2017 A-level H1 Mathematics (8865) Paper 1 Suggested Solutions

All solutions here are SUGGESTED. Mr. Teng will hold no liability for any errors. Comments are entirely personal opinions.

Numerical Answers (click the questions for workings/explanation)

Question 1:
Question 2:
Question 3:
Question 4:
Question 5:
Question 6: \mu = 1.69, \sigma^2 = 0.0121
Question 7: 0.254; 0.194; 0.908
Question 8: 40320; 0.0142; \frac{1}{4}
Question 9: \text{r}=0.978; a=0.182, b=2.56; 293 Question 10:latex 0.0336; \bar{y}=0.64, s^2 = 0.0400; Sufficient evidence. Question 11:latex \frac{48+x}{80+x}, \frac{32+x}{80+x}; x= 16; \frac{25}{32}; \frac{7}{16}; \frac{341}{8930}Question 12:latex 0.773; 0.0514; 0.866; 0.362[showhide type="Q1" more_text="Q1" less_text="Hide Q1"]  [/showhide]  [showhide type="Q2" more_text="Q2" less_text="Hide Q2"]  [/showhide]  [showhide type="Q3" more_text="Q3" less_text="Hide Q3"]  [/showhide]  [showhide type="Q4" more_text="Q4" less_text="Hide Q4"]  [/showhide]  [showhide type="Q5" more_text="Q5" less_text="Hide Q5"]  [/showhide]  [showhide type="Q6" more_text="Q6" less_text="Hide Q6"]  Letlatex Xdenote the height of adult males.latex X \sim \text{N} (\mu, \sigma^2) latex \text{P}( X \textless 1.6) = 0.2latex \text{P}( Z \textless \frac{1.6 – \mu}{\sigma}) = 0.2latex \frac{1.6 – \mu}{\sigma} = -0.8416212335 latex 1.6 = -0.8416212335 \sigma + \mu ---(1)latex \text{P}( X \textgreater 1.75 ) = 0.3latex \text{P}( X \textless 1.75 ) = 0.7latex \text{P}( Z \textless \frac{1.75 – \mu}{\sigma} ) = 0.7latex \frac{1.75 – \mu}{\sigma} = 0.5244005101latex 1.75 = 0.5244005101 \sigma + \mu---(2)  Using GC,latex \mu = 1.69241, \sigma = 0.1098079154Meanlatex = 1.69Variancelatex = 0.0121[/showhide]  [showhide type="Q7" more_text="Q7" less_text="Hide Q7"]  (i) Letlatex Xdenote number of ink cartridge that last for one week or more, out of 8.latex X \sim \text{B}(8, 0.7)latex \text{P}(X =5) = 0.254(ii) Letlatex Ydenote number of ink cartridge that last for less than one week, out of 8.latex Y \sim \text{B}(8, 0.3)latex \text{P}(Y \ge 4)latex = 1 – \text{P}(Y le 3)latex = 0.19410435 \approx 0.194 (iii) Letlatex Wdenote number of boxes of ink cartridges that will have at least half of the cartridges lasting less than one week, out of 6 boxes.latex W \sim \text{B} (6, 0.19410435)latex \text{P} ( W \le 2)latex = 0.9082304639 \approx 0.908[/showhide]  [showhide type="Q8" more_text="Q8" less_text="Hide Q8"] (i)latex {{6}\choose{3}} \times 3! \times {{8}\choose{3}} \times 3! = 40320ways  (ii) (a)latex \bigg[ {{5}\choose{1}} \times \frac{3!}{2!} + {{5}\choose{2}} \times 3! \bigg] \times {{7}\choose{1}} \times \frac{3!}{2!} = 1575Required probabilitylatex = \frac{1575}{6^3 \times 8^3} = 0.0142(b)latex \text{P}(\text{has~}2\text{~as~its~first~character}) = \frac{1}{6}latex \text{P}(\text{has~H~as~its~sixth~character}) = \frac{1}{8}latex \text{P}(\text{has~}2\text{~as~its~first~character~and~has~H~as~its~sixth~character}) = \frac{1}{6 \times 8} = \frac{1}{48}Required probabilitylatex = \frac{1}{6} + \frac{1}{8} – 2(\frac{1}{48}) = \frac{1}{4}[/showhide]  [showhide type="Q9" more_text="Q9" less_text="Hide Q9"] (i) Graph to be inserted  (ii) Using GC,latex \text{r}=0.978This show that there is a strong positive linear correlation between the weekly earnings of an employee and the number of years the employee is with the company.  (iii) Using GC,latex a=0.182, b=2.56 (iv)latex y = 0.1821185456 x + 2.564419724Letlatex x = 2, y = 0.1821185456 (2) + 2.564419724latex \Rightarrow y = 2.9287Thus, the employee earns an estimated weekly earnings of293.

(v)
Firstly, the linear model is not appropriate here. Since it suggests as the number of years increases, the weekly earnings will increase proportionately, which is not realistic.

Secondly, x = 2 is out of data range and this is extrapolation, which is a bad practice since our trend might not continue out of data range.
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KS Comments

Showing 3 comments
  • Leah
    Reply

    Hello!! Will you be uploading the answers for this paper? Thank you so much!!!!

    • KS Teng
      Reply

      yes, sorry was having a H2 math class for J2 just now.

      • Leah
        Reply

        it’s ok!! Thank u for doing this 🙂

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