AQA GCSE Maths: Sequences, Functions and Graphs

The line $L_1$L1​ has equation $2y = 6x - 5$2y=6x−5.

(a) Write down the gradient of $L_1$L1​. (1 mark)

(b) The line $L_2$L2​ is perpendicular to $L_1$L1​ and passes through the point $(6, 1)$(6,1). Find the equation of $L_2$L2​, giving your answer in the form $y = mx + c$y=mx+c. (3 marks)

(c) Find the coordinates of the point where $L_2$L2​ crosses the $x$x-axis. (1 mark)

Here are the first five terms of a quadratic sequence: $3, \quad 8, \quad 15, \quad 24, \quad 35.$3,8,15,24,35.

(a) Find an expression, in terms of $n$n, for the $n$nth term of this sequence. (3 marks)

(b) Hence find the $20$20th term. (1 mark)

A sequence is generated by the function machine: input $n$n $\to$→ multiply by $4$4 $\to$→ subtract $3$3 $\to$→ output.

(a) Write down the first three terms of the sequence. (2 marks)

(b) Show that $98$98 is not a term of this sequence. (2 marks)

A straight line passes through the points $A(-1, 5)$A(−1,5) and $B(3, -3)$B(3,−3). Find the equation of the line in the form $y = mx + c$y=mx+c. (3 marks)

The $n$nth term of an arithmetic sequence is $5n + 2$5n+2. Find the sum of the first three terms of the sequence. (2 marks)

Write down the gradient of the line with equation $y = 7 - 4x$y=7−4x. (1 mark)