L1 Mathematical Reasoning
Question Bank
In the diagram below, the two horizontal lines are parallel.
Find the value of $x$.
The two rugs shown in the diagram are mathematically similar. The area of the smaller rug is 3 m². Their widths are shown in the diagram below.
Find the area of the larger rug.
To find the height of a tree, a person places a mirror on the ground and stands where they can see the top of the tree in the mirror, as shown in the diagram. The person's eye level is 1.6 metres high.
Because the angle of incidence equals the angle of reflection, the two triangles formed are similar. Calculate the height, $h$, of the tree.
In the diagram below, the line segment EB is parallel to DC. All measurements are in metres.
Calculate the length of BC.
A cone-shaped cup is partially filled with water as shown in the diagram. The water has a depth of 6 cm and a volume of 50 cm³. The total height of the cup is 9 cm.
Calculate the volume of the cup when it is full.
The shape shown in the diagram is called a frustum. It is made by taking a large cone and chopping off a smaller cone from the top. The two cones are mathematically similar.
Based on the dimensions given in the diagram, calculate the height of the frustum.
The shape in the diagram is a frustum, which is created by slicing the top off a larger cone, leaving the bottom section. The smaller cone that was removed is mathematically similar to the original large cone.
Based on the dimensions provided in the diagram, calculate the height of the smaller cone that was chopped off.
A person who is 1.5 metres tall is standing near a 6-metre-tall lamppost. The person's shadow, cast by the lamp, is 2 metres long, as shown in the diagram.
How far away is the person from the lamppost?.
The diagram shows two concentric circles with radii of 3 and 10. The point A on the outer circle has coordinates (6, 8).
Find the coordinates of the point B on the inner circle.
The two triangles in the diagram below are mathematically similar.
Find an expression for $r$ in terms of $p$ and $q$.
The diagram below shows three similar triangles nested within each other, with the parallel sides measuring $5$, $8$, and $12$. Find the value of the length $x$. 
Two ladders are placed in a 12-metre-wide alley, leaning against opposite walls as shown in the diagram. One ladder reaches 8 metres up its wall, and the other reaches 10 metres up its wall.
Calculate the height, $h$, from the ground at which the two ladders cross.
