IB Math Studies Year II – Midterm Review Questions KEY 1. (a) Area

Transcription

IB Math Studies Year II – Midterm Review Questions KEY
1.
(a)
(b)
1
× 14 × 8 sin110°
2
= 52.62278676 m2
= 52.6 m2 (3s.f)
Area =
(M1)
(A1)
sin C
8
sin 110
(or equivalent)
18
8 sin 110
sin C =
18
C = 24.68575369
C = 24.7° (3s.f.)
Note: Accept all answers obtained from all appropriate
methods, given to the correct degree of accuracy.
(M1)
(A1)
[4]
2.
(a)
Compound interest
8% per year
(A1)
(A1)
(b)
Year
Value at beginning
of year
Value at end of year
1st
CHF 500
CHF 540
2nd
CHF 540
CHF 583.20
3rd
CHF 583.20
CHF 629.86
4th
CHF 629.86
CHF 680.25
5th
CHF 680.25
CHF 734.67
(A1)
6th
CHF 734.67
CHF 793.44
(A1)
[4]
3.
(a)
BC =
482
57 2
2(48)(57) cos117 (or equivalent)
89.7 m (3 s.f.)
(b)
1
1
ab sinC = (48)(57)sin117°
2
2
2
= 1220 m (3 s.f.)
Area of ABC =
(M1)
(A1)
(M1)
(A1)
[4]
IB Questionbank Mathematical Studies 3rd edition
1
4.
(a)
CAˆ B = 180 – 2×23°
= 134°
(M1)
(A1) (C2)
(b)
AB
sin 23
(M1)
15
sin 134
Note: Follow through with candidate’s answer from (a)
15 sin 23
sin 134
AB = 8.147702831...
= 8.15 (3 s.f.)
AB =
(A1) (C2)
[4]
5.
(a)
III
(A1)
(b)
I
(A1)
(c)
II
(A1)
(d)
IV
(A1)
[4]
6.
Note: Award (A1) for each pair of correct entries in parts (a) and (c).
A list of numbers with no set brackets is acceptable.
(a)
A
B = {1, 3, 4, 7, 8, 9}
(b)
A
B
(c)
A = {1, 3, 4, 7, 8, 9}
A
C = {6, 7}
(A
C) B = {3, 6, 7, 9}
C = {9}
(A1)(A1)(A1) (C3)
(A1) (C1)
(A1)
(A1)
(A1)(A1) (C4)
[8]
7.
(a)
u1 + 3d = 12
u1 + 9d = 42
(A1)(A1)
(A1)(A1) (C4)
Note: Award (A1) for left hand side correct, (A1) for right hand
side correct.
2
(b)
6d = 30
d=5
u1 = –3
(A1)
(A1)
(M1)(A1) (C4)
Note: Follow through (ft) from candidate's equations.
[8]
8.
(a)
(x – 3)(x + 1)
Note: Award (A0)(A1) if the signs are reversed.
(A1)(A1) (C2)
(b)
A(1, 0), B(3, 0)
(A1)(A1) (C2)
(c)
x = 1 or x =
( 1 3)
= 1 or x =
2
( 2)
=1
2(1)
(A1)(A1) (C2)
Note: Award (A1) for x = and (A1) for 1.
(d)
C(1, –4)
(A1)(A1) (C2)
[8]
9.
(a)
Angle A = 90 – 5 = 85°.
(M1)(A1) (C2)
(b)
BC2 = 62 + 82 – 2 × 8 × 6 cos(85°)
so BC = 91.6330487 = 9.57 (3 s.f.)
(M1)(A1)
(A1) (C3)
(c)
BC
sin (A)
AC
sin (B)
6 sin (85 )
sin (B) =
= 0.6244093654
9.572515275
Angle B = sin–1(0.6244093654) = 38.6°
Note: Allow 38.7° if obtained using 9.57.
(M1)
(A1)
(A1) (C3)
[8]
3
10.
(a)
(b)
U
U
B
A
B
A
C
(c)
C
(d)
U
B
A
(A2)(A2)
U
B
A
C
C
Note: Award (A0), (A0), (A2) ft, (A2) ft if
consistently reversed.
and
(A2)(A2)
are
[8]
11.
(a)
I = 0.04 × 2000 × 18 = 1440 Euros
Total amount = I + 2000 = 3440 Euros.
