代写 迪肯 SIT190 Assignment
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代写 迪肯 SIT190 Assignment
SIT190 Assignment 1
Trimester 2, 2016 Due Date: Friday 29 th July, 5 pm
Complete the following problems, showing all your working.
Marks are allocated to your steps, not just the final answer.
1. Evaluate the following expressions:
(i) 6 × 5 − 5 + ((−3) 3 × (−2)) ÷ 6 − 4
(ii) (5? − 3?) 2 + (−2? − (2?) 2 ) when ? = −1 and ? = 2
(iii)
−2? 3 −3?? 2 −3
? 2 + ? 2
when ? = 2 and ? = 1
2. Expand, and simplify, if possible:
(i) −2(4? − 3?) + 7(−5? + ?)
(ii) (4? − 3?)(−? + 2?)
(iii) (? + 2? 2 )(−3? +? − 1)
3. Simplify (write as a single fraction with no common factors):
(i)
−3 + 1 4
5
2 − 2
5
(ii) 9??
3 − 12? 2
−3? 2 ? + 4?
(iii) 3−2?
?+1
−
4?+1
2?−1
4. Solve for ?:
(i)
5?−12
6?+9
= 3
(ii) ?
2 +4?+7
5?+7
= 2
5. Make ? the subject:
(i) 3 −
2?
3? 2
= 1
(ii)
9??+8?
3
= 4 − ? +
2?
3
6. Solve 3? + 5? = −19 (1) and −4? −? = −3 (2) for ? and ? by
(i) elimination
代写 迪肯 SIT190 Assignment
(ii) substitution
7. Use elimination to show that there is no solution to the equations
5? − 3? = 2 (1) and −15? + 9? = −8 (2)
8. Find (a) ?(−3) (if it exists) and (b) the domain for each of the following functions:
(i) ?(?) =
8
4?+12
(ii) ?(?) =
6
? 2 −9
(iii) ?(?) = +√? 3 + 1
(iv) ?(?) =
? 3
3
+ 2? + 10
9.
(a) Find the equation of the straight line that:
) passes through the point (−3, 10) and has gradient −2
(ii) passes through the points (−1, 5) and ( −4, 26).
(b) (i) Sketch 3 ? = −9 ? + 18, showing the ? and ? intercepts.
(ii) What is the gradient of this line.
10. Factorise and solve the following quadratic equations:
(i) ? 2 − ? − 6 = 0
(ii) −2? 2 + ? + 30 = 3? − 10
(iii) 100 − 4? 2 = 0
11. Use the Quadratic Formula to solve:
(i) 3? 2 − 7? + 2 = 0
(ii) −5? 2 − 2? + 2 =−1
12. For the parabola ? = ? 2 + 2? − 15,
(i)
(ii) find the ?-intercepts
(iii) determine whether the parabola has a highest or lowest point
(iv) find the coordinates of the highest or lowest point
(v) sketch the curve indicating the coordinates of the intercepts and the turning point.
13. In a computer simulation game the height of a fighter jet above the earth’s surface is given by the
formula:
ℎ = 3? 2 − 12? + 20 for 0 ≤ ? ≤ 10 where ℎ is measured in hundreds of metres and ? is the
time measured in seconds after the start of the simulation.
(a) How high is the jet after:
(i) 1 second
(ii) 5 seconds
(b) (i) Does the jet crash into the earth’s surface? If you answer ‘yes’, after how many seconds
does it crash? If you answer ‘no’ calculate how close the jet comes to the earth’s surface.
(ii) How high is the jet at the end of the simulation? Is it moving towards or away from the
earth’s surface?
代写 迪肯 SIT190 Assignment
