| What do you do with a minus sign outside the brackets? | When there is a minus sign outside brackets when expanding brackets, flip all the signs so positives become negatives and negatives becomes positives |
| What are rational numbers | A rational number is any number that has a limited number of decimal places that can be written as a fraction such as integers, fractions, terminating decimals terminating (limited amount of numbers after the decimal) and recurring decimals |
| What are irrational numbers | Irrational numbers are numbers that continue forever without recurring numbers, examples include pi and surds e.g. square root 2 |
| What are the two steps to expanding triple brackets? | To expand three brackets expand the first two brackets, then expand that answer with the third bracket |
| What is the quadratic formula? | The quadratic formula is
x = -b + or – square root b2– 4ac / 2a
(where -b =/- is on the fraction line) |
| What is the quadratic equation for standard form? | The quadratic equation for standard form is
ax2 + bx + c = 0 |
| How do you use the quadratic formula to solve quadratic equations? | To use the quadratic formula,
write in the a, b, and c values in the quadratic formula, from the given equation such as 2x2 + 3x – 2 = 0, in which a = 2, b = 3, and c = -2, so x = -b + or – square root b2– 4ac /2a becomes x = -(3) + or –square root 32– 4(2)(-2) /2(2) which means = -3 +/- |square root 9 +16|/ 4 and as 9+16=25 and the square root of 25 is 5 the equation = -3+/- 5/ 4. Which is then broken into two equations because of the +/- symbol: x = -3 + 5 / 4 and – 3 – 5 / 4 and as – 3 + 5 = 2, and – 3 – 5 = =8 the equations become 2/4 and -8/4 which simplify to ½ and -2 so x = ½ or x = -2 |
| What is the inter quartile range? | The inter quartile range is the range from the first quartile range (value) to the last/third quartile range (value)
IQR = range from Q1 – Q3 |
| How do you turn a fraction into a recurring decimal? | To turn a fraction into a recurring decimal multiply the denominator so it has 9's in it, then multiply the nuetortor by the same number. e.g. 32/666 x 1.5 = 48/999, and because the numerator needs to have the same number of digits as the denominator, a 0 is before 48 so it becomes 048/999 which gives the recurring decimal 0.048 (where a dot is over the 0 and 8) |
| What is the surface area of a cuboid? | Becuase cuboids have 3 types of faces and 2 of each
Surface area of a cuboid = 2lw x 2lh x 2hw |
| What is the area of a sector? | The area of a sector is r^2 x a/2
where a is the interior angle |
| How do you do negative and fractional indices? | To do negative and fractional indices, when the number is whole put 1 over it and if the number is a fraction, flip it
And in both cases the negative indices then become positive and the expressions are simplified
And if an indice is negative and fractional first flip the fraction number then square root it |
| How do you simplify surds? | To simplify surds find the two highest common factors also in surd form – then undo the square root that has an integer answer, put it in front of the other surd, and simplify |
| How do you find the equation of a tangent? | To find the equation of a tangent, first, find the gradient of the radius, for example, if the radius went from the origin to (3,4), the gradient would be 4-0/3-0 =4/3 because the gradient = change in y/ change in x.
Then find the gradient of the tangent by taking the negative reciprocal of the first gradient which is – 3/4,
Now complete the rest of the equation, as the straight-line equation is y = -3/4x + c, and as y = 4 and x = 3, this = 4 = -9/4 + c, and as 25 the diameter, y = -3/4x + 25/4 |
| What is the equation for interior angles? | Interior angles = 180 (n-2), when n = number of sides |
| What is the equation for exterior angles? | The equation for exterior angles is 360/n, where n = number of sides, and all exterior angles = 360 |
| What is the formula for arc length? | The formula for arclength is L/ 0 = C / 2pi, where L = length and 0 = angle |
| What is 1kg in Pounds? | 1kg in Pounds is 2.205 pounds |
| What is 1L in m^3 | 1L in m^3 is 0.001m^3 |