(b)
2000 1
(M1)(A1)
(M1)(A1) (C4)
18 12
0.036
12
= 3819.72
= 3820 Euros, to nearest Euro.
(M1)(A1)
(A1)
(A1) (C4)
[8]
12.
(a)
Put x = 0 to find y = –2
(M1)
Coordinates are (0, –2)
(A1) (C2)
Note: Award (M1)(A0) for –2 if working is shown. If not, award
(M0)(A0).
4
(b)
Factorise fully, y = (x – 2) (x + 1).
(A1)(A1)
y = 0 when x = –1, 2.
(A1)(A1)
Coordinates are A(–1, 0), B(2, 0).
(A1)(A1) (C6)
Note: Award (C2) for each correct x value if no method shown
and full coordinates not given. If the quadratic formula is used
correctly award (M1)(A1)(A1)(A1)(A1)(A1). If the formula is
incorrect award only the last (A1)(A1) as ft.
[8]
13.
(a)
(b)
R2 = 36 so R = 6 cm
Use cosine rule. AB2 = 62 + 62 – 2
(M1)(A1) (C2)
6
6 cos (110 )
(M1)(A1)(ft)
AB2 = 96.6
AB = 9.83 cm
(A1)(ft)
OR
6
AB
sin (35 ) sin (110 )
(M1)(A1)(ft)
AB = 9.83 cm
(A1)(ft)
OR
110
55
2
1
AB
2
sin (55 ) =
6
(M1)(A1)(ft)
AB = 9.83
(A1)(ft) (C3)
Note: If this method is used, then the
1
AB must be evident to
2
obtain the (M1) and the
first (A1) requires the 55 and the 6 to be correct.
(c)
L=
36
or 6
or 10.6 cm
(A1) (C1)
[6]
14.
(a)
AC2 = 9 + 9=18
AC =
18 (= 4.24)
(M1)
(A1) (C2)
5
(b)
18
Area of triangle ACD = 0.5
4.5
sin 25
(M1)(A1)
= 4.03
(c)
(A1) (C3)
Area of triangle ABC = 0.5
3
3 = 4.5 cm2
(M1)(A1)
Total area = 8.53
(A1) (C3)
[8]
15.
(a)
correct
incorrect
correct
1
4
2
5 incorrect
3
4
3
5
2
4
correct
incorrect
(b)
(i)
2
5
=
(ii)
3
4
2
4
(A2) (C2)
3 2
5 4
Note: Award (A1) for each correct product.
(A1)(A1)
12
(= 0.6)
20
2
5
3
10
1
4
1
10
(A1) (C3)
1
= (0.25)
4
Note: Award (A1) for
(A1)(A1)(A1) (C3)
2
5
1
3
seen and (A1) for
4
10
1
seen.
10
[8]
6
16.
(a)
(A4) (C4)
Note: Award (A1) for some indication of scale on the y-axis.
Award (A1) for at least one asymptote drawn. Award (A1) for
each of the two (smooth) branches. The left hand branch must
pass through 0. One branch should be above the horizontal
asymptote and the other below but if the asymptote is not
drawn, then there should be little or no overlap in heights of the
branches. If this condition is not fulfilled, award (A1)(A0) for
the curve.
(b)
(i)
Horizontal asymptote y = 3
(ii)
Vertical asymptote x = 1
(A1)
(A1)(ft) (C2)
Equations for x and y must be seen, (ft) if reversed.
[6]
17.
(a)
sin 50 sin 30
AC
400
(M1)(A1)
Note: Award (M1) for using sine rule with values from the
problem, (A1) for correct substitution.
AC = 613 (3 s.f.)
(A1) (C3)
7
(b)
Perimeter = 400 + 613 + 788 = 1801m
Time in seconds =
1801
1000
1.8
(A1)(ft)(A1)
Note: Award (A1) for the perimeter, (A1) for finding the time in
seconds, and last (A1)(ft) for finding the time in minutes. The
time in minutes follow through from the time in seconds.
Time in minutes =
1000 50
( 16.7 to 3 s. f .)
60
3
(A1)(ft) (C3)
[6]
18.
