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Formulas: science and society, grade 10 (3 units)

Information and representations

  • p\displaystyle p percent of n\displaystyle n
    p%⋅n\displaystyle p\%\cdot n =\displaystyle = p100⋅n\displaystyle \frac{p}{100}\cdot n
  • A rate per 1,000 people – k\displaystyle k the number of cases, N\displaystyle N the number of people
    kN⋅1000\displaystyle \frac{k}{N}\cdot1000
  • The average rate of change between the points (x1,y1)\displaystyle (x_1,y_1) and (x2,y2)\displaystyle (x_2,y_2)
    y2−y1x2−x1\displaystyle \frac{y_2-y_1}{x_2-x_1}
  • A linear relation – m\displaystyle m the change in y\displaystyle y when x\displaystyle x grows by 1, b\displaystyle b the value of y\displaystyle y when x=0\displaystyle {x}={0}
    y=mx+b\displaystyle y=mx+b

Measures of centre

  • The mean of n\displaystyle n data
    xˉ=x1+x2+⋯+xnn\displaystyle \bar{x}=\frac{x_1+x_2+\dots+x_n}{n}
  • A weighted mean – w1,…,wk\displaystyle w_1, \dots, w_k the weights of the values x1,…,xk\displaystyle x_1, \dots, x_k
    xˉ=w1x1+w2x2+⋯+wkxkw1+w2+⋯+wk\displaystyle \bar{x}=\frac{w_1x_1+w_2x_2+\dots+w_kx_k}{w_1+w_2+\dots+w_k}
  • The mean of grouped data – m1,…,mk\displaystyle m_1, \dots, m_k the class middles, f1,…,fk\displaystyle f_1, \dots, f_k their frequencies
    xˉ≈m1f1+m2f2+⋯+mkfkf1+f2+⋯+fk\displaystyle \bar{x}\approx\frac{m_1f_1+m_2f_2+\dots+m_kf_k}{f_1+f_2+\dots+f_k}
  • The place of the median in an ordered list of n\displaystyle n data
    n+12\displaystyle \frac{n+1}{2}

Probability

  • Equally likely outcomes – k\displaystyle k the outcomes in the event A\displaystyle A, n\displaystyle n all the outcomes
    P(A)=kn\displaystyle P(A)=\frac{k}{n}
  • The complement A‾\displaystyle \overline{A} – A\displaystyle A does not happen
    P(A‾)\displaystyle P(\overline{A}) =\displaystyle = 1−P(A)\displaystyle 1-P(A)
  • A path of a tree diagram – the product of the probabilities p1\displaystyle p_1, p2\displaystyle p_2 on its branches
    P=p1⋅p2\displaystyle P=p_1\cdot p_2
  • An event of several paths – the sum of their probabilities
    P(A)=P1+P2+…\displaystyle P(A)=P_1+P_2+\ldots
  • Estimating a probability from relative frequency – A\displaystyle A happened f\displaystyle f times in n\displaystyle n experiments
    P(A)≈fn\displaystyle P(A)\approx\frac{f}{n}
  • How many times an event A\displaystyle A is expected to happen in n\displaystyle n experiments
    n⋅P(A)\displaystyle n\cdot P(A)