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Using Calculators for Graphs & Equations (Cambridge (CIE) IGCSE International Maths: Core): Exam Questions

Exam code: 0607

46 mins12 questions
Easy
Medium
Hard
11 mark

Complete the mapping diagram for the function straight f open parentheses x close parentheses equals 3 x minus 5.

Mapping diagram with two ovals; left labelled 'x', right 'f(x)'. Arrows connect 0, 1, 2, 3 from 'x' to 'f(x)'.

How did you do?

2
Sme Calculator1 mark

Complete the mapping diagram.

Mapping diagram showing a series of numbers with arrows connecting 6 to 2, 15 to 5, 27 to 9, 42 to 14, and 60 to an empty space.

How did you do?

3
Sme Calculator2 marks

On the diagram, sketch the graph of y equals x cubed minus 4 x for negative 2 less or equal than x less or equal than 2.

Cartesian coordinate plane with x-axis from -2 to 2 and y-axis from -4 to 4, both centred at the origin (0,0).

How did you do?

4
Sme Calculator2 marks

On the diagram, sketch the graph of y equals 0.25 x to the power of 4 for negative 2 less or equal than x less or equal than 2.

Cartesian coordinate axes with the x-axis ranging from -2 to 2 and the y-axis from -1 to 4, labelled "x" and "y" respectively, with arrows at ends.

How did you do?

5
Sme Calculator2 marks

On the diagram, sketch the graph of y equals 2 minus open parentheses x minus 1 close parentheses squared for negative 1 less or equal than x less or equal than 3

You are not required to find any axes intercepts.

A 2D Cartesian graph with x-axis from -1 to 3 and y-axis from -2 to 2. Axes are labelled 'x' and 'y' with arrows indicating positive directions.

How did you do?

1
Sme Calculator2 marks

Complete the mapping diagram for straight f open parentheses x close parentheses equals fraction numerator 3 open parentheses x plus 4 close parentheses over denominator 2 end fraction.

Diagram showing a function mapping from a set {0, 1, 2} to another set. Arrows indicate the relationships between elements of these sets.

How did you do?

2a
Sme Calculator2 marks

On the diagram, sketch the graph of y equals x cubed minus 12 x for negative 4 less or equal than x less or equal than 4

Graph with x-axis from -4 to 4 and y-axis from -20 to 20, both labelled. Origin marked at 0. Arrows indicate positive direction.

How did you do?

2b
Sme Calculator2 marks

Find the coordinates of the points where the curve crosses the x-axis.

Give your answers to 2 decimal places, where relevant.

How did you do?

2c
Sme Calculator2 marks

Find the coordinates of the local maximum.

How did you do?

2d
Sme Calculator2 marks

Find the coordinates of the local minimum.

How did you do?

3a
Sme Calculator2 marks

On the diagram, sketch the graph of y equals x cubed for negative 2 less or equal than x less or equal than 2

Graph with x and y axes. X-axis ranges from -2 to 2, y-axis from -8 to 8. Axes intersect at origin (0,0), with arrows indicating direction.

How did you do?

3b
Sme Calculator1 mark

On the same diagram as part (a), sketch the graph of y equals 2 minus x for negative 2 less or equal than x less or equal than 2

How did you do?

3c
Sme Calculator2 marks

Find the coordinates of the point of intersection of y equals x cubed and y equals 2 minus x.

How did you do?

3d
Sme Calculator1 mark

Solve the equation

x cubed equals 2 minus x

How did you do?

4a
Sme Calculator2 marks
Graph of a downward-opening parabola with vertex near y=10, crossing x-axis at -2 and 4, labelled "Not to scale", with x and y axes marked.

The diagram shows the graph of y equals straight f open parentheses x close parentheses where straight f open parentheses x close parentheses equals negative 2 x squared plus 5 x plus 6 for negative 2 less or equal than x less or equal than 4.

Use your calculator to find the zeros of straight f open parentheses x close parentheses .

How did you do?

4b
Sme Calculator2 marks

Use your calculator to find the co-ordinates of the local maximum.

(....................... , .......................)

How did you do?

4c
Sme Calculator1 mark

Write down the equation of the line of symmetry.

How did you do?

1
Sme Calculator4 marks

Find all three solutions to the equation

x cubed minus 4 x equals x squared minus 4

Show your working on the axes below.

Cartesian coordinate system with arrows. X-axis ranges from -2.5 to 2.5, and Y-axis ranges from -6 to 6. Origin is marked at (0, 0).

How did you do?

2a
Sme Calculator2 marks
Graph of a cubic curve crossing the x-axis at points P,Q and a third point near -6 not labelled. It has labelled axes and "NOT TO SCALE" text on the right.

The diagram shows a sketch of the graph of y equals 0.1 x cubed plus 0.25 x squared minus 2 x minus 1 for negative 7 less or equal than x less or equal than 5.

Two points, P and Q comma are also marked.

Draw the graph of y equals 0.1 x cubed plus 0.25 x squared minus 2 x minus 1 on your calculator and use it to answer the following questions.

Find the coordinates of point P and pointspace Q.

P equals ( ...................... , ......................)

Q equals ( ...................... , ......................)

How did you do?

2b
Sme Calculator2 marks

Find the coordinates of

(i) the local maximum point

( ...................... , ......................) [2]

(ii) the local minimum point.

( ...................... , ......................) [2]

How did you do?

2c
Sme Calculator2 marks

The line y equals a intercepts the graph of y equals 0.1 x cubed plus 0.25 x squared minus 2 x minus 1 at 3 points.

Complete the range of values for a.

.................. less than a less than..................

How did you do?

3a
Sme Calculator2 marks
Cartesian graph with x-axis from -3 to 3 and y-axis from -10 to 20. Axes are labelled with arrows, x pointing right, y pointing up.

On the diagram, sketch the graph of y equals x cubed minus 5 x plus 3 for negative 3 less or equal than x less or equal than 3.

How did you do?

3b
Sme Calculator2 marks

On the diagram, sketch the graph of y equals 2 over x squared for values of x from negative 3 to 3.

How did you do?

3c
Sme Calculator3 marks

Find the x-coordinate of each point of intersection of y equals x cubed minus 5 x plus 3 and y equals 2 over x squared.

How did you do?