Math Test Review
All answers should be left in simplified, reduced from unless you are told to round to a specific number of decimal places.
Knowledge (Answers should be in exact values only)
1. Simplify the following rational expressions.
3 √27 + 5√28 -- 4√63 -- √12 (3√7 – 3)2
2. Determine the maximum or minimum value for y = -3(x + 1)( x – 4) and state the value of x for which this occurs. Use your own convenient way.
3. Determine the number of zeros for the following functions:
Y = 2x² -- 11x – 4 y = - ½ (x – 3)² + 9
4. Determine the values of k for which the function f(x) = 4x² - 3x + 2kx + 1 has two zeros.
5. Determine the number of POI of the following linear – quadratic system, then solve the system.
Y = 2x² + 4x – 11
Y = -6x + 8
6. The height, h(t), of a baseball in metres, at time t seconds after it is tossed out of a window is modelled by the function h(t) = --5t² + 20t +15 a) For how long will the ball stay 20 metres above the ground? (a diagram might help)
b) A boy shoots at the baseball with a paintball gun. The trajectory of the paintball is given by the function g(x) = 3t +3. Will the paintball hit the baseball? If so, when? At what height will the baseball be?
7. A rectangular field with an area of 8000 m² is enclosed by 400 m of fencing. Determine the dimensions of the field to the nearest tenth of a metre.
8. Given f(x) = 3(x – 1)² - 2, determine he following. Thinking & Communication
A) F(-3) B) F¯¹ (x)
C) The domain and range of F¯¹ D) F¯¹ (10)
E) is the inverse a function? If not, how can you restrict the domain and range of the original function, so that the inverse is also a function? Graph the function and inverse if needed. | | | | | | | | | | | | | |
Knowledge (Answers should be in exact values only)
1. Simplify the following rational expressions.
3 √27 + 5√28 -- 4√63 -- √12 (3√7 – 3)2
2. Determine the maximum or minimum value for y = -3(x + 1)( x – 4) and state the value of x for which this occurs. Use your own convenient way.
3. Determine the number of zeros for the following functions:
Y = 2x² -- 11x – 4 y = - ½ (x – 3)² + 9
4. Determine the values of k for which the function f(x) = 4x² - 3x + 2kx + 1 has two zeros.
5. Determine the number of POI of the following linear – quadratic system, then solve the system.
Y = 2x² + 4x – 11
Y = -6x + 8
6. The height, h(t), of a baseball in metres, at time t seconds after it is tossed out of a window is modelled by the function h(t) = --5t² + 20t +15 a) For how long will the ball stay 20 metres above the ground? (a diagram might help)
b) A boy shoots at the baseball with a paintball gun. The trajectory of the paintball is given by the function g(x) = 3t +3. Will the paintball hit the baseball? If so, when? At what height will the baseball be?
7. A rectangular field with an area of 8000 m² is enclosed by 400 m of fencing. Determine the dimensions of the field to the nearest tenth of a metre.
8. Given f(x) = 3(x – 1)² - 2, determine he following. Thinking & Communication
A) F(-3) B) F¯¹ (x)
C) The domain and range of F¯¹ D) F¯¹ (10)
E) is the inverse a function? If not, how can you restrict the domain and range of the original function, so that the inverse is also a function? Graph the function and inverse if needed. | | | | | | | | | | | | | |