1. Graph the following functions f(x) =2x+13, if x>-5 and f(x) = x+ (1/2), if x<-5.
2. Find the maximum or minimum value of the function and then state the domain and range of the function y=8-3x-4x2.
3. Graph the equation y=|x+4|-5 and find its domain and range.
4. How many ways can 3 identical pen sets and 5 identical watches are given to 8 graduates if each receives one item?
5. Golf balls cost $0.90 each at Jerzy's Club, which has an annual $25 membership fee. At Rick & Tom's sporting-goods store, the price is $1.35 per ball for the same brand. Where you buy your golf balls depends on how many you wish to buy. Explain, and illustrate your reasoning for the above by drawing a graph.
6. If a and b are positive integers and a^2 - b^2 = 7, find the values of a and b.
7. A bacteria culture has an initial population of 600. After 4 hours the population has grown to 1200. Assuming the culture grows at a rate proportional to the size of the population, find the function representing the population size after t hours and determine the size of the population after 8 hours
8. A company involved in the assembly and distribution of printers in concerned with two types - laser and inkjet. Assembly of each laser printer takes 2 hours, while each inkjet printer takes 1 hour to assemble, and the staff can provide a total of 40 person-hours of assembly time per day. In addition, warehouse space must be available for the assembly and distribution of the printers,1m2for each laser printer and 3m2 for each inkjet printer; the company has a total of 45m2 of storage space available for assembled printers each day. Laser printers can be sold for a profit of Rs.30 per unit and inkjet printers earn a profit of Rs.25 each, but the market in which the company is operating can absorb a maximum of 12 laser printers per day. (There is no such limitation on the market for inkjet printers). Find the number of each type of printer the company should assemble and distribute in order to maximize daily profit.
9. Consider a quadratic equation (a+3) x2 + 2(1-a) x = -a + 1, has two different roots. Find the range values of a.
10. Find the sum of a geometric series for which a1 = 48, an = 3, and r = -1/2.
11. If the complex number z1 and z2 is represented by points A and B respectively on the Argand Plane, show that the middle point of AB will represent the complex z1+z2/2.
12. A sofa, love seat, and one chair cost $1600. A sofa and 2 chairs cost $1400. A sofa and a love seat costs $1300. What would just a sofa cost?
13. A surgery is performed for 7 patients you are told that 70 percent chance is for success. Find the probability that the surgery is successful for exactly 5 patients, at least 5 patients and less than 5 patients.
14. Question says that there is a triangle with a base of x units and height h units and two sides of length 10 units. Answer the following questions:
- Draw a representation of this situation (the triangle).
- Find a formula for h in terms of x.
- What is the domain of this function?
- Graph this function over its domain.
- How does h change as x changes?
- Find a formula for the area of the triangle in terms of x only. Graph this function.
- How does the area of the triangle change as x changes?
- For what value of x is the area of the triangle largest?
- For what value of h is the area of the triangle largest?
15. Consider the set S = {1, 2, 3, ..., 1000}. How many arithmetic progressions can be formed from the elements of S that start with 1 and end with 1000 and have at least 3 elements?
16. If A, B and C are matrices with orders 3×3, 4×3 and 3×2 respectively, which of the following matrix calculations are possible? 4B, A + B, 3BT + C, AB, BA, (CB)T, CBA.
17. Find zero(s) of a radical function,.
18. If roots of the equation x2 - 5x + 16 = 0 are α, β and roots of the equation X2 + px + q = 0 are α2 + β2 and 2α β then find the values of p and q?
19. Find the points on the parabola y2 = 16x which are at a distance of 13 units from the focus.
20. Find the angle between two asymptotes of the hyperbola x2 - 2y2 = 1.