XPD010 FOUNDATION MATHEMATICS

Part A Measurement [22 marks total]
Perimeter [4 marks]
a) Use Pythagoras’s theorem to find the length of the missing side. [2 marks]
b) Find the perimeter of the triangle. [1 mark]
c) Find the perimeter of the following shape. [1 mark]
Area [18 marks]
Write a formula for the area of each shape. You may use composite shapes to find the formula.
[4 marks]
Rectangle
Area = base x height
b
h
h
b
Calculate the areas of these shapes showing all working [14 marks]
An athlete runs around the track below.
What distance does he run after 3 laps?
(Figure is on the next page)
A sports field has a painted "D" with these
measurements. (Figure on next page)
a)
The shaded "D" is a semicircle. Find x.
a
b
h
b) Find the area of the shaded region
(to 2 decimal places).
Part B Trigonometry [28 marks total]
1) Label the sides of the triangles below in relation to the angle 𝜃. Your labels should be
opposite, hypotenuse and adjacent. [3 marks]
2) Calculate the value of the pronumerals showing working (to 1 decimal place). [3 marks]
3) Calculate the value of the angles showing working (to 1 decimal place). [2 marks]
4) [6 marks]
a)
b)
(to 1 decimal place)
(to 1 decimal place)
c)
(to 1 decimal place)
5) Angle of Elevation [1 mark]
When we look ______ from the horizontal the angle we turn through is called
the angle of elevation.
6) Angle of Depression [1 mark]
When we look ______ from the horizontal, the angle is called the angle of
depression
7) Complete these questions showing working. [12 marks]
a) A surveyor standing at the base of a hill, uses a levelling device to see that the top of
the hill is at an angle of elevation (angle between the horizontal up to the top of the
hill) is 33°. She then walks up the slope of hill which she measures at 150 meters.
What is the vertical height of the hill? (express your answer to 2 decimal places)
b) From the top of a lighthouse, a rescue coordinator can see a rescue boat at an angle of
depression (angle between the horizontal down to the yacht) of 25°. He knows
the lighthouse is 26 meters high. How far away from the base of the lighthouse is the
boat? (express your answer to 2 decimal places)
c) John wants to measure the height of a tree. He walks exactly 50 m from the base of the
tree and looks up. The angle from the ground to the top of the tree is 43º. How tall is
the tree? (express your answer to 2 decimal places)
d) An airplane is flying at a height of 1300m above the ground. The distance along the
ground from the airplane to the airport is 5km. What is the angle of depression from
the airplane to the airport? (express your answer to 1 decimal place)
Part C Angles [20 marks total]
Classify these angles (write the name of the angle above each box): [2.5 marks]
[2 marks]
[1.5 marks]
[12 marks] Solve the following problems for all of the unknowns.
a) b)
c) d)
e) f)
g)
[2 marks]
Part D Polygons [30 marks total]
Find the names of the following Polygons: [6 marks]
Polygon’s Name Definition
A polygon with 3 sides
A polygon with 4 sides
A polygon with 5 sides
A polygon with 6 sides
A polygon with 7 sides
A polygon with 8 sides
Find the definition of an Interior Angle: [1 mark]
Shape #1 Triangle [2 marks]
Are total number
of sides and total
degrees same for
all triangles?
What is the total
number of sides?
What is the total
degrees?
Now using what you learned about the interior angle total (sum) of a triangle, prove the total
angles of these other polygons by dividing the shapes into the fewest number of triangles as
possible. Use those triangles to calculate the sums of the new shapes.
[6 marks]
4. Find the sum of the interior angles of a hexagon. [2 mark]
5. Find the sum of the interior angles of a regular polygon that has 14 sides. [1 mark]
Interior Angle Theorem
The sum of the interior angles of any polygon is equal to the number of sides of the polygon
(n) minus 2 (this is the number of triangles in each polygon) then multiplied by 180 (the sum
of the degrees inside a triangle).
𝐼𝑜𝑢𝑒𝑠𝑖𝑝𝑠 𝑎𝑜𝑔𝑚𝑒 𝑡𝑣𝑛 = ሺ𝑜 − 2ሻ ∗ 180°
If the polygon is regular, you can find the measurement of each of the interior angles (if it is
regular all the angles will be the same) by dividing the interior angle sum by the number of
sides (n).
𝑅𝑒𝑔𝑣𝑚𝑎𝑠 𝑞𝑝𝑚𝑦𝑔𝑝𝑜 𝑖𝑜𝑢𝑒𝑠𝑖𝑝𝑠 𝑎𝑜𝑔𝑚𝑒 𝑛𝑒𝑎𝑡𝑣𝑠𝑒𝑛𝑒𝑜𝑢 = 𝑖𝑜𝑢𝑒𝑠𝑖𝑝𝑠 𝑎𝑜𝑔𝑚𝑒 𝑡𝑣𝑛 ÷ 𝑜
6. What is the unit used for an angle in a regular polygon? [1 mark]
7. Find the number of sides in a polygon whose sum of the interior angles is 1620 degs. [2 marks]
8. Find the number of sides in a polygon whose sum of the interior angles is 900 degs. [2 marks]
9. What is the measure of each angle of the regular polygon in #8? [2 marks]
Dog Pen Problem: Ms. Kim got a new dog and wants to make the largest possible pen for
him. She has 40 metres of fencing.
a) What shape will have the largest area. You will need to show some
calculations to justify this. [3 marks]
b) What is the largest area the pen can have? [2 marks]