SAT

📘 SAT study guides (4)

Start with the maths vocabulary: many students know the maths but lose marks on the English wording. Words in Context vocabulary, grammar rule cards and original practice questions are being added. SAT is a trademark of College Board; check the official site for the latest test details.

Grammar rule cards (240 practice questions)

Reading and Writing practice (100 questions)

Math practice (100 questions)

⏱ Timed module practice (Reading and Writing · Math)

• proportional relationship

  noun

  A relationship where two quantities have a constant ratio, so y = kx.

  Distance and time are in a proportional relationship at constant speed.

• propose

  verb

  To suggest an idea or plan for others to consider.

  The author proposes a new explanation for the pattern.

• provoke

  verb

  To cause a reaction, especially a strong one.

  The proposal provoked fierce debate.

• Pythagorean theorem

  noun

  In a right triangle, a² + b² = c², where c is the hypotenuse.

  By the Pythagorean theorem, 3² + 4² = 5².

• quadratic equation

  noun

  An equation with x² as the highest power, such as x² − 5x + 6 = 0.

  The quadratic equation has two solutions.

• quadratic formula

  noun

  The formula x = (−b ± √(b² − 4ac)) / 2a for solving quadratic equations.

  Use the quadratic formula when factorising is difficult.

• quadratic function

  noun

  A function of the form f(x) = ax² + bx + c, whose graph is a parabola.

  The quadratic function has a maximum value.

• quadrilateral

  noun

  A polygon with four sides.

  The angles of a quadrilateral add up to 360°.

• qualify

  verb

  In context: to limit or add conditions to a statement so it is less absolute.

  The author qualifies her claim by noting that the data are incomplete.

• quartile

  noun

  One of three values that divide ordered data into four equal parts.

  The first quartile is 12.

• quotient

  noun

  The result of dividing one number by another.

  The quotient of 20 and 4 is 5.

• radian

  noun

  A unit for measuring angles; π radians equals 180 degrees.

  90 degrees is π/2 radians.

• radical

  noun

  In maths, an expression with a root sign (√), such as √5 or ∛x.

  Simplify the radical √50 to 5√2.

• radical equation

  noun

  An equation with a variable inside a root sign.

  Check answers to a radical equation for extra solutions.

• radius

  noun

  The distance from the centre of a circle to its edge.

  The radius is half the diameter.

• random assignment

  noun

  Placing participants into groups by chance in an experiment.

  Random assignment allows cause-and-effect conclusions.

• random sample

  noun

  A sample where every member of the population has an equal chance of being chosen.

  A random sample allows conclusions about the whole population.

• range

  noun

  In maths, the set of all output values of a function; in statistics, the largest value minus the smallest.

  The range of the data set is 12.

• rate

  noun

  A comparison of two quantities with different units, such as kilometres per hour.

  The car travels at a rate of 60 km per hour.

• ratio

  nounAWL 5

  The relationship between two amounts, shown as two numbers.

  The student-teacher ratio is 25 to 1.

• rational expression

  noun

  A fraction whose numerator and denominator are polynomials.

  Simplify the rational expression (x² − 1)/(x − 1).

• rational number

  noun

  A number that can be written as a fraction of two integers, such as 3/4 or −2.

  0.75 is a rational number because it equals 3/4.

• real number

  noun

  Any number on the number line, including rational and irrational numbers.

  For all real numbers x, x² is never negative.

• reciprocal

  noun

  The number you multiply by to get 1; for a fraction, flip the numerator and denominator.

  The reciprocal of 2/3 is 3/2.

• reconcile

  verb

  To make two different ideas or facts fit together.

  The theory cannot reconcile the two sets of results.