5 self-marking GCSE practice questions on Recognising graph shapes, written specifically for AQA, Pearson, OCR across Foundation and Higher tier. Instant marking with full worked solutions on every question.
A few of the 5 questions, from easier to harder. Choose your exam board and tier to practise them, with every answer marked.
Question 12 marksGrade 6-7
Erika tries to sketch the graph of y=x1 (x=0
What are the common mistakes in Recognising graph shapes?
When a pupil makes one of these on Revision Workshop, the marking engine names the mistake and explains it, instead of just marking the answer wrong.
Assumed reciprocal graph passes through origin
Since x=0 is excluded from the domain (division by zero is undefined), the graph can never pass through or touch the origin.
Missed second branch of reciprocal graph
For y=−2/x, positive values of x
Quick answers about Recognising graph shapes
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There are 5 self-marking GCSE Maths questions on Recognising graph shapes, written for AQA, Pearson, OCR across Foundation and Higher tier. Each one is marked instantly and has a full worked solution.
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).
Her sketch shows a single curve passing through the point
(0,0)
, continuing only through the first quadrant (where both
x
and
y
are positive).
Choose the correct statement for each of Erika's two mistakes.
Show the worked solution
For y=x1: A1
As x gets close to 0 (from either side), y becomes very large in size, so the curve gets closer and closer to both axes but never touches or crosses them (this is different from passing through the origin)
Since x=0 can be positive or negative, and y takes the same sign as x, the graph has two separate branches - one in the first quadrant (x>0,y>0
Question 22 marksGrade 6-7
Marcus tries to sketch the graph of y=x3 (x=0).
His sketch shows a single curve passing through the point (0,0), continuing only through the first quadrant (where both x and y are positive).
Choose the correct statement for each of Marcus's two mistakes.
Show the worked solution
For y=x3: A1
As x gets close to 0 (from either side), y
Question 32 marksGrade 6-7
Sam tries to sketch the graph of y=−x2 (x=0).
His sketch shows a single curve passing through the point (0,0), continuing only through the second quadrant (where x is negative and y is positive).
Choose the correct statement for each of Sam's two mistakes.
Question 44 marksGrade 9
The graph of y=x3+4x2 is drawn for −5≤x≤1.
The equation x3+4x2=k, where k is an integer, has exactly one solution for −5≤x≤1.
Find the greatest possible value of k.
, producing a second branch in the fourth quadrant that Sam's sketch is missing.
Confuses a cubic graph/expression with a quadratic one
Chose the U-shaped quadratic graph instead of the S-shaped cubic graph
) and one in the third quadrant (
x<0,y<0
) - not just one
A2
becomes very large in size, so the curve gets closer and closer to both axes but never touches or crosses them (this is different from passing through the origin)
Since x=0 can be positive or negative, and y takes the same sign as x, the graph has two separate branches - one in the first quadrant (x>0,y>0) and one in the third quadrant (x<0,y<0) - not just one A2