WATP 2020_specialist_unit_1_solutions_.docx
Copyright for test papers and marking guides remains with West Australian Test Papers.
Test papers may only be reproduced within the purchasing school according to the advertised Conditions of Sale.
Test papers should be withdrawn after use and stored securely in the school until Thursday 2nd July 2020.
SEMESTER ONE
MATHEMATICS
SPECIALIST
UNIT 1
2020
SOLUTIONS
Calculatorfree Solutions
1. (a) (i) b
(ii)
(b)
=
= [5]
2. (a) (i) 5
(ii) 21
(b) (i) x = 3
(ii) x = 4
(iii) x = 7
(iv) x = 2
(c) (i)
(ii)
= 20
(d) (i)
(ii) [12]
3. (a) (i)
(ii) OA x OB = OC2
But OC = OX
OA x OB = OX2
This is the converse of the secant/tangent theorem
OX is a tangent
OA x OB = OC2
But OC = OY
OA x OB = OY2
This is the converse of the secant/tangent theorem
OY is a tangent
(b) or
(c) (i)
(ii) 3! = 6 ways [10]
4. (a) (i) i 13j
(ii) 5
(iii)
(iv)
(b)
(c)
[12]
5. (a)
Thale’s Theorem
(b)
Revolution equal to 360 degrees
(c)
Equal angles at base of isosceles triangle [6]
6.
This is a contradiction as (x – 3y) cannot both belong and not belong
to the integer set.
:. False, there are no integers for which this statement is true. [5]
CalculatorAssumed Solutions
7.
v = 0.46 km/h [6]
8. (a) (i) LM parallel to x–axis so b = 5
M = (5, 5)
(ii)
(b) (i) x = 5
y = 2
(ii) If y = 2 & x ≥ 6, then BC // AD
If AB // DC
(iii)
[13]
9. (a)
(b)
Bearing = 110T
(c)
Time taken = [7]
10. (a)
50 like tea only
(b) None like neither
(c)
100 = 70 + 50 + 60 20 40 30 + x
= 90 + x
x = 10
(d) (i)
(ii)
(e) 41 [8]
11. (a)
(b)
[8]
12. (a) 3 > 2 but 3 < 2 is false
(b) “If the triangle is not isosceles, then the triangle does not
have two equal sides.”
Yes is it always true since the original implication is always
true by definition of isosceles triangles.
(c) “If n is divisible by 4, then n is divisible by 8”.
The converse is not always true, as shown by the
counter-example where n = 12
(d) FOR ALL natural numbers p, EXISTS a real number q,
such that q is one less than p. [7]
13. (a)
Let BAD = x
reflex BOD = 2x Angle at the centre theorem
Similarly let BCD = y
BOD = 2y Angle at the centre teorem
Since 2x + 2y = 360
then x + y = 180
Hence BAD + BCD = 180
QED
(b) EAG + BCD = 180 Cyclic quadrilateral
EAG ECF
In EAG and ECF
AEG CEF Bisector
EAG ECF Proven
CFE BFG Vertically Opposite
AGF BFG QED
(c) (i) Converse
(ii) Yes [10]
14. (a) (i)
x = 1
(ii)
0.13
(iii) a b = 13i 4j
| a b | =
(b) (i)
(ii) cos(0) = 1
So, the dot product of a vector with itself is its magnitude
squared multiplied by 1.
(iii)
[14]
15. (a)
F1 + F2 + F3 =
276T
(b) a + b = 5i + j
c = 5i j
| c | =
Direction = 101T [10]
16.
[4]
17.
[5]
18. (a) Independent term is the middle term.
8064
(b)
Hence,
[8]