7. (i) 324 (ii) 33⋅75 (iii) 14⋅06 (iv) 180 000 (or 1⋅8 × 105
3. (i) 20 (ii)
)
8. (i) €18 (ii) No, he is not correct; the new price of the ticket will be €14⋅40
(iii) When dealing with percentage increase or decrease, we must focus on the whole value involved (or any other valid mathematical explanation)
9. (i) 20% (ii) No, do not agree; David will pay back Robin €60 instead of €50 if he does this
10.€1⋅27 11.€3⋅79 12.(i) €888⋅89 (ii) 44⋅44%
13.(i) €26⋅67 (ii) 50%
4B Taking it further
1. Percentage mark-up is the ratio of profit with respect to the cost price, whereas percentage margin is the ratio of profit with respect to the selling price
2. (i) 50% (ii) 33%
3. (i) 38 cents (ii) 75%
4. Nikki purchased the camera for the lowest price; it was €10 cheaper than what Jakub paid
5. (i) €75, 150% (ii) €5 000, 25% (iii) €11 947⋅43, 19⋅47% (iv) €22 047⋅24, 4⋅99% (v) €400 000, 87⋅5%
6. (i)
(a) Mark-up = 87⋅5% (b) 46⋅7%
(ii) 525 t-shirts
7. €1 794⋅21 8. Yomi will receive £497.55 from Smart Savers OR £494.67 from Currency Converters, so they should chose Smart Savers
9. (i) $896 (ii) $1 = €1⋅12 (iii) 1⋅7%
10.(i) 62% (ii) 38% (iii) €100
Unit 5 Probability
Practice questions 5.1 1. (i) The outcome is a possible result of an experiment
(ii) The sample space is the set of all possible outcomes
(iii) An event is a successful outcome (iv) A trial is the act of doing an experiment in probability
2. (i)
_ 6
1
(ii) 5 (iii) 1 (iv) 0
_ 6
_ 2
_ 6
(a) 1
4 (i) 36 (ii) 1
(iii) Star, it is the most common shape
(iv) Star
5. (i) Nine possible combinations: coffee, muffin; tea, muffin; juice, muffin; coffee, cookie; tea, cookie; juice, cookie; coffee, fruit pot; tea, fruit pot; juice, fruit pot
(ii) 1 (iii) 1
_ 9
_ 3
6. (i) 24 outfits (ii) 6 outfits
(iii) 1
_ 8
_ 3
1 (iii) (a) 1
_ 3 588 000
_ 8
_ 8
= 1 024
__ 9; (b) 5
10.3 588 000 1
11.(ii) 2 (odd or even) (iii) 1
(iv) 3 (v) 210 Practice questions 5.2
1. 0⋅1 2. (i) 0⋅24 (ii) 0⋅76
3. (i) 0⋅7 (ii) Any valid mathematical answer,
e.g. the belief is false; more trials needed to create a more accurate answer
4. (i) 0⋅125 (ii) 0⋅08 (iii) The second example, as it has a larger sample of 1 000 TVs
(iv) 0⋅92
5. 0⋅15 6. The bottle will land upright 48 times 7. (i) A = 600, B = 0⋅125, C = 0⋅2, D = 0⋅15, E = 0⋅3, F = 1
(ii) Collie
8. (i) Frequency: 4, 4, 7, 5, 20; Relative frequency: 0.2, 0⋅2, 0⋅35, 0⋅25, 1
(ii)
(a) x = 15; Frequency: 20, 45, 15, 20, 100; Relative frequency: 0⋅2, 0⋅45, 0⋅15, 0⋅2, 1
(b) The spinner that is spun 100 times, as it is a larger sample.
9. (i) x = 0.08 (ii) 0.72 (iii) 0.4 (iv) 0.32
(c) 1 000
__ 9; (c) 4
__ 9; (iv) 27; (v) 1
__ 27
_ 24
7. (i) 0⋅5 (iii) 3
8. 0⋅1 9. (i)
(ii) WW, WD, WL; DW, DD, DL; LW, LD, LL
__ 4; (b) 3
__ 10; (c) 11
__ 20
(iv) Based on the data the die may appear to be biased, but the sample size is quite small. More trials needed to make an informed decision.
11.(i)
_ 6
1
(ii) Frequency: 92, 92, 76, 70, 91, 79; Relative frequency: 0⋅18, 0⋅18, 0⋅15, 0⋅14, 0⋅18, 0⋅16
(iii) Relative frequency and theoretical probability can differ by a small amount, however this difference can decrease as the sample size (or number of trials) increases
12.(i) 2, 3, 4, 5, 6; 3, 4, 5, 6, 7; 4, 5, 6, 7, 8 (ii) 1
__ 15
(iii) 90 (iv) 19 students received €8 back (v) No, they are incorrect. Supporting work and clear explanation must be shown for this answer.
Revision questions
5A Core skills 1. (i) 27 (ii) 18
(iii) 1 (iii) 1
_ 18
2. (i) 96 (ii) 48
_ 48
3. (i) y = 0⋅2 (ii) 4
4. (i) 150 (ii) 100
5. (a) has the highest relative frequency 6. (i) 50 (ii) Number of babies: 100, 150, 150, 100, 50, 30, 20; Relative frequency: 0⋅17, 0⋅25, 0⋅25, 0⋅17, 0⋅08, 0⋅05, 0⋅03
(iii) 0⋅17 OR 17%
7. (i) W = 13, D = 12, L = 15 (ii) Frequency = 0.325, 0.3, 0.375
8. (ii) 1 (iii) 5
_ 4
9. Higher 10.(ii) 0 (zero)
_ 7
(iv) Number 6
11.(i) Number 8 (ii) 1
_ 2
(iii) 60 (iv) x = 58; Relative frequency: 0⋅16, 0⋅17, 0⋅17, 0⋅18, 0⋅16, 0⋅16
(v) 0⋅67 OR 67% 5B Taking it further
1. Frequency: 2, 3, 2, 2, 3, 1, 1, 3, 2, 1; Relative frequency: 0.1, 0.15, 0.1, 0.1, 0.15, 0.05, 0.05, 0.15, 0.1, 0.05
2. (i) 0⋅79 (ii) Yes, the number of heads is too high
10.(i) 10 times (ii) Frequency: 4, 3, 3, 2, 3, 5, Total 20; Relative frequency: 0⋅2, 0⋅15, 0⋅15, 0⋅1, 0⋅15, 0⋅25, Total 1
(iii) 15 times Answer key 373
(iii) (a) 0⋅498 (b) 0⋅502 (iv) As the number of trials increases,
the actual number of heads and tails should move closer to the predicted value
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