Mat 10 Answers to Review Questions for Final Exam Jan 2006

Mat 10 Answers to review questions for final exam Jan 2006

1. Graphs

2. (a) (b)

3. (a) x = 4 ; y = or –2.4 (b) x = or 10.5 ; y = 7

4. (a) y = – x (b)

5. (c) y = 2x + 5

6. (a) $10/h (b) $5 (c) $105 (d) y = 10x + 5

7. (a) (b)

(e) x = – 4 (f) *

* ‘y’ is missing in second equation in (f). It should read 6x – 5y = 12

8. (a) –12 (b) (c) or – 5

(d) 10 (e)

9. (a) (6, – 5) (b)

10. (a) (b) (c) continuous

(d) discrete

11. (a) Domain or

Range or

(b) Domain or

Range or

11. (c) Domain or

Range

(d) Domain: Hard to tell. Includes –3, 0, 3 but others not clear

Range: Similarly only 0 and 3 obvious.

12. (a)

(b)

(c)

(d)

13. (a) (b) (c)

(d) (e) (f)

(g) (h) (i)

(j) (k) Can’t factor (l)

14. (a) (b) a (c)

15. (a) (b) (c)

16. (a) Positive slopes – moving away from starting position

Negative slope – returning to starting position

(b) Stationary (no movement)

17. Graph

18. (a) (c) (e) (f) Yes

(b) (d) No

19. (a) 17 (b) – 8 (c) – 2 (d) or 0.2

(e) (f) – 3 (g) 5 (h) or – 2.625

(i) – 2 , – 8

20.

Transformation / Vertex / Axis of symmetry / Mapping rule
(a) / vt of 6, ht of –1 / (–1, 6) / x = – 1 /
(b) / Rx, vt of 3, ht of 5 / (5, 3) / x = 5 /
(c) / vs of 3, vt of –4, ht of – 7 / (– 7, – 4) / x = – 7 /
(d) / Rx, vs of , vt of – 1 / (0, –1) / x = 0 /
(e) / ht of –4 / (–4, 0) / x = –4 /
(f) / Rx, vs of, vt of 2, ht of –1 / (–1, 2) / x= –1 /
(g) / Rx, ht of 2 / (2, 0) / x = 2 /
(h) / Rx, vs of , ht of 2 / (2, 0) / x = 2 /

21. (a) (b)

22. (a) – 8, 4 (b) 2, 7 (c) –5,

(d) –3, 3 (e) (f) 0

23. Dependent variable – height of tree (over time)

Independent variable – volume of water added

24. Only the first situation represents a cause an effect relationship with the grade in math being the dependent variable and the time spent studying being the independent variable.

25. (a) (Some values rounded to nearest tenth)

Tree farm / Lower extreme / Lower Quartile / Median / Upper Quartile / Upper extreme
Firs ‘r’ Us / 1.4 / 1.8 / 2.2 / 2.5 / 2.8
Balsam City / 1.4 / 1.6 / 1.9 / 2.4 / 2.9

(b) Firs ‘r’ Us

26. (a) 5.8 – 9.4 (b) 95 % (c) 2.5 %

(d) 84 % of 1200 = 1008 (e) 68% of 1200 = 816 (f) < 2 or > 3

27. (a) 3.5 cm – 6.5 cm (b) 2 cm to 8 cm

28. (a)

bin / frequency
0 - 10 / 2
10 - 20 / 8
20 - 30 / 10
30 - 40 / 8
40 - 50 / 2

29. (a) Mean = 4.0 (b) standard deviation = 0.054

(c) Shipment will likely pass inspection since the standard deviation is very low indicating very little variation from the mean.

30.

(a)

Lower extreme / Lower Quartile / Median / Upper Quartile / Upper extreme
Blood pressure / 99 / 115 / 120 / 124 / 155

(b)

bin / frequency
90 – 100 / 1
100 – 110 / 1
110 – 120 / 11
120 – 130 / 11
130 – 140 / 4
140 – 150 / 0
150 – 160 / 2

(iii) Mode 110 (iv) Median 120

(v) Standard deviation 11.7

31. (a)

Model / r / r2 / R2
Linear / -.8089 / .6543 / na
Quadratic / na / na / .9982
Exponential / -.4241 / .1799 / na

Note:

Exponential regression can only be performed with positive y-values. (30, 0) was replaced with (30, 0.001) to obtain the r and r2 values for the exponential model above!

The data is best modeled by the quadratic regression. (R2 value closest to 1)

31. (b)

Model / r / r2 / R2
Linear / .9985 / . 9970 / na
Quadratic / na / na / .9999
Exponential / .9447 / .8924 / na

The data is best modeled by the quadratic regression. (R2 value closest to 1)

(c)

Model / r / r2 / R2
Linear / .9059 / . 8206 / na
Quadratic / na / na / .9864
Exponential / .9974 / .9949 / na

The data is best modeled by the exponential regression. (R2 value closest to 1)

32. (a) Exponential. (r2 value closest to 1)

(b)

It is the best fit of the three but since the r2 value is not that close to 1 there is indication that there might be a lot of scatter in the data or that some other function might fit it better. (Really need to see the scatterplot!)

33. (a) Quadratic. (R2 value closest to 1, but not that much different from linear.)

(b) Quadratic model would predict 39 goals. (Linear predicts 40)

34. (a) 39° (b) 36.8 cm (c) 5.3 (d) 13.3

(e) CB = 17.3 CD = 20.0 AC = 34.6

35. (a) (b) Yes (c) No

36. p = 14.4,

37. It is a right-angled triangle

38. 3.8 m 39. 25°

40. 54.1 km (54 to nearest km) 41. 25.7 m

42. 21 m

43. If distance on line of sight, approximately 190 000 m. If horizontal (land) distance, approximately 130 000 m. (Rounded off)

44. A, B and D are similar to each other. C and E are similar to each other.

45. (a) (b) (c) 864

46. (a) x > –6 (b) x > 2

47. Graphs

48. (a) (–4, 0) (b) (8, 1)

49. (a) (6, 2) (b) (1, 2) (c) (3, 2) (d) (4, –2)

(e) (f) (g) (0, 1) (h) no solution

(i) (8, –4) (j) (–1, 2)

50. 4 jibs, 1 spinnaker, $550 51. 3 easy bounce, 3 catch a spin, $240

52. 20 standard, 20 deluxe, $140 52. 90 low grade, 105 high grade, $69.75