Finding the nth term, recognising sequence types, the equation of a straight line, gradients including parallel and perpendicular, and the shapes of common graphs.
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1.What is a linear sequence?
One where the difference between consecutive terms is constant.
2.How do you find the nth term of a linear sequence?
The common difference gives the coefficient of n, then adjust by adding or subtracting to match the first term.
3.Find the nth term of 4, 7, 10, 13.
The difference is 3, so start with 3n. 3 times 1 = 3, but the first term is 4, so the nth term is 3n + 1.
4.Find the nth term of 20, 17, 14, 11.
The difference is -3, so the nth term is -3n + 23.
5.How do you find a term from the nth term rule?
Substitute the position number for n.
6.The nth term is 5n - 2. Find the 10th term.
5 times 10 minus 2 = 48.
7.What is a quadratic sequence?
One where the second differences are constant rather than the first.
8.What is a geometric sequence?
One where each term is multiplied by a constant to get the next term.
9.What is a Fibonacci type sequence?
One where each term is the sum of the two previous terms.
10.State the equation of a straight line.
y = mx + c
11.What does m represent?
The gradient, which is how steep the line is.
12.What does c represent?
The y intercept, the value of y where the line crosses the y axis.
13.How do you calculate a gradient from two points?
Change in y divided by change in x.
14.Find the gradient through (1, 3) and (4, 12).
(12 minus 3) divided by (4 minus 1) = 9 divided by 3 = 3.
15.What does a negative gradient mean?
The line slopes downwards from left to right.
16.What is true of the gradients of parallel lines?
They are equal.
17.What is true of the gradients of perpendicular lines?
They multiply to give -1, so each is the negative reciprocal of the other.
18.A line has gradient 2. What is the gradient of a line perpendicular to it?
Minus one half.
19.How do you find the midpoint of two points?
Find the mean of the x coordinates and the mean of the y coordinates.
20.Find the midpoint of (2, 4) and (8, 10).
(5, 7)
21.What shape is the graph of a quadratic?
A parabola, a symmetrical U shape, or an upside down U if the x squared term is negative.
22.What shape is the graph of a cubic?
An S shaped curve.
23.What shape is the graph of y = 1 over x?
A reciprocal graph, two curves in opposite quadrants that never touch the axes.
24.What does the graph of an exponential function look like?
A curve that rises increasingly steeply, or falls towards zero without reaching it.
25.How do you find where a graph crosses the x axis?
Set y equal to zero and solve for x.
26.How do you use a graph to solve an equation?
Read off the x values where the graph crosses the required y value.
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