(a)
a
8
1
2
a=4
(A1)
OR
2 1
a 2
a=4
(b)
(A1) (C1)
7
1
8
2
0.0625
(M1)(A1)(ft)
0.0625
(M1)(A1)(ft) (C2)
OR
2
8
(c)
5
1
2
1
2
12
1
1
2
1
16.0 (3 s. f ) ( 4095/256)
(M1)(A1)(ft)
(A1)(ft) (C3)
Note: Award (M1) for using correct formula and correct
substitution, (A1) for correct answer (15.99...). (A1) for correct
answer to 3 s.f.
[6]
8
19.
(a)
6x + 3 – 6 + 2x = 13
8x = 16
(M1)
x=2
(b)
(x + 3) (x – 1)
(c)
x = 1.64575..
(A1) (C2)
(A1)(A1) (C2)
x = 1.65
(A2) (C2)
Note: If formula is used award (M1)(A1) for correct solution. If
graph is sketched award (M1)(A1) for correct solution.
[6]
20.
(a)
19 seedlings
(A1) (C1)
(b)
(i)
median 88 cm
(A1)
(ii)
1st quartile 78 cm, 3rd quartile 103 cm (both correct)
(A1) (C2)
112
63 = 49 cm
(A1) (C1)
(c)
Note: Accept 63 and 112 both seen, if they appear in the answer space
for (c) or under working for (c) (but not just implied or written
on the box plot).
(d)
(C2)
Notes:
Box with correct median and quartiles marked.
(A1)(ft)
Both correct whiskers joined to box with straight lines
(A1)(ft) (C2)
Allow maximum errors of
2.
Perfectly ruled lines are not essential.
[6]
9
21.
(A1) (A1)
(A1)
(A1)
(A1)
(A1)
Notes:
(C6)
For any number entered exactly once, in the correct position,
award (A1) if incorrect award (A0).
If all numbers entered in all regions award (A0).
If any number is entered in more than one region, penalize that
number as follows:
(i) If none of the regions is correct award (A0)
(ii) If one of the regions is correct but other appearances of
that number are in the COMPLEMENT of the correct set,
award (A0) the first time this is seen.
(iii) If one of the regions is correct but other appearances of
that number are in a SUBSET of the correct set award (A0) the
first time this is seen.
Apply each of (ii) and (iii) at most once and award ft marks
when the error is seen repeatedly, however, (ii) and (iii) may
not both be applied to the same number and if both these errors
are present with more than one number involved, follow
through cannot be used until both penalties have been applied.
[6]
22.
(a)
d = –7
(b)
S50 =
(A1) (C1)
50
(2(124) + 49(–7))
2
Note: (M1) for correct substitution.
(M1)
10
= –2375
(A1)(ft) (C2)
11
(c)
124 – 7(k – 1) < 0
(M1)
k > 18.7 or 18.7 seen
(A1)(ft)
k = 19
(A1)(ft) (C3)
Note: (M1) for correct inequality or equation seen or for list of
values seen or for use of trial and error.
[6]
23.
(a)
0.965
(A1) (C1)
(b)
y = 1.15x + 0.976
(A1) for 1.15x (A1) for +0.976
(A1)(A1) (C2)
(c)
y = 1.15 (7) + 0.976
(M1)
Chemistry = 9.03
(accept 9)
(A1)(ft) (C2)
Note: Follow through from candidate’s answer to (b) even if no
working is seen. Award (A2)(ft).
(d)
the correlation coefficient is close to 1
OR strongly correlated variables
OR 7 lies within the range of physics marks.
(R1) (C1)
[6]
24.
(a)
(x − 5) (x + 2)
(A1)(A1)
Note: Award (A1) for (x + 5)(x−2), (A0) otherwise.
If equation is equated to zero and solved by factorizing
award (A1) for both correct factors, followed by (A0).
(C2)
(b)
(i)
(ii)
−3, −2, −1, 0, 1, 2, 3
Notes: Award (A2) for all correct answers seen
and no others.
Award (A1) for 3 correct answers seen.
(A1)(A1)
−26,−7, 0, 1, 2, 9, 28
Notes: Award (A2) for all correct answers seen
and no others.
Award (A1) for 3 correct answers seen.
If domain and range are interchanged award
(A0) for (b)(i) and (A1)(ft)(A1)(ft) for (b)(ii).
(A1)(A1)
(C2)
(C2)
[6]
12
25.
(a)
To double, interest = 3000
3000 =
(A1)
3000 4 n
100
Note: For substituting into the simple interest formula
(M1)
n = 25 years
(A1)(ft)
Note: (A1) for 3000 on one side of equation if not seen
separately.
