A sequence starts 5, 9, 13, 17, ... Write down the next term.
(1)
2
A sequence starts 40, 35, 30, 25, ... Write down the next term.
(1)
3
The nth term of a sequence is 4n + 1. Work out the 3rd term.
(1)
4
The nth term of a sequence is 5n - 2. Work out the 1st term.
(1)
5
A straight line has equation y = 3x + 2. Write down the gradient of the line.
(1)
6
A straight line has equation y = 3x + 2. Write down the y-intercept of the line.
(1)
7
Work out the gradient of the line that passes through (0, 0) and (2, 8).
(1)
8
Find an expression, in terms of n, for the nth term of the sequence 2, 5, 8, 11, ...
(2)
9
Find an expression, in terms of n, for the nth term of the sequence 7, 4, 1, -2, ...
(2)
10
A sequence has nth term 6n - 5. Work out the 10th term, showing your substitution.
(2)
11
A straight line has gradient -2 and passes through (0, 5). Write down the equation of the line.
(2)
12
Work out the gradient of the line joining the points (1, 2) and (4, 11).
(2)
13
The first term of a sequence is 3 and each term is found by adding 4 to the previous term. Write down the first four terms.
(2)
14
A sequence has nth term 2n2 + 1. Work out the 4th term, showing your method.
(3)
15
Kofi makes patterns from tiles. Pattern 1 uses 3 tiles, Pattern 2 uses 7 tiles, Pattern 3 uses 11 tiles and Pattern 4 uses 15 tiles. Find an expression, in terms of n, for the number of tiles in Pattern n, then use it to find the number of tiles in Pattern 10.
(3)
16
A straight line passes through the points (0, -1) and (3, 8). Find the equation of the line in the form y = mx + c.
(3)
17
A conversion graph changes between miles and kilometres. The graph is a straight line through the origin, showing that 5 miles is equivalent to 8 kilometres. (a) Find the gradient of the graph, in kilometres per mile. (b) Use your gradient to convert 15 miles into kilometres.
(4)
18
Priya cycles from home to the park, a distance of 9 km, at a constant speed, taking 30 minutes. She stays at the park for 20 minutes, then cycles home again, taking 45 minutes. (a) Work out her speed, in km/h, cycling to the park. (b) Work out her speed, in km/h, cycling home.
(4)
19
Stretch. A quadratic sequence has nth term of the form an2 + b. The sequence is 4, 7, 12, 19, 28, ... Find the values of a and b, then use the formula to find the 6th term.
(4)
Mark scheme · KS3.M-A3D Algebra: Sequences and Graphs: Fluency and Exam Drill