Download IB Math Studies Geometry and Trigonometry Review

IB Math Studies Geometry and Trigonometry Review
1) The diagram below shows an equilateral triangle ABC, with each side 4 cm long. The
side [BC] is extended to D so that CD= 5 cm. Calculate, correct to two decimal places,
the length of [AD].
A
B
C
D
2) A gardener pegs out a rope, 19 metres long, to form a triangular flower bed as shown
in the diagram below.
B
6m
5m
A
C
Calculate
a) the size of the angle BAC;
b) the area of the flower bed.
3) The triangle ABC is below with AB = 8 m, AC = 14 m, BC = 18 m, and angle
BAC = 110 degrees. Find angles B and C.
A
B
C
4) The figure shows two adjacent triangular fields ABC and ACD where AD=60 m,
CD = 80 m, BC = 50 m. Angle ACD = 30 degrees and angle BAC = 20 degrees.
D
C
B
A
a) Using triangle ACD calculate the length AC.
b) Calculate the size of angle ABC.
5) In the diagram below find the vertical height of C if AB = 8 cm, BC = 5 cm and angle
BAE = 28 degrees.
C
B
E
A
6) Graph y = 2 sin 3x +1 from 0  x  360 and -3  y  3 . Let 1 cm represent 30 degrees
on the horizontal axis and 2 cm represent 1 unit on the vertical axis.
a) Write down the amplitude.
b) Write down the period.
7) ABCD is a trapezium with AB = CD and [BC] parallel to [AD]. AD = 22 cm, BC =
12 cm, AB = 13 cm.
B
C
A
D
E
a) Show that AE = 5 cm.
b) Calculate the height BE of the rrapezium.
c) Calculate
i) angle BAE
ii) angle BCD
d) Calculate the length of the diagonal CA.`
8) The triangle ABC is below with AB = 9 m, AC = 15 m, BC = 19 m, and angle
BAC = 120 degrees. Find angles B and C.
A
B
C
9) In triangle ABC, AB = 11cm, AC = 13cm and angle ACB = 42 degrees. Find all of
the missing sides and angles.
10) In triangle ABC, AB = 7cm, BC = 8 cm and AC = 5 cm. Find all of the angles.
8 cm
The cuboid on the left has sides
ABCD with length of 6 cm.
a) What is the length of AC?
b) What is the m<A?
c) What is the size of the
longest rod that will fit in the
cuboid?
The cuboid on the left is square
base with length of 12 cm.
a) Find the length of longest
rod that will fit in the bottom of
the box.
b) Find the length of the longest
rod that will fit in the box.
PQRS is the square base of a solid right
pyramid with vertex V. The sides of the
square are 10 cm, VG = 15 cm and M is
the midpoint of QR.
a) Write down the length of GM.
b) Find the length of VM.
c) Find the surface area of the pyramid.
d) Find m<VMG.
e) Find the volume of the pyramid.
f) What is the capacity in mL?
g) What is the mass if the pyramid has a
density of 2.45 g/cm3?
Volume - Capacity Connection
1 cm3 = 1 mL
1000 cm3 = 1 L
1 m3 = 1000 L
Density: mass/volume