IB Math SL/Intensified Precalculus
Additional Review for Test on Chapters 8 & 9
1.
In triangle PQR, PR = 12 cm, RQ = 11 cm, and angle RPQ = 60 degrees. Find the length of [PQ],
giving your answer in radical form.
2.
Find the perimeter of the segment cut off by a chord of length 14 m from a circle with radius 25 m.
3.
Find the exact value of x in the diagram.
4.
ABCD is a quadrilateral. The measure of angle BAC is 80 degrees, BCA is 30 degrees, ACD is 50
degrees, and ADC is 60 degrees. The length of [AB] is 3 cm. Calculate
a.
AC
b. CD
c. the area of ABCD
5.
A van moves from a point X on a bearing of 25 degrees for 4 miles. The van then changes direction
and travels on a bearing of 115 degrees for 7 miles. Calculate:
a.
the bearing of the van from X
b.
the direct distance of the van from X, to the nearest mile
For 6 and 7: Solve these triangles AND find their areas.
6.
7.
x = 14, y = 23, Y = 105°
a = 25, A = 70°, c = 26
The following are all questions from previous IB exams.
8.
A rectangle is drawn around a sector of a circle as shown. If the angle of the sector is 1 radian and
the area of the sector is 7 cm2, find the dimensions of the rectangle, giving your answers to the
nearest millemetre.
9.
A circular disc is cut into twelve sectors whose areas are in an arithmetic sequence. The angle of the
largest sector is twice the angle of the smallest sector.
Find the size of the angle of the smallest sector.
10.
Farmer Bill owns a rectangular field, 10 m by 4 m. Bill attaches a rope to a wooden post at one
corner of his field, and attaches the other end to his goat Gruff.
a. Given that the rope is 5 m long, calculate the percentage of Bill’s field that Guff is able to graze.
Give your answer correct to the nearest integer.
b. Bill replaces Gruff’s rope with another, this time of length a, 4 < a < 10 , so that Gruff can graze
exactly one half of Bill’s field. Show that a satisfies the equation
⎛ 4⎞
a 2 arcsin ⎜ ⎟ + 4 a 2 − 16 = 40
⎝ a⎠
c. Find the value of a.
11.
Two discs, one of radius 8 cm and one of radius 5 cm, are placed such that they touch each other. A
piece of string is wrapped around the discs. This is show in the diagram below.
Find the area of the shaded region.
12.
A circle of radius 4 cm, centre O, is cut by a chord [AB] of length 6 cm.
a.
b.
µ
Find AO B , expressing your answer in radians correct to four significant figures.
Determine the area of the shaded region.
ANSWER KEY
1.
6 ± 13cm
2.
28.2 m
3.
x = 13
4.
a) AC = 5.64 cm
b) CD = 6.12 cm
5.
a) 85.30
b) 8.06 miles
6.
Z = 15
7.
Two possible triangles:
8.
3.6 cm X 3.7 cm
9.
π
9
X = 36.00
c) A = 21.5 cm2
Z = 39.00 area = 101
b1 = 14.2 B1 = 32.20
C1 = 77.80
area1 = 173
b2 = 3.59 B2 = 7.76
C2 = 102
area2 = 43.9
0
0
10. a. 44% b. it works – the image to the right should help where AE is the length of the rope.
A
G E
B
D
F
C
c. 5.53 m (solve calculatorically: be sure you are in radian mode on your calculator!)
11. 16.9 cm2
12. a. 1.696 b. 5.63 cm2