Question 8

Question 1: Algebra Solve the following equations for � x : a) 3 � +7=163 x +7=16 b) 2( � −5)=182( x −5)=18 Sample Answers: a) � =3 x =3 b) � =14 x =14 Question 2: Geometry Find the area and perimeter of the following shapes: a) Rectangle with length = 8 cm and width = 5 cm. b) Circle with radius = 6 cm. (Use � ≈3.14 π ≈3.14 ) Sample Answers: a) Area = 4040 sq. cm, Perimeter = 2626 cm b) Area = 113.04113.04 sq. cm, Circumference = 37.6837.68 cm Question 3: Trigonometry

a) Find sin(60 ∘ )sin(60 ∘ ) and cos(45 ∘ )cos(45 ∘ ) . b) Solve the triangle XYZ: XY = 55 cm, XZ = 77 cm, and angle Y = 30 ∘ 30 ∘ . Sample Answers: a) sin(60 ∘ )=32sin(60 ∘ )= 23 , cos(45 ∘ )=22cos(45 ∘ )= 22 b) YZ = 1010 cm, angle X = 90 ∘ 90 ∘ , angle Z = 60 ∘ 60 ∘ Question 4: Calculus a) Compute lim � →3 � 2−9 � −3lim x →3 x −3 x 2 −9 . b) Find the derivative of � ( � )=3 � 4−2 � 2+5 f ( x )=3 x 4 −2 x 2 +5 . Sample Answers: a) The limit is 66 . b) � ′( � )=12 � 3−4 � f ′ ( x )=12 x 3 −4 x Question 5: Statistics Calculate the mean, median, and mode for the following data set: 15,18,20,22,25,30,35,4015,18,20,22,25,30,35,40 Sample Answers:

Question 8: Differential Equations Solve the differential equation: ���� =3 � 2−6 � +9 dxdy =3 x 2 −6 x +9 Sample Answer: � = � 3−3 � 2+9 � + � y = x 3 −3 x 2 +9 x + C where � C is the constant of integration.