AQA
FP1
2009
January
Q1
5 marks
Moderate -0.5
1 A curve passes through the point \(( 0,1 )\) and satisfies the differential equation
$$\frac { \mathrm { d } y } { \mathrm {~d} x } = \sqrt { 1 + x ^ { 2 } }$$
Starting at the point \(( 0,1 )\), use a step-by-step method with a step length of 0.2 to estimate the value of \(y\) at \(x = 0.4\). Give your answer to five decimal places.
AQA
FP1
2013
January
Q1
5 marks
Moderate -0.3
1 A curve passes through the point (1,3) and satisfies the differential equation
$$\frac { \mathrm { d } y } { \mathrm {~d} x } = \frac { x } { 1 + x ^ { 3 } }$$
Starting at the point ( 1,3 ), use a step-by-step method with a step length of 0.1 to estimate the value of \(y\) at \(x = 1.2\). Give your answer to four decimal places.
AQA
FP1
2010
June
Q1
6 marks
Moderate -0.5
1 A curve passes through the point ( 1,3 ) and satisfies the differential equation
$$\frac { \mathrm { d } y } { \mathrm {~d} x } = 1 + x ^ { 3 }$$
Starting at the point ( 1,3 ), use a step-by-step method with a step length of 0.1 to estimate the \(y\)-coordinate of the point on the curve for which \(x = 1.3\). Give your answer to three decimal places.
(No credit will be given for methods involving integration.)
AQA
FP1
2011
June
Q1
5 marks
Moderate -0.5
1 A curve passes through the point \(( 2,3 )\) and satisfies the differential equation
$$\frac { \mathrm { d } y } { \mathrm {~d} x } = \frac { 1 } { \sqrt { 2 + x } }$$
Starting at the point \(( 2,3 )\), use a step-by-step method with a step length of 0.5 to estimate the value of \(y\) at \(x = 3\). Give your answer to four decimal places.