Question 10

Question 1: Algebra Solve the following equations for � x : a) 4 � −7=94 x −7=9 b) 2( � +3)=202( x +3)=20 Sample Answers: a) � =4 x =4 b) � =7 x =7 Question 2: Geometry Find the area and circumference of the following shapes: a) Circle with radius = 1010 cm. (Use � ≈3.14 π ≈3.14 ) b) Triangle with side lengths 66 cm, 88 cm, and 1010 cm. Sample Answers: a) Area = 314314 sq. cm, Circumference = 62.862.8 cm b) Area = 2424 sq. cm, Circumference = 2424 cm Question 3: Trigonometry

a) Find sin(30 ∘ )sin(30 ∘ ) and tan(60 ∘ )tan(60 ∘ ) . b) Solve the triangle XYZ: XY = 1212 cm, XZ = 1515 cm, and angle Y = 45 ∘ 45 ∘ . Sample Answers: a) sin(30 ∘ )=12sin(30 ∘ )= 21 , tan(60 ∘ )=3tan(60 ∘ )=3 b) YZ = 99 cm, angle X = 45 ∘ 45 ∘ , angle Z = 90 ∘ 90 ∘ Question 4: Calculus a) Compute lim � →0sin( � ) � lim x →0 x sin( x ) . b) Find the derivative of � ( � )=5 � 2−3 � +2 f ( x )=5 x 2 −3 x +2 . Sample Answers: a) The limit is 11 . b) � ′( � )=10 � −3 f ′ ( x )=10 x −3 Question 5: Statistics Calculate the mean, median, and range for the following data set: 15,18,21,24,27,30,33,36,3915,18,21,24,27,30,33,36,39

Question 8: Differential Equations Solve the differential equation: ���� =3 � 2+2 � −4 dxdy =3 x 2 +2 x −4 Sample Answer: � = � 3+ � 2−4 � + � y = x 3 + x 2 −4 x + C where � C is the constant of integration.