For interest of 6000 award (M1)(A1)(ft) for answers
of 50 years.
(b)
6000 = 3000 1
3.5
200
(C3)
2n
(M1)(A1)
Note: (M1) for substituting values into a compound
interest formula,
(A1) for correct values with a variable for the power.
n = 20 years
(A1)
Note: If n used in formula instead of 2n, can allow
as long as final answer is halved to get 20.
(C3)
[6]
26.
(a)
(b)
FV = 8000 (1.0125)60
Note: (M1) for substituting in compound interest
formula, (A1) for correct substitution
(M1)(A1)
€16857 only
(A1) (C3)
8000 (1.0125)n = 9058.17
Note: (M1) for equating compound interest formula
to 9058.17
(M1)
n =10 correct answer only
(A1)
So 30 months, (ft) on their n
Note: Award (C2) for 2.5 seen with no working
(A1)(ft)
(C3)
[6]
13
27.
(a)
20 = u1 + 3d
32 = u1 + 7d
(A1)
(A1)
Note: Award (A1) for each equation, (A1) for correct answer.
OR
d=
32 20
4
(A1)(A1)
Note: Award (A1) for numerator, (A1) for denominator.
d=3
(b)
(A1) (C3)
10
10
(2 × 11 + 9 × 3) or
(11 + 38)
(M1)(A1)(ft)
2
2
Note: Award (M1) for correct substituted formula, (A1) for
correct substitution, follow through from their answer to part
(a).
OR
11 + 14 + ... + 38
(M1)(A1)(ft)
Note: Award (M1) for attempt at the sum of a list, (A1)(ft) for
all correct numbers, follow through from their answer to part
(a).
= 245
(A1)(ft) (C3)
[6]
28.
(a)
3
(b)
−1/3
(c)
Substituting (6, 7) in y = their mx + c or equivalent to find c.
y=
(d)
(A1) (C1)
(ft) from (a)
1
x 9 or equivalent
3
(1.5, 8.5)
(A1)(ft) (C1)
(M1)
(A1)(ft) (C2)
(A1)(A1)(ft)
Note: Award (A1) for 1.5, (A1) for 8.5. (ft) from (c),
brackets not required.
(C2)
[6]
14
29.
(a)
(A1)(A1)(A1) (C3)
Note: Award (A1) for a labeled Venn diagram with appropriate
sets.
(A1) for 7, (A1) for 8 and 5.
(b)
P (Spanish / one language only) =
8
20
(M1)(A1)(ft)
8
5
20 20
Note: Award (M1) for substituted conditional probability
formula, (A1) for correct substitution. Follow through from
their Venn diagram.
=
8
(0.615, 61.5%)
13
(A1)(ft)
OR
P (Spanish / one language only) =
8
(A1)(ft)(M1)
8 5
Note: Award (A1) for their correct numerator, (M1) for correct
recognition of regions.
Follow through from their Venn diagram.
=
8
(0.615, 61.5%)
13
(A1)(ft) (C3)
[6]
30.
Financial penalty applies in part (a)
(a)
FP
I = 1200 1
7.2
600
5 12
1200
(M1)(A1)
I = 518.15 euros
(A1) (C3)
Notes: Award (M1) for substitution in the compound interest
formula, (A1) for correct substitutions, (A1) for correct answer.
If final amount found is 1718.15 and working shown award
(M1) (A1)(A0).
(b)
1200 r 5
100
r = 8.64 % (% sign not required)
518.15 =
(M1)(A1)(ft)
(A1)(ft) (C3)
15
Note: Award (M1) for substitution in the simple interest
formula, (A1)(ft) for correct substitution, (A1)(ft) for answer.
[6]
31.
(a)
=
(b)
=
91
(0.607, 60.6 % , 60.7%)
(A1)(A1) (C2)
150
111 37
, 0.74, 74%
150 50
(A1)(ft)(A1) (C2)
Note: Award (A1)(ft) for their numerator in (a) +20 provided
the final answer is not greater than 1. (A1) for denominator.
(c)
16
(0.176, 17.6%)
(A1)(A1)(ft) (C2)
91
Note: Award (A1) for numerator and (A1)(ft) for denominator.
Follow through from their numerator in (a) provided answer is
not greater than 1.
[6]
32.
