Reference no: EM13544550
1. Use your calculator and calculate the value of the following, write your answer in fractions.
a) tan 60o - tan 30o/1 + tan30o.tan60o
b) 5 tan 60° -3 sin 60°
2. Solve the following triangle.
![1964_Calculate the area of the triangle.png](https://secure.expertsmind.com/CMSImages/1964_Calculate%20the%20area%20of%20the%20triangle.png)
3. Solve the following triangle and calculate the area of the triangle.
![156_Calculate the area of the triangle1.png](https://secure.expertsmind.com/CMSImages/156_Calculate%20the%20area%20of%20the%20triangle1.png)
4. Evaluate the following
(a) secant 5.37 (b) cosecant
(c) cotangent Π/24
5. Evaluate the following trignomentric functions
(s) sec-1 2.3164 (b) cosec-1 1.1784
(c) cot-1 2.1273
6. In a triangle XYZ, ?X = 51°, ?Y=67° and YZ=15.2 cm. Solve the triangle and find its area. (Apply sine or cosine rule accordingly)
7. Sole the follwing triangle and find the area of the triangle.
![1131_Calculate the area of the triangle2.png](https://secure.expertsmind.com/CMSImages/1131_Calculate%20the%20area%20of%20the%20triangle2.png)
8. Prove the following identities
a) cos²x tan²x + cos²x = 1
b) 1 + cotθ/1 + tanθ = cotθ
c) 1/cos2x - 1/cot2x - 1/cosec2x = cos2x
9. Expand
(x³-x+1) (x³-2x²-1)
10. Factorise the following
a) 5x²y - 10ax² + 5x²
b) X(2a-y) + 3b(2a-y)
c) K(2x-1) - m(1-2x)
d) 16a² - 25b²c²
e) t² - t - 6
f) 2x² - 5x + 3
11. Simplify sin (45° + ?) - sin (45° - ?)
12. Factorise where possible and simplify
(3x² - 7x + 4) / (x² - 1)
13. Given that the roots/solutions of the quadratic equation ax2+ bx + c =0 are x1,2 = -b ± √(b2 -4ac)/2a, solve the equation below, giving the roots correct to three significant figures: -4y2 + 3y + 2 = 0.
14. Solve the following
(2t - 1)/ 3 = (9 - 2t) / 6t
15. Evaluate the following
(a) log3 9 (b) log10 10 (c) log16 8
16. Simplify the following
a) Log 4 + log 0.25
b) Log 3 - log 2 - log 6
c) Log2 100
17. Solve the following exponential functions using logarithms
a)4(3-x) = 2√2
18. Given that
M - 5t = 3
-2m + 4t = -1
Evaluate using determinent method a)Δ b) Δ m c) Δt
19. Write each of the following in the form a log x + b log y + . . .
a) log P/Qn
b) log (xy)n
20. Find the product of the two matrices given below
![583_Calculate the area of the triangle3.png](https://secure.expertsmind.com/CMSImages/583_Calculate%20the%20area%20of%20the%20triangle3.png)
21.
![704_Calculate the area of the triangle4.png](https://secure.expertsmind.com/CMSImages/704_Calculate%20the%20area%20of%20the%20triangle4.png)
Write down the matrix A.
22. For the system of forces acting at a point, determine the magnitude and direction of the resultant force.
![572_Calculate the area of the triangle5.png](https://secure.expertsmind.com/CMSImages/572_Calculate%20the%20area%20of%20the%20triangle5.png)
23. Expand (i.e. multiply out):
a) 4n-2/3(n-2n-1/2)
b) (et + e-t)(et - e-t)
24. Multiply and divide out, expressing in simplest exponential form:
a) e-x - ex/ex
b) 2x1/2(3x-1/2 - 6x0)/3x
25. Draw the graph for the following sine function. (Use the graph sheet attached)
Y = 5 cos (½) x - 3