WS Fall Semester Final Review 2018 [198 marks]

Transcription

1 WS Fall Semester Final Review 2018 [198 marks] 1a. [4 marks] (A1)(A1)(A1)(A1)(C4) [4 marks] 1b. Incorrect (A1) Natural numbers are positive integers. Integers can also be negative. (or equivalent) (R1) Accept a correct justification. Do not award (R0)(A1). Accept: a statement with an example of an integer which is not natural. 2. [6 marks] (A1)(A1)(A1)(A1)(A2) (C6) Row 1 has been given in the question. Row 2 to row 5: Award (A1) for each correct row. Row 6: Award (A1) for both N not selected and Z selected; award (A1) for both Q and R selected. Do not penalize if crosses (or similar) appear in the empty cells.

2 3a. (A1)(A1)(A1)(A1)(A1)(A1) (C6) Award (A1) for each number correctly placed. Award (A0) for any entry in more than one region. 3b. (A1)(A1)(A1)(A1)(A1)(A1) (C6) Award (A1) for each number correctly placed. Award (A0) for any entry in more than one region.

3 3c. (A1)(A1)(A1)(A1)(A1)(A1) (C6) Award (A1) for each number correctly placed. Award (A0) for any entry in more than one region. 3d. (A1)(A1)(A1)(A1)(A1)(A1) (C6) Award (A1) for each number correctly placed. Award (A0) for any entry in more than one region.

4 3e. (A1)(A1)(A1)(A1)(A1)(A1) (C6) Award (A1) for each number correctly placed. Award (A0) for any entry in more than one region. 3f. (A1)(A1)(A1)(A1)(A1)(A1) (C6) Award (A1) for each number correctly placed. Award (A0) for any entry in more than one region. 4a. r = (A1) (C1) Accept and 0.019

5 4b. r = (A1)(ft)(A1)(ft) Notes: Award (A1) for 1.924, (A1) for Accept 1.92 and 1.9. Follow through from their part (a). 4c. (A1)(A1)(A1) (C3) Notes: Award (A1) for each true statement circled. Do not follow through from part (a). Award (A1)(A1)(A0) if 1 extra term seen. Award (A1)(A0)(A0) if 2 extra terms seen. Award (A0)(A0)(A0) if all terms circled. Accept other indications of the correct statements i.e. highlighted or ticks. 5a Award for multiplying by 25. = (612500) (A1) 5b Award for correct substitution into the percentage error formula. = ( ) (A1)(ft) Follow through from part (a). 100

6 5c (A1)(ft)(A1)(ft) Award (A0)(A0) for answers of the type Follow through from part (b). Ignore % sign. 6a. BD 2 = Award for correct substitution into Pythagoras. Accept correct substitution into cosine rule. BD = (A1) = 93 (AG) Both the rounded and unrounded value must be seen for the (A1) to be awarded. 6b. 115 cosc = (93 2 = cosc) (A1) Award for substitution into cosine formula, (A1) for correct substitutions. = 53.7 ( ) (A1)(G2) 6c. 1 1 (40)(84) + (115)(60) sin( ) 2 2 (A1)(ft) [4 marks] Award for correct substitution into right-angle triangle area. Award for substitution into area of triangle formula and (A1)(ft) for correct substitution. = 4460 m 2 ( m 2 ) (A1)(ft)(G3) Notes: Follow through from part (b). [4 marks]

7 6d. (40+60)(84+115) 4 Award for correct substitution in the area formula used by Ancient Egyptians. = 4980 m 2 (4975 m 2 ) (A1)(G2) 6e Notes: Award for correct substitution into percentage error formula. = 11.6 (%) ( ) (A1)(ft)(G2) Notes: Follow through from parts (c) and (d)(i).

8 7a (1 + ) (A1) Award for substitution in compound interest formula, (A1) for correct substitution. OR N = 5 I = 3.5 PV = 1000 P/Y = 1 C/Y = 4 Award (A1) for C/Y = 4 seen, for other correct entries. OR N = 5 4 I = 3.5 PV = 1000 P/Y = 1 C/Y = 4 Award (A1) for C/Y = 4 seen, for other correct entries. = (USD) (A1) Award for substitution in compound interest formula, (A1) for correct substitution. 7b (USD) (A1)(ft) (C4) Award (A1)(ft) for subtraction of 1000 from their part (a)(i). Follow through from (a)(i). 7c Award for division of 170 by their part (a)(ii). = 0.89 (A1)(ft) Follow through from their part (a)(ii).

