Algebra Statistics Calculus Worksheet

1. Calculate the following: a. What is (y+5)4 b. Simplify, if possible, 2×2 −3x+6x−2 c. What is the LCM of 10, 15 and 20? 2. Determine if a=−1 is a solution to 4a −a2 +11=−2 − 2a. 3. Solve the simultaneous equations x + y = 5 and y = x +1 using graphs. 4. Solve the simultaneous equations (Linear and quadratic) y = x2 and y = x + 2 using graphs. 5. Calculate the following: a. The coordinates of two points are A (-1, -3) and B (5, 7). Calculate the equation of the perpendicular bisector of AB. b. The line y = 2x – 3 meets the x-axis at the point P, and the line 3y + 4x = 8 meets the x-axis at the point Q. The two lines intersect at the point R. Find the coordinates of R. 6. Find the coordinates of the vertices of triangle TRI with T(2, −1),R( 4, 3) and I(−3, −2) if it is to be moved 5 units to the left and 2 units up. 7. Sketch the graph of the function f(x) = ax for the following values of a, on the same axes. a. a = 3 b. a = 6 c. a = 1 d. a = 1/3 e. a = 1/6 8. Sketch the graph of the function f(x) = logax for the following values of a, on the same axes. f. a=3 g. a = 6 h. a = 1/3 i. a = 1/6 9. The sector of a circle has centre C as shown. Find the area of the sector and the arc length to 1decimal place. 10. A tree 50 m tall casts a shadow 60 m long. Find the angle of elevation of the sun at that time. 11. The position of an object at any time t is given by s(t) = 3t4 − 40t3 + 126t2 − 9. Determine the velocity of the object at any time t. 12. An alternating voltage is given by v = 282.8 sin314t volts. Find a. the rms voltage, b. the frequency and c. the instantaneous value of voltage when t = 4 ms.