Diagnostic Assessment

1. Bananas cost $1.50 per kg. You have $4.25, what weight of bananas can you buy?

A) This is easy to do. I have seen this type of question.
B) This is a very hard question. I have seen this type of question.
C) This is very easy. I can do this question.
D) I have never seen this type of question. I cannot do this question.
E) This is a harder question. I have seen this type of question.

2. Calculate the value of "b" for the right triangle below.

A) This is easy to do. I have seen this type of question.
B) I have never seen this type of question. I cannot do this question.
C) This is a harder question. I have seen this type of question.
D) This is a very hard question. I have seen this type of question.
E) This is very easy. I can do this question.

3. Simplify this expression.

A) This is easy to do. I have seen this type of question.
B) This is a harder question. I have seen this type of question.
C) This is a very hard question. I have seen this type of question.
D) I have never seen this type of question. I cannot do this question.
E) This is very easy. I can do this question.

4. What is this expression's value when n = 5?

A) This is very easy. I can do this question.
B) I have never seen this type of question. I cannot do this question.
C) This is easy to do. I have seen this type of question.
D) This is a harder question. I have seen this type of question.
E) This is a very hard question. I have seen this type of question.

5. What is the slope (gradient) of the line that is perpendicular to the following line?

A) This is a harder question. I have seen this type of question.
B) I have never seen this type of question. I cannot do this question.
C) This is very easy. I can do this question.
D) This is easy to do. I have seen this type of question.
E) This is a very hard question. I have seen this type of question.

6. Solve this equation.

A) This is a harder question. I have seen this type of question.
B) This is a very hard question. I have seen this type of question.
C) This is very easy. I can do this question.
D) I have never seen this type of question. I cannot do this question.
E) This is easy to do. I have seen this type of question.

7. The formula for the surface area of a cone is A = πrs. The formula for the volume of a cone is V = πr²h ÷ 3. What is the surface area and the volume of this cone?

A) This is a harder question. I have seen this type of question.
B) This is easy to do. I have seen this type of question.
C) This is very easy. I can do this question.
D) I have never seen this type of question. I cannot do this question.
E) This is a very hard question. I have seen this type of question.

8. What is the value of the unknown angle?

A) I have never seen this type of question. I cannot do this question.
B) This is a harder question. I have seen this type of question.
C) This is very easy. I can do this question.
D) This is a very hard question. I have seen this type of question.
E) This is easy to do. I have seen this type of question.

9. Where is the point (coordinate) that these two lines meet?

A) This is very easy. I can do this question.
B) This is a harder question. I have seen this type of question.
C) This is a very hard question. I have seen this type of question.
D) I have never seen this type of question. I cannot do this question.
E) This is easy to do. I have seen this type of question.

10. Solve this equation.

A) This is a harder question. I have seen this type of question.
B) This is very easy. I can do this question.
C) I have never seen this type of question. I cannot do this question.
D) This is a very hard question. I have seen this type of question.
E) This is easy to do. I have seen this type of question.

11. Where is the point (coordinate) of intersection of the following two lines?

A) I have never seen this type of question. I cannot do this question.
B) This is a very hard question. I have seen this type of question.
C) This is a harder question. I have seen this type of question.
D) This is very easy. I can do this question.
E) This is easy to do. I have seen this type of question.

12. What is the slope (gradient) of the line that connects the two points: (-5, -11) and (7, 15)?

A) This is a harder question. I have seen this type of question.
B) I have never seen this type of question. I cannot do this question.
C) This is a very hard question. I have seen this type of question.
D) This is very easy. I can do this question.
E) This is easy to do. I have seen this type of question.

13. What is the equation of the line that is perpendicular (at a 90° angle) to 2x - 5y = -20 and passes through (8,-20)?

14. Use analysis (a formula) to calculate the length of RQ.

A) This is very easy. I can do this question.
B) I have never seen this type of question. I cannot do this question.
C) This is a very hard question. I have seen this type of question.
D) This is a harder question. I have seen this type of question.
E) This is easy to do. I have seen this type of question.

15. Where is the vertex and the x-intercepts of this parabola?

16. Fully simplify this expression.

A) This is very easy. I can do this question.
B) This is easy to do. I have seen this type of question.
C) This is a harder question. I have seen this type of question.
D) I have never seen this type of question. I cannot do this question.
E) This is a very hard question. I have seen this type of question.