9 8a. r = 14000(1 + ) (A1) Award for substitution into the compound interest formula, (A1) for correct substitution. Award at most (A0) if not equated to OR N = 5 PV = ±14000 FV = P/Y = 1 C/Y = 1 (A1) Award (A1) for C/Y = 1 seen, for all other correct entries. FV and PV must have opposite signs. = 4.56 (%) ( (%)) (A1) (G3) 8b Award for multiplying by (INR) (A1) (G2) Answer must be given to the nearest whole number.

10 8c (1 + ) (A1)(ft) Award for substitution into the compound interest formula, (A1)(ft) for their correct substitution. OR N = 60 I% = 5.2 PV = ± P/Y= 12 C/Y= 12 (A1) Award (A1) for C/Y = 12 seen, for all other correct entries. OR N = 5 I% = 5.2 PV = ± P/Y= 1 C/Y= 12 (A1) Award (A1) for C/Y = 12 seen, for all other correct entries = (INR) (A1)(ft) (G3) Follow through from part (b). Answer must be given to the nearest whole number. 8d Award for dividing their (c) by ( ) = (USD) (A1)(ft) (G3) Award for finding the difference between their conversion and Answer must be given to the nearest whole number. Follow through from part (c). 9a. In this question, the first time an answer is not to 2 dp the final (A1) is not awarded Award for dividing 350 by = (ARS) (A1)

11 9b Award for multiplying their answer to part (a) by = (ARS) OR (A1)(ft) Award for multiplying their answer to part (a) by = = (ARS) (A1)(ft) Follow through from part (a). 9c Award for dividing by 585. = 7.23 (A1) 10a. 5d = OR u 1 + 2d = 21 and u 1 + 7d = 46 Award for a correct equation in d or for two correct equations in u 1 and d. (d =) 5 (kg) (A1)

12 10b. u = 21 OR u = 46 Award for substitution of their d into either of the two equations. (u 1 =) 11 (kg) (A1)(ft) Follow through from part (a)(i). 10c. 12 ( (12 1) 5) 2 Award for correct substitution into arithmetic series formula. = 462 (kg) (A1)(ft) Follow through from parts (a) and (b). 11a (A1) Award for substitution into the arithmetic sequence formula, (A1) for correct substitution. = ($) 160 (A1)(G3) 11b. 12 ( ) 2 (A1)(ft) Award for substituting the arithmetic series formula, (A1)(ft) for correct substitution. Follow through from their first term and common difference in part (a). = ($) 1380 (A1)(ft)(G2)

13 11c (A1) Award for substituting the geometric progression nth term formula, (A1) for correct substitution. = ($) 156 ( ) (A1)(G3) Accept the answer if it rounds correctly to 3 sf, as per the accuracy instructions. 11d. 60( ) (A1)(ft) Award for substituting the geometric series formula, (A1)(ft) for correct substitution. Follow through from part (c) for their first term and common ratio. = ($)1280 ( ) (A1)(ft)(G2) 11e. 60(1.1 n 1) n 2 > ( (n 1) 10) [4 marks] Award for correctly substituted geometric and arithmetic series formula with n (accept other variable for n ), for comparing their expressions consistent with their part (b) and part (d). OR Award for two curves with approximately correct shape drawn in the first quadrant, for one point of intersection with approximate correct position. Accept alternative correct sketches, such as Award for a curve with approximate correct shape drawn in the 1 st (or 4 th) quadrant and all above (or below) the x-axis, for one point of intersection with the x-axis with approximate correct position. 17 (A2)(ft)(G3) Follow through from parts (b) and (d). An answer of 16 is incorrect. Award at most (A0)(A0) with working seen. Award (G0) if final answer is 16 without working seen. [4 marks]

