Edexcel GCSE Maths: Sequences, Functions and Graphs

The line $L_1$L1​ has equation $3y = 12x - 9$3y=12x−9.

(a) Find the gradient of $L_1$L1​ and the coordinates of the point where $L_1$L1​ crosses the $y$y-axis. (2 marks)

(b) The line $L_2$L2​ is perpendicular to $L_1$L1​ and passes through the point $(8, 1)$(8,1). Find an equation of $L_2$L2​, giving your answer in the form $y = mx + c$y=mx+c. (3 marks)

Here are the first five terms of a quadratic sequence.

$3, \quad 10, \quad 21, \quad 36, \quad 55$3,10,21,36,55

Find an expression, in terms of $n$n, for the $n$nth term of this sequence. (4 marks)

(a) Find the $n$nth term of the arithmetic sequence $5, 8, 11, 14, \ldots$5,8,11,14,… (2 marks)

(b) Show that $150$150 is not a term in this sequence. (2 marks)

A straight line passes through the points $A(-2, 9)$A(−2,9) and $B(4, -3)$B(4,−3).

Find an equation of the line in the form $y = mx + c$y=mx+c. (3 marks)

The $n$nth term of a sequence is $n^2 - 4n$n2−4n.

Work out the difference between the $7$7th term and the $5$5th term of the sequence. (2 marks)

Write down the gradient of the line $y = 7 - 5x$y=7−5x. (1 mark)