative reciprocal of the other.
- Function notation
- The notation f(x) names a function; f(a) means substitute a for x and calculate the corresponding output value.
- Speed-time graph
- On a speed-time graph, the gradient represents acceleration and the area under the graph represents distance travelled.
- Pythagoras theorem
- In a right-angled triangle, the square of the hypotenuse equals the sum of the squares of the other two sides: a² + b² = c².
- Trapezium area
- The area of a trapezium equals half the sum of the parallel sides multiplied by the perpendicular distance between them.
- Sector area
- The area of a circle sector is θ/360 × πr², where θ is the sector angle in degrees and r is the radius.
- Similar areas ratio
- If two similar figures have corresponding lengths in ratio k:1, their areas are in ratio k²:1.
- Sine rule
- In any triangle, a ÷ sin A = b ÷ sin B = c ÷ sin C, where a, b, c are sides opposite angles A, B, C.
- Cosine rule
- In any triangle, a² = b² + c² − 2bc cos A, where a is opposite angle A and b, c are the other sides.
- Bearing definition
- A bearing is an angle measured clockwise from north, written as a three-figure number between 000° and 360°.
- Angle of elevation
- The angle of elevation is the angle measured upward from a horizontal line to an object above the observer.
- Vector magnitude
- The magnitude of column vector (x, y) is √(x² + y²), giving its length in the coordinate plane.
- Position vector
- The position vector of point A from the origin O is vector OA; the vector AB equals b − a.
- Enlargement area factor
- An enlargement with linear scale factor k multiplies lengths by k and areas by k².
- Mean definition
- The mean is found by adding all the data values and dividing the total by the number of values.
- Interquartile range
- The interquartile range is the upper quartile minus the lower quartile; it measures the spread of the middle half of the data.
- Frequency density
- Frequency density equals frequency divided by class width; in a histogram, bar area represents frequency.
- Complementary probability
- For any event E, the probability that E does not occur is 1 − P(E), so P(E) + P(not E) = 1.
- Independent events
- Two events are independent when the occurrence of one does not affect the probability of the other; P(A and B) = P(A) × P(B).