OCR GCSE Maths: Sequences, Functions and Graphs

The straight line $L$L passes through the points $A(-2, 7)$A(−2,7) and $B(4, -5)$B(4,−5).

(a) Work out the gradient of $L$L. (2 marks)

(b) Find the equation of $L$L, giving your answer in the form $y = mx + c$y=mx+c. (2 marks)

(c) The line $M$M is perpendicular to $L$L and passes through the point $(6, 1)$(6,1). Find the equation of $M$M, giving your answer in the form $y = mx + c$y=mx+c. (1 mark)

Here are the first five terms of a quadratic sequence: $4, \quad 13, \quad 26, \quad 43, \quad 64.$4,13,26,43,64.

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

(b) Hence work out the $10$10th term. (1 mark)

A cyclist rides from home to a village and the distance–time graph of the journey is a series of straight line segments through the points listed below, where $t$t is the time in hours and $d$d is the distance from home in kilometres.

$t$t (hours)	$0$0	$2$2	$3$3	$5$5
$d$d (km)	$0$0	$30$30	$30$30	$50$50

(a) Work out the cyclist's speed, in km/h, during the first stage of the journey (from $t = 0$t=0 to $t = 2$t=2). (2 marks)

(b) Work out the cyclist's speed, in km/h, during the final stage of the journey (from $t = 3$t=3 to $t = 5$t=5). (2 marks)

The function $f$f is defined by $f(x) = 3x - 5$f(x)=3x−5.

Find an expression for the inverse function $f^{-1}(x)$f−1(x). (3 marks)

Here are the first four terms of an arithmetic sequence: $7, \quad 11, \quad 15, \quad 19.$7,11,15,19.

Find an expression, in terms of $n$n, for the $n$nth term of the sequence. (2 marks)

Here are the first four terms of a sequence: $2, \quad 6, \quad 18, \quad 54.$2,6,18,54.

Write down the next term of the sequence. (1 mark)