Functions and Graphs - Short Problems
Bucket of Water
Lisa's bucket weighs 21 kg when full of water. After she pours out half the water it weighs 12 kg. What is the weight of the empty bucket?
Straight Line Spin
Can you draw the graph of $y=x$ after it has been rotated $90$ degrees clockwise about $(1,1)$?
Circumference and Diameter
Which of these graphs could be the graph showing the circumference of a circle in terms of its diameter ?
Paper Weight
How could you use this graph to work out the weight of a single sheet of paper?
Spiral Snail
A snail slithers around on a coordinate grid. At what position does he finish?
Lattice Points on a Line
How many lattice points are there in the first quadrant that lie on the line 3x + 4y = 59 ?
Graph Area
Can you find the area between this graph and the x-axis, between x=3 and x=7?
Point in Between
Find the point on the line segment AB that is twice as far from B as it is from A.
Linear Area
Find the area of the triangle enclosed by these lines.
Graphical Triangle
What is the area of the triangle formed by these three lines?
Triangular Slope
Can you find the gradients of the lines that form a triangle?
Graph Triangles
Use the information about the triangles on this graph to find the coordinates of the point where they touch.
Inside a Parabola
A triangle of area 64 square units is drawn inside the parabola $y=k^2-x^2$. Find the value of $k$.
Quadratic Rotation
The curve $y=x^2−6x+11$ is rotated through $180^\circ$ about the origin. What is the equation of the new curve?
Curve Fitter
This problem challenges you to find cubic equations which satisfy different conditions.
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