14 12a OR Award for dividing any u n+1 by u n. 1 = (0.333, ) 3 (A1) 12b ( ) n 1 = 2 3 Award for their correct substitution into geometric sequence formula. n = 6 (A1)(ft) Follow through from part (a). Award (A1)(A0) for u 6 = 2 or u 6 with or without working. 12c. S 30 = 486( ) Award for correct substitution into geometric series formula. = 729 (A1)(ft) 13a. 1 2 (0.5) (A1) (C1)

15 13b ( ) 4 2 Award for their correct substitution into the geometric sequence formula. Accept a list of their five correct terms (1.13, 9 ) 8 (A1)(ft) Follow through from their common ratio from part (a). 13c. 18 ( 1 ) n 1 < Notes: Award for their correct substitution into the geometric sequence formula with a variable in the exponent, for comparing their expression with ( ) Accept an equation. n = 16 (A1)(ft) (C3) Follow through from their common ratio from part (a). n must be a positive integer for the (A1) to be awarded. 14a. (A2) Award (A2) for all correct entries, (A1) for 3 correct entries.

16 14b. continuous (A1) (C1) 14c. 60 (cm) < trout length 70 (cm) (A1) (C1) Accept equivalent notation such as (60, 70] or ]60, 70]. Award (A0) for (incorrect notation). 14d Award for their 4 divided by their 22. = 18.2 ( ) (A1)(ft) Follow through from their part (a). Do not accept a. 180 (A1) (C1) 15b. 36, 24 (A1)(A1) Award (A0)(A1) for two incorrect values that add up to c. 125 (accept 125.5) (A1)

17 15d Award for correct substitution of their mid-interval values, multiplied by their frequencies, into mean formula. =156 ( ) (A1)(ft) (C3) Follow through from parts (b) and (c)(i). 16a. 60 (A1) 16b (A1) 16c Award for an attempt to substitute their mid-interval values (consistent with their answer to part (b)) into the formula for the mean. Award where a table is constructed with their (consistent) mid-interval values listed along with the frequencies = (, 17.9, ) (A1)(ft)(G2) Follow through from their answer to part (b). 16d. a = 34, b = 60 (A1)(A1)

18 16e. (i) minutes (A1) [4 marks] Accept Accept any answer between 21 and (Accept 21.5, but do not accept 21.) (ii) 5 (A1) Accept < 6. Do not accept 6. Answer must be an integer. (iii) = 15 (A1)(G2) Notes: Award for subtraction from 60. Accept 15 ± 1. Answer must be an integer. [4 marks] 17a Award for correct substitutions into mean formula. (=) 17.5 (A1) 17b (A1) (C1)

19 17c. (A1)(A1)(A1)(ft) (C3) Award (A1) for correct endpoints, (A1) for correct quartiles, (A1)(ft) for their median. Follow through from part (a)(ii), but only if median is between 16 and If a horizontal line goes through the box, award at most (A1)(A1)(A0). Award at most (A0)(A1)(A1) if a ruler has not been used. 18a. 48 (A1) (C1) 18b Award for 58 and 40 seen. = 18 (A1) 18c. (A1)(A1)(ft)(A1)(ft) (C3) Award (A1) for the correct maximum and minimum, (A1)(ft) for their correct median and (A1)(ft) for 40 and their upper quartile. Follow through from parts (a) and (b). Award a maximum of (A1)(A1)(ft)(A0) if the horizontal line goes through the box or if a ruler has clearly not been used.

20 19a. x+11 2 = 10 Award for correct substitution into median formula or for arranging all 9 values into ascending/descending order. (x =) 9 (A1) 19b ( ) (A2)(ft) Follow through from part (a). 19c Award for 13 and 8 seen. = 5 (A1)(ft) (C4) Follow through from part (a). 20a. A' (A1) Accept alternative set notation for complement such as U A. 20b. C D OR D C (A1) Accept alternative set notation for complement. 20c. (E F) G OR G (E F) (A2) (C4) Accept equivalent answers, for example (E G) (F G).