17. What is the equation of the quadratic relation whose x-intercepts are at (-6, 0) and (14, 0) that passes through (-1, -84)?

A) This is a very hard question. I have seen this type of question.
B) This is very easy. I can do this question.
C) This is easy to do. I have seen this type of question.
D) This is a harder question. I have seen this type of question.
E) I have never seen this type of question. I cannot do this question.

18. A "factored" expression will have the form: x² + 11x + 30 = (x + 6)(x + 5). Factor the expression, 3y² - 21y - 24.

19. Solve the equation, 2x² + 5x - 14, using the given formula.

A) This is easy to do. I have seen this type of question.
B) This is very easy. I can do this question.
C) This is a harder question. I have seen this type of question.
D) This is a very hard question. I have seen this type of question.
E) I have never seen this type of question. I cannot do this question.

20. Use right-angled trigonometry to calculate the length of QS in this right angled triangle.

A) This is very easy. I can do this question.
B) This is a very hard question. I have seen this type of question.
C) This is easy to do. I have seen this type of question.
D) I have never seen this type of question. I cannot do this question.
E) This is a harder question. I have seen this type of question.

21. Use trigonometry to complete this application question.

A) This is very easy. I can do this question.
B) This is easy to do. I have seen this type of question.
C) This is a very hard question. I have seen this type of question.
D) This is a harder question. I have seen this type of question.
E) I have never seen this type of question. I cannot do this question.

22. Use sine law to calculate the unknown angle in this diagram.

A) I have never seen this type of question. I cannot do this question.
B) This is a harder question. I have seen this type of question.
C) This is a very hard question. I have seen this type of question.
D) This is very easy. I can do this question.
E) This is easy to do. I have seen this type of question.

23. Use cosine law to calculate the unknown side of this non-right triangle.

A) This is a very hard question. I have seen this type of question.
B) This is very easy. I can do this question.
C) This is a harder question. I have seen this type of question.
D) I have never seen this type of question. I cannot do this question.
E) This is easy to do. I have seen this type of question.

24. Given the function, g(x) = 2(x - 5)² - 9, what is the value of g(-3)?

A) This is a very hard question. I have seen this type of question.
B) I have never seen this type of question. I cannot do this question.
C) This is very easy. I can do this question.
D) This is easy to do. I have seen this type of question.
E) This is a harder question. I have seen this type of question.

25. If f(x) = 2x - 3, what is f^-1(x)?

26. Determine the domain and range for the following function.

A) This is very easy. I can do this question.
B) This is a very hard question. I have seen this type of question.
C) This is easy to do. I have seen this type of question.
D) This is a harder question. I have seen this type of question.
E) I have never seen this type of question. I cannot do this question.

27. Simplify the following expression; state any restrictions on the variable.

28. Based on the given description, calculate the temperature of the coffee after 48 minutes.

29. Prove the following trigonometric identity.

A) This is easy to do. I have seen this type of question.
B) This is a harder question. I have seen this type of question.
C) I have never seen this type of question. I cannot do this question.
D) This is a very hard question. I have seen this type of question.
E) This is very easy. I can do this question.

30. Based on the given description, what is the angle of sunset on February 15?

A) This is a very hard question. I have seen this type of question.
B) This is very easy. I can do this question.
C) I have never seen this type of question. I cannot do this question.
D) This is a harder question. I have seen this type of question.
E) This is easy to do. I have seen this type of question.

31. Expand and simplify:

A) This is very easy. I can do this question.
B) This is a harder question. I have seen this type of question.
C) This is easy to do. I have seen this type of question.
D) I have never seen this type of question. I cannot do this question.
E) This is a very hard question. I have seen this type of question.

32. Determine the sum of the first 25 terms of an arithmetic series in which t₁ = 91 and t₂₅ = 374

A) This is a harder question. I have seen this type of question.
B) I have never seen this type of question. I cannot do this question.
C) This is easy to do. I have seen this type of question.
D) This is a very hard question. I have seen this type of question.
E) This is very easy. I can do this question.

33. Eden borrows $2611.03 to buy a TV by making monthly payments of $106.17 for 2½ years. What annual interest rate, compounded monthly, is she being charged?

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