(A1)(A1)(A1)
(A1)(A1)(A1) (C6)
Note: Award (A1) for each number placed once in the correct
region. Accept equivalent forms for numbers.
[6]
33.
(a)
(i)
8.5 (cm)
(A1)
(ii)
120°
(A1)
16
(iii)
(b)
30°
BC
sin120
(A1) (C3)
8.5
(M1)(A1)(ft)
sin 30
Note: Award (M1) for correct substituted formula, (A1) for
correct substitutions.
BC = 14.7
17 3
2
(A1)(ft) (C3)
[6]
34.
(a)
(x + 8)2 = (x + 7)2 + x2
Note: Award (A1) for a correct equation.
(A1)
x2 + 16x + 64 = x2 + 14x + 49 + x2
Note: Award (A1) for correctly removed parentheses.
(A1)
x2 – 2x –15 = 0
Note: Accept any equivalent form.
(A1) (C3)
(b)
x = 5, x = –3
(A1)(ft)(A1)(ft) (C2)
Notes: Accept (A1)(ft) only from the candidate’s quadratic
equation.
(c)
30 cm
(A1)(ft) (C1)
Note: Follow through from a positive answer found in part (b).
[6]
35.
Financial penalty applies in parts (b) and (c).
(a)
0.88×16000 OR 0.12×16000 OR 1920
14080
(b)
1.6407×5.25×14080
121280.54 USD
Note: Follow through from their answer to part (a).
(c)
12 ×
FP
FP
1
0.8739
13.73 AUD
(M1)
(A1) (C2)
(M1)
(A1)(ft) (C2)
(M1)
(A1) (C2)
Note: If division used in part (b) and multiplication used in part
(c), award (M0)(A0) for part (b) and (M1)(A1)(ft) for part (c).
[6]
17
36.
Unit penalty applies in part (b).
4
(M1)
9
ˆ D)
100 + their (AB
(M1)
126°
(A1) (C3)
Notes: Accept an equivalent trigonometrical equation involving
angle ABD for the first (M1).
Radians used gives 100°. Award at most (M1)(M1)(A0) if
working shown.
BD = 8 m leading to 127°. Award at most (M1)(M1)(A0)
(premature rounding).
(a)
ˆD
sin AB
(b)
AC2 = 102 + 92 – 2 × 10 × 9 × cos(126.38...)
(M1)(A1)
Notes: Award (M1) for substituted cosine formula.
Award (A1) for correct substitution using their answer to part
(a).
UP
AC = 17.0 m
(A1)(ft) (C3)
Notes: Accept 16.9 m for using 126.
Follow through from their answer to part (a).
Radians used gives 5.08. Award at most (M1)(A1)(A0)(ft) if
working shown.
[6]
37.
(a)
108 54
, 0.432, 43.2%
250 125
(A1)(A1) (C2)
(b)
(c)
25
(0.236, 23.6%)
(A1)(A1) (C2)
106
71
(0.418, 41.8%)
(A1)(A1) (C2)
170
[6]
38.
(a)
(b)
–4, –3, –2, –1, 0, 1, 2
(A1) (C1)
Note: Award (A1) for correct numbers, do not penalise if
braces, brackets or parentheses seen.
4
(0.571, 57.1%)
7
(A1)(ft)(A1)(ft) (C2)
18
Notes: Award (A1)(ft) for numerator, (A1)(ft) for denominator.
Follow through from part (a).
Note: There is no further penalty in parts (c) and (d) for use of
denominator consistent with that in part (b).
(c)
(d)
1
(0.143, 14.3%)
7
Note: Follow through from part (a).
(A1)(ft) (C1)
1
(0.143, 14.3%)
(A1)(ft)(A1)(ft) (C2)
7
Note: Award (A1)(ft) for numerator, (A1)(ft) for denominator.
Follow through from part (a).
[6]
39.
(a)
(b)
0 16 1 22 2 19
(M1)
80
Note: Award (M1) for substituting correct values into mean
formula.
1.75
(A1) (C2)
An attempt to enumerate the number of goals scored.
(M1)
2
(A1) (C2)
19
(c)
2 1.75
× 100
1.75
14.3 %
(M1)
(A1)(ft) (C2)
Notes: Award (M1) for correctly substituted % error formula.
% sign not required.
Follow through from their answer to part (a).
If 100 is missing and answer incorrect award (M0)(A0).
