Pythagoras (Cambridge International IGCSE Maths): Exam Questions

Calculate the value of $k$.

$k=$...............................

The diagram shows a flagpole in a garden.

The flagpole has height 25 m.

A rope from the top of the flagpole is tied to the ground 8m from its base.

Calculate the length of this rope.

................................................ m

The diagram shows a right-angled triangle.

Show that the value of $x$ is 41.8, correct to 3 significant figures.

Calculate $PR$.

$PR$ = ......................................... cm

Calculate $AC$.

$AC=$........................... m

Calculate $PQ$.

$PQ$ = ........................................... cm

The diagram shows a rectangle 14cm by $w$cm. The diagonal is 23 cm.

Calculate the value of $w$.

$w=.................................................$

The diagram shows a right-angled triangle.

Calculate the value of $x$.

$x$= ...................................................

The diagram shows a right-angled triangle $ABC$. Calculate the length of $AB$.

$AB$ = ................................................m

The diagram shows a rectangular playground $ABCD$. $AB=23.4$m and $AC=35.1$m.

Calculate $BC$.

$BC=$ ............................ m [3]

The length of one side of a rectangle is 12cm.

The length of the diagonal of the rectangle is 13cm.

Calculate the area of the rectangle.

.......................................... cm²

Triangles $ABC$ and $BCD$ are both right-angled triangles.

Calculate the value of $y$.

$y=$................................

The diagram shows a field in the shape of a trapezium. $AB=150m,BC=90m$ and $CD=120m$. Angle $ABC$ = angle $BCD$ = $90^{\circ}$.

i) Show that $AD=95m$, correct to the nearest metre.

ii)A fence is built around the perimeter of the field.

It costs $ 48 to build each 5-metre section of the fence. Calculate the cost of building this fence.

$ .................................... [3]

Sam has a rectangular pond, $ABCD$.

i) Calculate $BC$.

$BC$ = ...............................m [3]

ii) He puts a fence around the edge of the pond. Calculate the length of the fence.

................................m [1]

The diagram shows a right-angled triangle.

Calculate the perimeter.

............................................ cm [3]

The length of the diagonal of the rectangle is 10 cm.

The width of the rectangle is 6 cm.

Work out the area of the rectangle.