failingTheHsc
Member
- Joined
- Oct 27, 2003
- Messages
- 37
here ya go guys:
Question 1
(a) 0.0302
(b) 3+sec^2 x
(c) 95 degrees
(d) $280
(e) x^3-8x+5
(f) x=10, -4
__________________
Question 2
(a) ex + 2y - 4 + e^2 = 0
(b) i) root(2)
ii) -1
iii) 135
iv) y = -x + 10, C(10, 0)
v) is a proof
vi) 35
__________________
Question 3
(a) i) 18e^x(2e^x-4)^8
ii) x (2 sin x + x cos x)
(b) 89
(c) a graph
(d) i) ln (x^2 + 5) + C
ii) root(3) - 1
_________________
Question 4
(a) i) 55
ii) 64 degreees 28 minutes
(b) i) 1/6
ii) 1/2
c) i) A(1, -3)
ii) 4.5
________________
Question 5
(a) i) proof
ii) (0,0) inflexion and (3, -27) min t.p.
iii) graph
iv) 0 < x < 2
b) i) 63 blocks
ii) 73 rows
iii) 3738 blocks
___________________
Question 6
(a) x = 12
(b) i) alt angles, parallel lines
ii) proof, using supplementary angle and angle sum of triangle
iii) use parallel lines from a single point in ratio
(c) i) C<sub>0</sub> = 5, k = 0.5798
ii) 5.6 years
___________________
Question 7
(a) i) 2 + root(2)
ii) r = 1/(root(2) - 1), |r| < 1. Therefor no limiting sum
b) i) pi/3, 5pi/3
ii) 6ms^-1
iii) is a graph
iv) 9m
___________________
Question 8
(a) y = 2
(b) v = pi {5, 1 (ln y)^2 dy
(c) 11.9
(d) i) proof. do normal thing to see where the lines would intersect and show the discriminant is positive for all values m, so will always have a solution.
ii) m=1 or m= 2/3
iii) y = x - 3 and y = 2/3 x - 4/3
__________________
Question 9
(a) x = 7pi/6, 11pi/6
(b) i) pi/6
ii) pi r^2 / 2
iii) pi r^2 / 3
iv) (pi r^2 - 3 root(3) r^2 ) / 6
(c)I) dL/dt = v - u, v and u are constants, L = (v-u)t. Substitue with the E equation given
ii) v = 3u/2
___________________
Question 10
(a)i) 120000a^2 - Fr - F, r = 1 + 0.06/k
ii) proof.
iii) $2324.47
iv) $498
(b)i) proof. note that XA = 1 - x, PM = 2 - PA, l = XP + PM
ii) just differentiate i) (too much algebra 4 me, i skipped it)
iii) M is closest when l is largest. solve dl/dx = 0, and using the factorisation
x = 1 and some other number involving r's. so i just used 1 ;o)
edit: changed a few answers and got rid of those <sup> things
there ya go. thats wat i did. let me know any agreements disagreements.
Question 1
(a) 0.0302
(b) 3+sec^2 x
(c) 95 degrees
(d) $280
(e) x^3-8x+5
(f) x=10, -4
__________________
Question 2
(a) ex + 2y - 4 + e^2 = 0
(b) i) root(2)
ii) -1
iii) 135
iv) y = -x + 10, C(10, 0)
v) is a proof
vi) 35
__________________
Question 3
(a) i) 18e^x(2e^x-4)^8
ii) x (2 sin x + x cos x)
(b) 89
(c) a graph
(d) i) ln (x^2 + 5) + C
ii) root(3) - 1
_________________
Question 4
(a) i) 55
ii) 64 degreees 28 minutes
(b) i) 1/6
ii) 1/2
c) i) A(1, -3)
ii) 4.5
________________
Question 5
(a) i) proof
ii) (0,0) inflexion and (3, -27) min t.p.
iii) graph
iv) 0 < x < 2
b) i) 63 blocks
ii) 73 rows
iii) 3738 blocks
___________________
Question 6
(a) x = 12
(b) i) alt angles, parallel lines
ii) proof, using supplementary angle and angle sum of triangle
iii) use parallel lines from a single point in ratio
(c) i) C<sub>0</sub> = 5, k = 0.5798
ii) 5.6 years
___________________
Question 7
(a) i) 2 + root(2)
ii) r = 1/(root(2) - 1), |r| < 1. Therefor no limiting sum
b) i) pi/3, 5pi/3
ii) 6ms^-1
iii) is a graph
iv) 9m
___________________
Question 8
(a) y = 2
(b) v = pi {5, 1 (ln y)^2 dy
(c) 11.9
(d) i) proof. do normal thing to see where the lines would intersect and show the discriminant is positive for all values m, so will always have a solution.
ii) m=1 or m= 2/3
iii) y = x - 3 and y = 2/3 x - 4/3
__________________
Question 9
(a) x = 7pi/6, 11pi/6
(b) i) pi/6
ii) pi r^2 / 2
iii) pi r^2 / 3
iv) (pi r^2 - 3 root(3) r^2 ) / 6
(c)I) dL/dt = v - u, v and u are constants, L = (v-u)t. Substitue with the E equation given
ii) v = 3u/2
___________________
Question 10
(a)i) 120000a^2 - Fr - F, r = 1 + 0.06/k
ii) proof.
iii) $2324.47
iv) $498
(b)i) proof. note that XA = 1 - x, PM = 2 - PA, l = XP + PM
ii) just differentiate i) (too much algebra 4 me, i skipped it)
iii) M is closest when l is largest. solve dl/dx = 0, and using the factorisation
x = 1 and some other number involving r's. so i just used 1 ;o)
edit: changed a few answers and got rid of those <sup> things
there ya go. thats wat i did. let me know any agreements disagreements.
Last edited:
