IGCSE Maths Graphs of functions topical questions

A conversion graph maps units of currency A (horizontal) to currency B (vertical). Its straight line passes through (0, 0) and (10, 8).

1. (a)Convert 5 units of A to B.[1]
2. (b)Convert 12 units of B to A.[1]
3. (c)State the gradient of the line and what it represents.[2]

A delivery van drives 30 km in half an hour, waits half an hour, then returns the 30 km in one hour.

1. (a)Find the speed of the outward trip.[1]
2. (b)How long is the van stationary?[1]
3. (c)Find the average speed for the whole journey.[2]

The curve is y = x² + x − 6.

1. (a)Find the value of y when x = 2 and when x = −1.[2]
2. (b)Write down the roots of x² + x − 6 = 0.[2]

A taxi charges a fixed 3 plus 1.80 per kilometre. The line C = 3 + 1.8d is drawn for journeys up to 20 km.

1. (a)Find the cost of a 12 km journey.[2]
2. (b)A journey cost 21. Find its length.[2]
3. (c)State what the point (0, 3) represents.[1]

Cara cycles 12 km to a park in 40 minutes, stays for 50 minutes, then cycles home along the same route in 30 minutes.

1. (a)Find her speed on the way out, in km/h.[3]
2. (b)During which part of the trip is she exactly 12 km from home?[1]
3. (c)Find her mean speed for the whole trip, including the stop.[2]

The graph of y = x² − 4x + 3 is drawn for −1 ⩽ x ⩽ 5.

1. (a)Complete the table of values for x = −1, 0, 1, 2, 3, 4, 5.[2]
2. (b)Write down the roots of x² − 4x + 3 = 0.[1]
3. (c)Write down the equation of the line of symmetry.[1]
4. (d)Write down the coordinates of the minimum point.[1]

A train accelerates from rest to 12 m/s in 6 s, travels at 12 m/s for 10 s, then brakes to rest in 3 s. (Extended)

1. (a)Find the acceleration.[1]
2. (b)Find the deceleration.[1]
3. (c)Find the total distance travelled.[2]
4. (d)Find the average speed for the whole journey.[1]

The graph of y = x² − 4x + 3 has been drawn on a grid. (Extended)

1. (a)State the line you would draw to solve x² − 4x + 3 = 4.[1]
2. (b)Explain why that line works.[1]
3. (c)Give the solutions of x² − 4x + 3 = 4 to 2 decimal places.[2]

The table gives values of y = 6 − x − x² for values of x from −3 to 3, and the points are plotted on a grid.

1. (a)Copy and complete the table of values. (x = −3, −2, −1, 0, 1, 2, 3)[2]
2. (b)Write down the two roots shown by your graph.[1]
3. (c)Write down the greatest value of y on the curve and the x-value where it occurs.[2]

A car speeds up from rest to 24 m/s in 8 s, travels at 24 m/s for 20 s, then slows steadily to 4 m/s in 8 s. (Extended)

1. (a)Find the acceleration in the first stage.[1]
2. (b)Find the distance travelled in each of the three stages.[3]
3. (c)Find the total distance and the mean speed for the whole 36 s.[2]

A cubic curve crosses the x-axis at −1, 2 and 3, and y is positive for large positive x. (Extended)

1. (a)Write down a possible equation for the curve.[2]
2. (b)Describe the behaviour of the curve for large negative x.[1]
3. (c)Find the y-intercept of your curve.[2]

Curve families. (Extended)

1. (a)State the asymptotes of y = 1⁄x.[2]
2. (b)Write down two integer points on the graph of y = 2ˣ.[2]
3. (c)Hence solve 2ˣ = 8.[1]

The graph of y = x³ − 4x has been plotted for values of x from −3 to 3. (Extended)

1. (a)Copy and complete the table of values. (x = −3, −2, −1, 0, 1, 2, 3)[2]
2. (b)Write down the three roots of x³ − 4x = 0.[1]
3. (c)By drawing a suitable straight line on the same axes, state the number of solutions of x³ − 4x = 2x.[3]

Tangents to the curve y = x³. (Extended)

1. (a)The tangent at (2, 8) passes through (0, −4). Find its gradient.[2]
2. (b)The tangent at (−2, −8) passes through the origin. Find its gradient.[2]
3. (c)What happens to the gradient of the tangent as x increases?[1]
4. (d)State the coordinates where y = 2ˣ crosses the y-axis.[1]