7B Taking it further 1. (i) 9 (ii) Bar chart because the data is discrete
(iii) 7⋅25 (iv) No, sample size is too small to
be representative of the general population
2. (i) 60–80 (ii) 60–80 (iii) 59 km/hr (iv) 66 cars (v) 96 cars
3. (i) 14 (iii) €178 (iv) 34
4. (ii) Lowest value for oral = 53, for written = 38; highest value for oral = 85, for written = 73; range for oral = 32, for written = 35; median for oral = 71, for written = 52
(iii) 17 students sat both exams (iv) Yes, the data on the stem and leaf is higher for the oral exam; the mean, median and mode are higher for the oral exam than the written
5. (i) Relate back to the original question; support with reasons based on analysis of the data collected; link evidence from the sample to the general population; use numerical statistics and descriptions of the graphs
(ii) Only as good as sample being analysed so sample should be large enough, random and representative; be wary of claims made which no information about the sample; statistics can be manipulated
6. (i) Statistics based on a bad sample; choice of average; using detached statistics; misleading graphs; biased questions
(ii) To show the results that they want to show
7. Many possible answers
Unit 8 Geometry revisited
Practice questions 8.1 2. (iii) |AM| = 4 cm, |BM| = 4 cm 3. (iii) |∠XYM| = 30°, |∠ZYM| = 30°
5. (ii) |AC| = 10 cm, |BD| = 10 cm 6. (ii)
10.(ii) |XZ| = 5 cm, |YZ| = 3 cm; 52
7. (ii) 38° is opposite 5 cm and 93° is opposite 8 cm
|∠PQR| = 60°, |∠PRQ| = 60°, |∠QPR| = 60°
= 42 + 32
11.(i) 5 cm and 2 cm are too small to meet on a triangle with a third side of 10 cm; the sum of any 2 sides of a triangle must be greater than the length of the third side
(ii) Some possible answers, e.g. 4 cm, 5 cm, 6 cm
Practice questions 8.2 3. (ii) Parallelogram 4. (iv) Rectangle 5. B: Draw a line m and a point P not on m. Choose a point Q anywhere on the line m and draw QP. C: Place the compass point on Q and draw an arc that crosses QP and line m. Label the points of intersection A and B. Using the same compass setting, place the compass point on P and draw an arc on QP. Label point C.
D: With a compass width |AB|, place the compass point on C and draw an arc such that it intersects the arc through C. Label the intersection of these arcs D. A: Draw PD. This line is parallel to line m.
Practice questions 8.3
1. (i) C = 124°, vertically opposite; A = 56°, straight line; D = 56°, vertically opposite
(ii) C = 100°, vertically opposite; A = 80°, straight line; D = 80°, vertically opposite
(iii) C = 149°, vertically opposite; A = 31°, straight line; D = 31°, vertically opposite
(iv) B = 30°, vertically opposite; A = 150°, straight line; D = 150°, vertically opposite
(v) D = 112°, vertically opposite; B = 68°, straight line; C = 68°, vertically opposite
(vi) A = 144°, vertically opposite; B = 36°, straight line; C = 36°, vertically opposite
3. (i) B = 113° (vertically opposite); A = 67° (straight line); D = 67° (vertically opposite A); E = 67° (alternate to D); F = 113° (corresponding to B); G = 113° (vertically opposite F); H = 67° (vertically opposite E)
(ii) E = 118° (vertically opposite); A = 118° (corresponding to E); D = 118° (vertically opposite A); G = 62° (straight line); F = 62° (vertically opposite G); C = 62° (alternate to F); B = 62° (corresponding to F)
(iii) H = 133° (vertically opposite); A = 133° (corresponding to 133°); D = 133° (alternate to 133°); F = 47° (straight line); G = 47° (vertically opposite F); C = 47° (alternate to F); B = 47° (vertically opposite to C)
(iv) C = 103° (vertically opposite); G = 103° (corresponding to C); F = 103° (vertically opposite to G); A = 77° (straight line); D = 77° (vertically opposite A); E = 77° (alternate to D); H = 77° (vertically opposite to E)
(v) F = 85° (vertically opposite); B = 85° (corresponding to F); C = 85° (alternate to F); A = 95° (straight line); D = 95° (vertically opposite A); E = 95° (alternate to D); H = 95° (vertically opposite E)
(vi) G = 81° (vertically opposite 81°); B = 81° (corresponding to 81°); C = 81° (vertically opposite B); H = 99° (straight line); E = 99° (vertically opposite H); D = 99° (alternate to E); A = 99° (vertically opposite D)
3. (i) 34°, 3 angles of a triangle sum to 180°
(ii) 35°, angles opposite equal sides in an isosceles triangle are equal
(iii) 16°, 3 angles of a triangle sum to 180°
(iv) 70°, vertically opposite angles and 3 angles in a triangle sum to 180°
(v) 16°, exterior angle is equal to the sum of the interior opposite angles
(vi) 9°, straight line and 3 angles in a triangle sum to 180°
4. (i) x = 14, y = 10 (opposite sides in a parallelogram are equal)
(ii) a = 79°, b = 101° (opposite angles in a parallelogram are equal, parallelogram angles sum to 360°)
(iii) r = 6, s = 3⋅5 (diagonals of a parallelogram bisect each other)
(iv) p = 5, a = 9 (opposite sides in a parallelogram are equal)
(v) m = 35°, n = 110° (opposite angles in a parallelogram are equal, parallelogram angles sum to 360°)
(vi) m = 8, k = 7 (diagonals of a parallelogram bisect each other)
5. (i) 25°, angles opposite equal sides in a triangle are equal
(ii) 130° (iii) 65°
6. (i) 150°, corresponding angle (ii) 95°, corresponding followed by straight angle
7. 19° 8. 25° 9. (i) SAS (ii) SSS (iii) ASA (iv) RHS
10.Congruent by SSS: |AB| = |CD|, opposite sides of a parallelogram are
equal; |BC| = |AD|, opposite sides of a parallelogram are equal; |BD| = |BD|, common side
11.Congruent by ASA: |∠DCG| = |∠GEF|, alternate angles; |CD| = |FE|, given; |∠CDG| = |∠GFE|, alternate angles
12.Congruent by RHS: |∠DGE| = |∠DGF|, right angle; |DE| = |DF|, equilateral triangle; |DG| = |DG|, common side
Answer key
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