Grade 12 Mathematics AssessmentInstructions: Answer each question carefully. Write your answer in the space provided.Please enable JavaScript in your browser to complete this form.Please enable JavaScript in your browser to complete this form.Name *FirstLastGrade *Contact Number *Phone number or WhatsApp numberEmail *1. Solve for x: 2x²-5x+3=02. Simplify the expression: (x²−4x+3)−(2x²−x−1)3. Factor the expression: x²−6x+94. Solve for x: x²+4x−5=05. Find the inverse of the function: f(x)=3x−46. Solve for x: 3x-2 / x+1 = 4 7. Solve for y: 5y−7=2(3y+1)8. Find sin(45°)9. Solve for x: cos (x)=1/2, where 0°≤x<360°10. Solve for θ: tan(θ)=1, where 0°≤𝜃<360°11. Find cos(120°)12. Simplify the expression: 2sin(x)cos(x)13. If sin sin (x) = 1/3, find cos (x) using the identity sin²(x) + cos² (x) =114. Find sin(90°)15. Differentiate the function f(x)=3x²-5x²+2x-116. Find the derivative of g(x)=sin (x) +cos (x)17. Find the integral of 5x⁴dx18. Find the area under the curve of f(x)=x² from x = 0 to x=3integration:19. Find the derivative f′(x)20. Find the second derivative of f′′(x)21. Find the equation of the tangent line to the curve y=x²+1 at x=2.22. If two dice are rolled, what is the probability of rolling a sum of 7?23. Find the mean of the following data set: 3,5,7,8,1024. Find the standard deviation of the data set: 2,4,6,8,10 the x²−6x+9 face 25. A card is drawn from a deck of 52 cards. What is the probability of drawing a King?26. If a coin is tossed 3 times, what is the probability of getting exactly 2 heads?27. Find the probability of drawing a red card or a face card from a deck of 52 cards:28. A survey found that 70% of people prefer tea over coffee. If 5 people are selected randomly, what is the probability that exactly 3 prefer tea?29. Find the dot product of the vectors a=(a₁,a₂,a₃) and b=(b₁,b₂,b₃) is30. What is the volume of a cube with a side length of 6 cm?Assess My Answers
