Answer Key
University
High SchoolCourse
MPM1D | Principles of MathematicsPages
4
Academic year
2023
anon
Views
18
Review: Correlations, Algebra and Exponents Part A: 30 multiple choice [1 mark each]Part B: 15 full solution [75 marks]Exponent Laws π₯ π Γ π₯ π = π₯ π+π π₯ π Γ· π₯ π = π₯ πβπ π₯ π ( ) π = π₯ π Γπ π₯ 0 = 1, π₯ β 0 π₯π¦π§ ( ) π = π₯ π π¦ π π§ π π₯π¦ ( ) π = π₯ π π¦ π , π¦ β 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 11β6 = 2 5 = 2 Γ2 Γ2 Γ2 Γ2 = 32 b) β 3 ( ) 2 ( ) 3 = β 3 ( ) 2 Γ3
= β 3 ( ) 6 = (β 3)(β 3)(β 3)(β 3)(β 3)(β 3) = 729 c) β 1000 ( ) 0 = 1 d) 2π 3 ( ) β 9π 2 ( ) = 2 Γ β 9 ( )π 3 π 2 =β 18π 3+2 =β 18π 5 e) 3π₯ 3π¦ 6 ( ) β4π₯ 2π¦ ( ) β2π₯ 4 π¦ 4 = β12 π₯ 3+2 π¦ 6+1 β2π₯ 4 π¦ 4 = 6π₯ 5 π¦ 7 π₯ 4 π¦ 4 = 6π₯ 5β4 π¦ 7β4 = 6π₯π¦ 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
Review: Correlations, Algebra and Exponents
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