Question 9

Question 1: Algebra Solve the following equations for � x : a) 2 � +5=152 x +5=15 b) 3( � −4)=213( x −4)=21 Sample Answers: a) � =5 x =5 b) � =9 x =9 Question 2: Geometry Find the area and perimeter of the following shapes: a) Square with side length = 1212 cm. b) Triangle with base = 1010 cm and height = 88 cm. Sample Answers: a) Area = 144144 sq. cm, Perimeter = 4848 cm b) Area = 4040 sq. cm, Perimeter = 2828 cm Question 3: Trigonometry

a) Find tan(45 ∘ )tan(45 ∘ ) and cos(30 ∘ )cos(30 ∘ ) . b) Solve the triangle XYZ: XY = 55 cm, XZ = 88 cm, and angle Y = 60 ∘ 60 ∘ . Sample Answers: a) tan(45 ∘ )=1tan(45 ∘ )=1 , cos(30 ∘ )=32cos(30 ∘ )= 23 b) YZ = 1010 cm, angle X = 30 ∘ 30 ∘ , angle Z = 90 ∘ 90 ∘ Question 4: Calculus a) Compute lim � →2 � 2−4 � −2lim x →2 x −2 x 2 −4 . b) Find the derivative of � ( � )=4 � 3−3 � 2+7 � −2 f ( x )=4 x 3 −3 x 2 +7 x −2 . Sample Answers: a) The limit is 44 . b) � ′( � )=12 � 2−6 � +7 f ′ ( x )=12 x 2 −6 x +7 Question 5: Statistics Calculate the mean, median, and standard deviation for the following data set: 12,14,16,18,20,22,24,26,2812,14,16,18,20,22,24,26,28

Question 8: Differential Equations Solve the differential equation: ���� =2 � −5 dxdy =2 x −5 Sample Answer: � = � 2−5 � + � y = x 2 −5 x + C where � C is the constant of integration