Use LEFT and RIGHT arrow keys to navigate between flashcards;
Use UP and DOWN arrow keys to flip the card;
H to show hint;
A reads text to speech;
74 Cards in this Set
- Front
- Back
|
What are natural numbers |
whole positive numbers (0,1,2,3,4...) |
|
|
Which number set does N stand for? |
Natural numbers |
|
|
What are integers? |
All whole numbers (positive and negative) (-4,-3,-2,-1,0,1,2,3,4...) |
|
|
Which number set does Z stand for? |
integers |
|
|
What are rational numbers? |
Numbers that can be written as a fraction (or its decimal expansion is finite/ recurring/ a pattern of digits) |
|
|
Which number set does Q stand for? |
Rational numbers |
|
|
What are irrational numbers? |
Numbers that can't be put as a fraction (e.g. pi, surds) |
|
|
What are real numbers? |
Every single number (includes rational and irrational numbers) |
|
|
Which number set does R stand for? |
Real numbers |
|
|
rounding to the nearest 10 is the same as... |
rounding to the nearest multiple of 10 |
|
|
What are the rules for rounding? |
if the digit after the one you're rounding is less than 5, then keep the rounded digit unchanged and make the following digits zeros if the digit after is 5 or more, then add 1 to the rounded digit and change all remaining digits right to zero (or if its a decimal delete the zeros) |
|
|
Rounding a number correct to one decimal place is the same as.. |
rounding it to the nearest tenth |
|
|
rounding a number correct to two decimal places is the same as... |
rounding it to the nearest hundredth |
|
|
What does the number of significant figures in a result mean? |
The number of figures that are known with some degree of reliability |
|
|
Which digits are significant? |
All non-zeros, zeros between non-zeros, and zeros placed after other digits but right of the decimal place |
|
|
Which digits aren't significant? |
Zeros to the left of the first non-zero digit |
|
|
How many significant figures do you round if you need to estimate the answer to a calculation |
1 |
|
|
What is error? |
The difference between an estimated or approximated value(Va) and the exact value (Ve) Error = Va - Ve |
|
|
What is percentage error? |
((Va-Ve)/Ve ) * 100% APPROX. VALUE - EXACT VALUE / EXACT *100% |
|
|
How do you know if a number is written in standard form? |
its in the form a x 10^k 1<=a<10, k is an integer |
|
|
What is discrete data? |
Data that can be counter or data that can only take specific values |
|
|
what is continuous data? |
Data that can be measures. They can take any value within a range |
|
|
How do you draw a frequency histogram? |
Draw a bar chart where classes/ bars start at the lower boundary (and ends at the upper) (with no spaces between bars) |
|
|
What's the mode |
The value that occurs most frequently |
|
|
What's the median |
the value that lies in the middle when the data are arranged in size order ( (n+1)/2th value ) |
|
|
What's the mean? |
the sum of all the values divided by the number of values |
|
|
What's cumulative frequency? |
the sum of all the frequencies up to and including the new value. |
|
|
How to draw a cumulative frequency curve |
Draw cumulative frequency table with variable, frequency, upper boundary of each class interval and cumulative frequency. Plot UPPER class boundary on X-AXIS and cumulative frequency on y-axis (this is always on the vertical axis.. because the numbers rise as they accumulate) |
|
|
How to draw a box and whisker graph |
You need lower quartile, median and upper quartile and the range of values. |
|
|
How to find the range? |
Subtract the smallest value from the largest |
|
|
How to find the interquartile range? |
subtract the lower quartile from the upper |
|
|
What is standard deviation also referred to as? |
'root-mean-square deviation' |
|
|
What is the gradient of L if A(x1, y1) and B(x2, y2) lie on line L? |
m = (y2-y1)/(x2-x1) (Basically in the triangle you draw under the line between two points, its the vertical - horizontal) |
|
|
What gradient do parallel lines have? |
The same |
|
|
what are perpendicular lines?
