IB Math Studies
Topic 5 Review: Geometry & Trigonometry
1.
Name: ______KEY_________________
Date:__________________Block:_____
page 1
The equation of line l is 2x + y - 4 = 0.
(a)
Find the gradient (slope) of l. m = gradient = -2
(b)
Find the gradient of a line perpendicular to l. m =
(c)
Find the equation of the line perpendicular to l which cuts the x-axis at –5. Give your
answer in the form ax + by + c = 0, where a, b, c  . x – 2y + 5 = 0
2.
ABCDEFGH is a rectangular box in which AD = 4 cm, DC = 12 cm and DH = 5 cm. P and Q are the midpoints of
AD and FG respectively.
Calculate correct to three significant figures:
B
C
(a)
the length of HC. 13 cm
(b)
the angle between the plane EBCH and the base EFGH. 22.6°
(c)
the length of PQ. 13 cm
A
D
F Q
P
G
1x
E
3.
4.
10
H
The angles of a triangle are in the ratio 1 : 2 : 3. Its longest side is 10 cm long.
(a)
Draw a diagram to represent this information.
Diagram:
(b)
Calculate the size of the largest angle. 90°
(c)
Calculate the length of the shortest side. 5 cm
The following diagram shows a straight line l.
l
(a)
y
10
(b)
8
(c)
6
2x
3x
Find the equation of the line l. y = 2x
The line n is parallel to l and passes through the point (0, 8).
Write down the equation of the line n. y = 2x + 8
The line n cross the horizontal axis at the point P. Find the
coordinates of P. P = ( - 4, 0)
4
2
0
x
0
5.
1
2
3
4
5
6
The height of a flagpole is 12 metres. A person standing x metres from the bottom of the flagpole determines the
0
angle of elevation to the top of the flagpole to be 57 .
(a)
Draw a diagram to illustrate this information.
Diagram:
(b)
Calculate the value of x. 7.79 m
12 m
57°
6.
7.
A cylindrical drum for storing industrial waste
3
has a volume of 10 m . If the height of the
drum is 3m, find the radius. r = 1.03 m
3m
An object moving in a straight line passes through the points (3, 0) and (2, 2). The object also passes through
the point (0, a).
Calculate the value of a. a = 6
IB Math Studies
Topic 5 Review: Geometry & Trigonometry
8.
Name: ______KEY_________________
Date:__________________Block:_____
page 2
A right pyramid with a rectangular base and vertical height of 60 cm is shown in the diagram. The points X
and Y are the midpoints of the sides AB and BC respectively.
Calculate:
(a)
the length of AP. AP = AC = 12.8 cm
(b)
the length of edge AV. AV = 61.4 cm
(c)
the angle that the edge AV makes with the base ABCD. 78.0°
(d)
the length of YV. YV = 60.8 cm
9.
AT is a vertical telegraph pole standing on horizontal ground. Two wires are attached to the top of the pole at T,
0
and are fixed in the ground at P and Q. Angle PAQ = 90 and PQ = 20 m. The lengths of the wires TP and TQ
are 30 m and 35 m respectively.
T
(a)
(i)
(ii)
x1
A
Draw a diagram that shows the given information.
Draw separate diagrams for PAQ, PAT and QAT.
Clearly mark all right angles.
P
T
T
35 m
30m
A
x2
20 m
30 m
h
35 m
h
Q
Q
x1
A
P
x2
P
Q
A
(b)
(i)
Show that, if h is the height of the pole in metres,
(ii)
Calculate h. h = 29.4 m
2
2
Then (900 – h ) + (1225 – h ) = 400.
2
2
2
2
2
2
2
2
2
30 = h + x1
35 = h + x2
x1 + x2 = 20
2
2
2
2
2
2
900 – h = x1
1225 – h = x2
so (900 – h ) + (1225 – h ) = 400
(c)
Find the angle the longer wire makes with the ground. 57°
B
10.
Three points A (5, 3), B (-1, 7), and C (-4, 5) are joined to form a triangle.
The mid-point of AB is D and the midpoint of AC is E.
(a)
Plot the points A, B, and C on the grid.
(b)
Find the distance DE. Give your answer to 3 significant figures.
DE = 1.80
11.
C
D
E
The diagram below shows a large lot ABCD with a fence BD crossing it.
AB = 12m, AD = 10m and angle BAD = 100°. BC = 15m and angle BDC = 40°.
diagram not drawn to scale
A
10m
100°
D
12m
40°
B
C
(a)
Find the length of the fence BD. 16.9 m
(b)
Calculate the size of angle BCD.
(c)
Find the perimeter of the lot labeled ABCD. 60.3 m
46.4°
A