If 100 is missing and answer incorrectly rounded award (M1)
(A1)(ft)(AP).
[6]
40.
(a)
1 (one)
(A1) (C1)
Note: 6, {6} or {1} earns no marks.
(b)
1, 3, 5, 7, 9, 11
(A1) (C1)
Note: Do not penalise if braces, parentheses or brackets are
seen.
(c)
(A1)(A1)(ft)(A1)(ft)(A1)(ft) (C4)
Notes: Award (A1) for the empty set A B C .
Award (A1)(ft) for the correct placement of 6, 5, 1 and 3.
Award (A1)(ft) for the correct placement of 2, 4, 12, 7, 9, 11, 8.
Award (A1)(ft) for the correct placement of 10.
Follow through from part (b).
[6]
20
41.
(a)
x=
4
2
x=2
(M1)
(A1)
OR
dy
= 4 – 2x
dx
x=2
(M1)
(A1)
(2, 7) or x = 2, y = 7
(A1) (C3)
Notes: Award (M1)(A1)(A0) for 2, 7 without parentheses.
(b)
(i)
C labelled in correct position on graph
(A1) (C1)
(ii)
3 = 3 + 4x – x2
Note: Award (M1) for correct substitution of y = 3 into
quadratic.
(M1)
(x =) 4
(A1) (C2)
OR
Using symmetry of graph x = 2 + 2
(M1)
Note: Follow through from their x-coordinate of the vertex.
(x =) 4
(A1)(ft) (C2)
[6]
21
42.
(a)
r=
36 1
108 3
(A1) (C1)
Note: Accept 0.333.
(b)
u1
1
3
7
= 36
(M1)
Note: Award (M1) for correct substitution in formula for nth
term of a GP. Accept equivalent forms.
u1 = 78732
(A1)(ft) (C2)
Notes: Accept 78700. Follow through from their common ratio
found in part (a). If 0.333 used from part (a) award
(M1)(A1)(ft) for an answer of 79285 or 79300 irrespective of
whether working is shown.
78732 1
(c)
118096 =
1
3
k
(M1)(M1)
1
1
3
Notes: Award (M1) for correct substitution in the sum of a GP
formula, (M1) for equating their sum to 118096. Follow
through from parts (a) and (b).
OR
1
Sketch of the function y = 78732
1
3
1
1
3
Indication of point where y = 118 096
k
(M1)
(M1)
OR
78 732 + 26 244 + 8748 + 2916 + 972 + 324 + 108 + 36 + 12 + 4
= 118 096
(M1)(M1)
Note: Award (M1) for a list of at least 8 correct terms, (M1) for
the sum of the terms equated to 118096.
k = 10
(A1)(ft) (C3)
Notes: Follow through from parts (a) and (b). If k is not an
integer, do not award final (A1). Accept alternative methods.
If 0.333 and 79285 used award (M1)(M1)(A1)(ft) for k = 5.
If 0.333 and 79300 used award (M1)(M1)(A0).
[6]
22
43.
(a)
45000 + (5 – 1)1750
(M1)(A1)
Note: Award (M1) for substituted AP formula, (A1) for correct
substitutions.
= 52000 USD
(A1) (C3)
Notes: If a list is used, award (M1) for recognizing AP, award
(A1) for seeing 52000 in their list, (A1) for final answer.
(b)
10
(2(45000) + (10 – 1)(1750))
(M1)(A1)
2
Notes: Award (M1) for substituted AP formula, (A1)(ft) for
correct substitutions. Follow through from their common
difference used in part (a).
= 528750 USD
(A1)(ft) (C3)
Notes: Accept 529000.
If a list is used, award (M1) for recognizing sum of AP, (A1) for
seeing 60750 included in the sum or 528750 in a cumulative
list.
[6]
44.
(a)
(i)
(ii)
(b)
area =
0 2
6 0
1
=
3
y=
(M1)
2
, 0.333
6
(A1) (C2)
1
x+2
(A1)(ft) (C1)
3
Notes: Follow through from their gradient in part (a)(i).
Accept equivalent forms for the equation of a line.
6 1.5
(A1)(M1)
2
Note: Award (A1) for 1.5 seen, (M1) for use of triangle formula
with 6 seen.
= 4.5
(A1) (C3)
[6]
23

IB Math Studies Year II – Midterm Review Questions KEY 1. (a) Area

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