Review: Correlations, Algebra and Exponents

Review: Correlations, Algebra and Exponents Part A: 30 multiple choice [1 mark each]Part B: 15 full solution [75 marks]Exponent Laws 𝑥 𝑚 × 𝑥 𝑛 = 𝑥 𝑚+𝑛 𝑥 𝑚 ÷ 𝑥 𝑛 = 𝑥 𝑚−𝑛 𝑥 𝑚 ( ) 𝑛 = 𝑥 𝑚 ×𝑛 𝑥 0 = 1, 𝑥 ≠0 𝑥𝑦𝑧 ( ) 𝑚 = 𝑥 𝑚 𝑦 𝑚 𝑧 𝑚 𝑥𝑦 ( ) 𝑚 = 𝑥 𝑚 𝑦 𝑚 , 𝑦 ≠0 1. Use the exponent laws (rules) to express each as a single power. Evaluate whereappropriate. a) 2 4 2 7 ( ) 2 6 = 2 4+7 2 6 = 2 11−6 = 2 5 = 2 ×2 ×2 ×2 ×2 = 32 b) − 3 ( ) 2 ( ) 3 = − 3 ( ) 2 ×3

= − 3 ( ) 6 = (− 3)(− 3)(− 3)(− 3)(− 3)(− 3) = 729 c) − 1000 ( ) 0 = 1 d) 2𝑚 3 ( ) − 9𝑚 2 ( ) = 2 × − 9 ( )𝑚 3 𝑚 2 =− 18𝑚 3+2 =− 18𝑚 5 e) 3𝑥 3𝑦 6 ( ) −4𝑥 2𝑦 ( ) −2𝑥 4 𝑦 4 = −12 𝑥 3+2 𝑦 6+1 −2𝑥 4 𝑦 4 = 6𝑥 5 𝑦 7 𝑥 4 𝑦 4 = 6𝑥 5−4 𝑦 7−4 = 6𝑥𝑦 3 2. Simplify each expression completely. a) 4p+7q-3q-p =4p-p+7q-3q =3p+4q b) 4(3w-1)-3(2w-5) =4(3w)+4(-1)-3(2w)-3(-5)

=12-4-6w+15 =12-6w+15-4 =6w+11 3. The yearly interest, I, in dollars, is given by the formula I=0.11P where P is theprincipal. Determine the principal that provides an interest of $159.30, in one year. Solution: I=159.30 Sub. I in I=0.11P 159.30=0.11P (159.30)/(0.11)=(0.11P)/(0.11) P=1448.18 The principal that provides an interest at $159.30 in one year is $1448.18 4. Doctors measured the ages, in months, and the heights, in centimeters, of a sampleof baby boys. results were recorded as follows. Age (months) 0 15 18 9 1 3 6 10 Height(cm) 56 84 85 76 54 57 70 66 a) Identify the independent and dependent variables Age - indep.variable Height - dep. variable b) Draw a scatter plot for the data on the grid below and then draw a line of best fitthrough the data points.

c) Using your line of best fit, predict the height of a baby boy who is 12 months old.A 12-month old baby is approx. 75 cm tall