LC Foundation Maths flashcards
LC Foundation Maths · 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.
- Order of operations
- Evaluate expressions in this order: brackets, indices, multiplication and division from left to right, then addition and subtraction from left to right.
- Standard form
- Standard form is a × 10^n, where 1 ≤ a < 10 and n is an integer; for example, 0.0036 is written as 3.6 × 10^−3.
- HCF and LCM
- The highest common factor is the largest number dividing two or more numbers exactly; the lowest common multiple is the smallest number that both or all divide into exactly.
- Negative index rule
- A negative index means the reciprocal of the positive power: a^−n = 1/a^n, so 2^−3 = 1/2^3 = 1/8.
- Percentage change
- Percentage change = (new value − original value) ÷ original value × 100%; a positive result is an increase and a negative result is a decrease.
- Upper and lower bounds
- For a value rounded to the nearest whole unit, the lower bound is value − 0.5 and the upper bound is value + 0.5; for other accuracies use half the rounding unit.
- Quadratic formula
- For ax² + bx + c = 0, the solutions are x = [−b ± √(b² − 4ac)] ÷ (2a), provided a is not zero.
- Difference of squares
- The difference of two squares factorises as a² − b² = (a + b)(a − b); for example, x² − 9 = (x + 3)(x − 3).
- Gradient of a line
- The gradient of a straight line is (change in y) ÷ (change in x), calculated from two points as m = (y₂ − y₁)/(x₂ − x₁).
- Simultaneous equations
- Two equations solved together; elimination makes the coefficients of one variable equal and opposite, then adding or subtracting removes that variable.
- Index law for multiplication
- When multiplying powers with the same base, add the indices: a^m × a^n = a^(m+n); for example, x^3 × x^4 = x^7.
- Rearranging a formula
- To make a variable the subject, apply inverse operations to both sides, usually undoing addition or subtraction before multiplication or division.
- Dividing in a ratio
- To share an amount in the ratio a : b, add the parts to get a + b, divide the amount by this total, then give a parts and b parts.
- Direct proportion
- Two quantities are in direct proportion when one is a constant multiple of the other, y = kx; doubling x doubles y and the ratio y/x stays constant.
- Inverse proportion
- Two quantities are inversely proportional when y = k/x; doubling x halves y, and the product xy remains constant.
- Speed formula
- Speed = distance ÷ time; rearrange to distance = speed × time or time = distance ÷ speed, keeping distance and time units consistent.
- Compound interest
- Compound interest is calculated with A = P(1 + r)^n, where P is the principal, r is the decimal interest rate per period and n is the number of periods.
- Map scale
- A map scale 1 : n means one unit on the map represents n of the same units in real life; convert both lengths to the same unit before calculating.
- 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.
- SOH CAH TOA
- In a right-angled triangle: sin θ = opposite/hypotenuse, cos θ = adjacent/hypotenuse, and tan θ = opposite/adjacent.
- Circle circumference and area
- For a circle of radius r: circumference = 2πr and area = πr²; use π ≈ 3.142 or the calculator's π key.
- Sector area formula
- The area of a sector with central angle θ degrees is (θ/360) × πr²; its arc length is (θ/360) × 2πr.
- Similar shape scale factors
- For similar shapes with length scale factor k, corresponding lengths multiply by k, areas by k², and volumes by k³.
- Three-figure bearings
- A bearing is measured clockwise from north and written with three digits, such as 045° for north-east or 270° for west.
- Mean
- The mean is the sum of all values divided by the number of values; for a frequency table, use Σfx ÷ Σf.
- Median
- The median is the middle value when data are arranged in order; with an even number of values, it is the mean of the two middle values.
- Mode
- The mode is the value that occurs most often in a data set; a set can have one mode, several modes, or no mode if all values occur equally often.
- Interquartile range
- The interquartile range is upper quartile minus lower quartile, Q3 − Q1; it measures the spread of the middle half of the data.
- Probability scale
- Probability is measured from 0 to 1: 0 means impossible, 1 means certain, and 0.5 means an even chance.
- Complement rule
- The probability that event A does not happen is P(not A) = 1 − P(A), because all outcomes together have probability 1.
- Mutually exclusive events
- Events that cannot happen at the same time; for mutually exclusive events, P(A or B) = P(A) + P(B).
- Tree diagram multiplication
- On a probability tree, multiply probabilities along each branch to get the probability of that sequence of outcomes; add branch results for all successful sequences.