21 20d. (A1) 20e. (A1) 21a. a = 0.2 (A1) 21b. b = 0.85 (A1) 21c Award for a correct product. 1 = 0.2 (, 20%) 5 (A1)(G2)

22 21d (A1)(ft) Award (A1)(ft) for their ( ) and ( ), for adding two products. 5 = (0.3125,, 31.3%) 16 (A1)(ft)(G3) Award the final (A1)(ft) only if answer does not exceed 1. Follow through from part (b)(i). 21e (A1)(ft)(A1)(ft) Award (A1)(ft) for a correct numerator (their part (b)(i)), (A1)(ft) for a correct denominator (their part (b)(ii)). Follow through from parts (b)(i) and (b)(ii). 16 = 0.64 (, 64% ) 25 (A1)(ft)(G3) Award final (A1)(ft) only if answer does not exceed 1. 21f. (x =) 3 (A1) [1 Mark] 21g. (y =) 10 (A1)(ft) Following through from part (c)(i) but only if their x is less than or equal to 13. [1 Mark] 21h. 54 ( ) Award for subtracting their correct sum from 54. Follow through from their part (c). = 8 (A1)(ft)(G2) Award (A1)(ft) only if their sum does not exceed 54. Follow through from their part (c).

23 21i Award for summing 6, 8 and (A1)(G2) 22a. 15 (A1) (C1) 22b. no (A1) (C1) Accept it is only offered in Winter and Spring. 22c. volleyball, golf, cycling (A1) (C1) Responses must list all three sports for the (A1) to be awarded. 22d. 4 (A1) (C1) 22e. (F W S) OR F W S (or equivalent) (A2)

24 23a. (A1)(A1) Award (A1) for 30 in correct area, (A1) for 60 and 10 in the correct areas. 23b (, , %) (A1)(ft)(A1)(ft) Award (A1)(ft) for correct numerator of 30, (A1)(ft) for correct denominator of 90. Follow through from their Venn diagram. 23c P(S) P(M) = = (R1) 1 Award (R1) for multiplying their by. 3 therefore the events are independent (as P(S M) = 1 ) (A1)(ft) 4 Award (R1)(A1)(ft) for an answer which is consistent with their Venn diagram. Do not award (R0)(A1)(ft). Do not award final (A1) if P(S) P(M) is not calculated. Follow through from part (a). 24a. 20 (A1) (C1)

25 24b ( , % ) (A1)(A1) Award (A1) for correct numerator, (A1) for correct denominator. 24c (A1) Award (A1) for first or second correct product seen, for adding their two products or for multiplying their product by two. 14 = ( , % ) 111 (A1) (C3) 25a. (A1)(A1)(A1) (C3) Award (A1) for each correct pair of probabilities. 25b (A1)(ft) Award (A1)(ft) for two correct products of probabilities taken from their diagram, for the addition of their products. 491 = (98.2%, ) 500 (A1)(ft) (C3) Follow through from part (a).

26 26a. 1 x 2 (A1) (C1) 26b. (A1)(A1)(ft) Notes: Award (A1) for 15 placed in the correct position, award (A1)(ft) for x and their 1 x placed in the correct positions of diagram. 2 Do not penalize the absence of 0 inside the rectangle and award at most (A1)(A0) if any value other than 0 is seen outside the circles. Award at most (A1)(A0) if 35 and 70 are seen instead of x and their 1 x. 2 26c. 1 x + x + 15 = or equivalent Award for adding the values in their Venn and equating to 120 (or equivalent). (x =) 70 (A1)(ft) Follow through from their Venn diagram, but only if the answer is a positive integer and x is seen in their Venn diagram. 26d. 85 (A1)(ft) (C1) 120. Follow through from their Venn diagram and their answer to part (c), but only if the answer is a positive integer and less than

27 27a. (A1)(A1) Award (A1) for each correct pair of probabilities. 27b p + = 3 5 (A1)(ft) [4 marks] Award (A1)(ft) for two correct products from part (a), for adding their products, for equating the sum of any two 3 probabilities to (p =) (0.688, ) 16 (A1)(ft) (C4) Award the final (A1)(ft) only if 0 p 1. Follow through from part (a). [4 marks] International Baccalaureate Organization 2018 International Baccalaureate - Baccalauréat International - Bachillerato Internacional Printed for Raymore-Peculiar High School