|
Two lines that make an angle of 90 degrees and if the product of their gradients is -1 |
|
|
Equation(s) of a straight line? |
y=mx+c ax+by+d=0 where a, b, d are integers |
|
|
Equation of any vertical line? |
x= k (k is constant) |
|
|
Equation of any horizontal line? |
y=k (k is constant) |
|
|
How to find point of intersection between Line L1 and Line L2 |
M1*X1 + C1 = M2*X2 + C2 |
|
|
Trigonometry ratios in a right-angled triangle |
SOH CAH TOA Sin = opposite side / hypotenuse Cos = Adjacent side / hypotenuse Tan = Opposite side/ adjacent side |
|
|
What is the angle of elevation? |
the angle you lift your eyes through to look at something above |
|
|
What is the angle of depression? |
The angle you lower your eyes through to look at something below |
|
|
Sine rule |
Any triangle, Angles (ABC), opposite sides (abc): a / sin A = b / sin B = c / sin C |
|
|
cos rule |
a^2 = b^2 + c^2 - 2bccos A cos A = (b^2 + c^2 - a^2) / 2bc |
|
|
Area of triangle using sin |
1/2 absinC |
|
|
What is a function? |
A relationship between two sets. Each element 'x' of the first set is related to one element 'y' of the second set |
|
|
What is the domain? |
The first set of the function. They are the 'x' values. They are independent. |
|
|
For each 'x' (input), there is one output, which is called what? |
the image of 'x'. The set of these images is the range of the function. 'y' values. dependent variables. |
|
|
What form does the linear function have? |
f(x) = mx + c m = gradient c = constants the graph passes through the origin (0,0) |
|
|
What form does a quadratic function have? |
f(x) = ax^2 + bx^2 + c If a>0 then the graph is U-shaped (concave up), and a<0 is opposite (concave down). The curve intersects y-axis at (0,c) |
|
|
What is a parabola and what are its characteristics |
A graph of any quadratic functions. It has an axis of symmetry and either a minimum or maximum point (vertex of the parabola) |
|
|
In a quadratic function, what s the equation of the axis of symmetry? |
x= -(b/2a), a does not equal 0 |
|
|
In a quadtratic function, what is the x-coordinate of the vertex? |
x= - b/ 2a |
|
|
What is the factorised form of a quadtratic function, where does the curve intersect x axis and whats the equation of axis of symmetry and vertex? |
f(x) = a(x-k)(x-l) In a quadratic equation, the curve intersect the x-axis at (k,0) and (l,0) equation of the axis of symmetry and vertex is x= (k+l)/2 |
|
|
Where does the function f(x)=ax^2+bx+c intersect the x-axis? |
where f(x) = 0.
The x-values of intersection points are two solutions (or roots) of the equation ax^2+bx+c (the y-values at these points of intersection are zero.) |
|
|
Where do the two functions f(x) and g(x) intersect? |
at the point(s) where f(x)=g(x) |
|
|
What happens in an exponential function? |
The independent variable is the exponent (or power) |
|
|
What are the characteristics of normal distribution? |
It's a bell-shaped curve It is symmetrical about the mean (the mean, the mode and the median are all the same value) The x-value is an asymptote to the curve The total area under the curve is 1 (100%) 50% of the area is to the left of the mean (and 50% to the right) 65% ish of the area is within 1 standard deviation of the mean 95% ish is within 2 standard deviations 99% ish is within 3 standard deviations The expected value is found by multiplying the number in the sample by probability |
|
|
In Pearson's product-moment correlation coefficient, r, What happens when r= -1, 0, and +1 ? |
when r= -1 there is a perfect negative correlation between the data sets when r= 0, there is no correlation when r= +1, there is a perfect positive correlation |
|
|
In Pearson's PMCC, what is a perfect correlation? |
where all the plotted points lie on a straight line |
|
|
What is the regression line? |
a more accurate version of a line of best fit. If there is a strong or moderate correlation, you can use the regression line to predict values of y for values of x within the range of the data. |
|
|
What do you do to differentiate? |
f'(x) = nax ^(n-1) |
|
|
How do you calculate the gradient of a curve at a given point? |
Use the gradient function to determine the exact value of the gradient at any specific point on the curve local minimum or maximum, f'(x) = 0 (dy/dx =0) |
|
|
How to calculate the equation of the tangent to the curve at point P(a,b) |
1. calculate b, the y coordinate of P, using the equation of the curve 2. Find the gradient function (dy/dx) 3. Substitute a, the x coordinate of P, into dy/dx to calculate, m, the value of the gradient at P 4. Use the equation of a straight line (y-b) = m(x-a) |
|
|
How to calculate the normal to a curve |
Its perpendicular to the tangent so its gradient, m', is found using the formula m' = -1/m (where m is the gradient of the tangent) |
|
|
What does the gradient function dy/dx = f'(x) mean |
the rate of change of y with respect to x |
|
|
What happens at a local maximum point (turning point) |
as x increases, the three gradients occur in the order positive, zero , negative. The gradient is zero at the maximum point |
|
|
What happens at a local minimum |
as x increases the three gradients occur in the order: negative, zero (minimum point), positive |
|
|
How to use optimization |
use differentiation to find an optimal value or a function as two variables interact. |
|
|
Whats the formula for the nth term of an arithmetic sequence |
Un = U1 + (n-1)d |
|
|
What's the sum to n terms of an arithmetic sequence is given by the formula? |
Sn = n/2(2U1 + (n-1)d) or Sn = n/2(U1+Un) |
|
|
Whats the formula for the nth term of a geometric sequence? |
Un = U1r^(u-1) |
|
|
Whats the formula for the sum to n terms of a geometric sequence? |
Sn = (U1((r^n) - 1))/(r-1) where r doesn't equal 1 or Sn = (U1(1-r^n)/ (1-r) |
|
|
Whats the formula for calculating he future value of an investment with compound interest? |
Future value = PresentValue (1+(r/k(100))^kn r = rate n = number of years k= number of compounding periods per year |
