Study with the several resources on Docsity
Earn points by helping other students or get them with a premium plan
Prepare for your exams
Study with the several resources on Docsity
Earn points to download
Earn points by helping other students or get them with a premium plan
The final exam questions for a university-level mathematics course, covering topics such as simplifying expressions, factoring polynomials, rationalizing denominators, long division, distance and midpoint calculations, solving equations, function operations, graphing functions, and logarithms.
Typology: Exams
1 / 18
This page cannot be seen from the preview
Don't miss anything!
(Marks)
(a)
18 a^4 b−^2 c^4 12 ab−^3 d^3
(b)
√ (^3) − 27 x 18 √ 9 x−^16
x
[2] ÷ (3x)^0
[2] (a) 9x^4 − 25 y^2
[2] (b) 6a^2 b^2 + 9ab^2 + 3b^2
[2] (c) 5ax − 35 bx − 2 ay + 14by
(Marks)
(a)
x^2 + 5x − 24 x^2 + 6x − 16 ÷^
x^2 − 9 [3] 3 x (^2) − 6 x
(b)
x x − 2 x x − 2
− x x + 2
[2] 4. Rationalize the denominator and simplify: 9 3 +
x
(Marks) [1.5] (e) an equation of the line containing points A and B.
[1.5] (a) −3(x + 6) − (3x − 2) = 4
[2] (b) 6x^3 + 2x^2 = 4x
(Marks) [2] (c) (3x + 1)^2 − 2 = 0
[1.5] (d) 6 − 10 x < 9 − 2(3x + 6)
(e)
[2] x + 6 = x + 4
(Marks) [1] (b) find (g ◦ f )(x),
[1] (c) find the range of f (x),
[1] (d) find the domain of g(x),
[2] (e) find f −^1 (x), the inverse of f (x).
(Marks)
(a) find the vertex, the equation of the axis of symmetry, the y-intercept, and the x- [2] intercept(s),
[1] (b) find the range of g(x),
[2] (c) sketch the graph of g(x) and label all the information obtained in part (a).
(Marks)
−x^2 + 5 if x ≤ 3 3 x − 10 if x > 3
[1] (a) find f (7),
[2] (b) sketch the graph of f (x),
[1] (c) find the domain and the range of f (x).
(Marks)
[2] (a) graph the function,
[1] (b) find the domain and range of f (x),
[2] (c) find the coordinates of x and y-intercepts, and the equation of the asymptote.
(Marks) [2] 15. Simplify:
e2 ln 5^ + ln
e
[2] (a) 2x^2 −x^ = (0.5)−^3 −x
[2] (b) ex−^5 = 2
(Marks) [2] (c) log 3 (x + 16) − log 3 x = 2
[1] 17. If $25, 000 is invested at 4% interest compounded quarterly, what will the value of the invest- ment be after 10 years? (Round your answer to the nearest dollar.)
[2] 2 where θ is an acute angle, find sin θ and cot θ.
(Marks)
(b) tan^ y^ + cot^ y csc y
[2] = sec y
[2] 22. Find the side x to two decimal places.
x
[2] 23. Find the angle x.
x◦^7
(Marks) [2] 24. Find the exact value of csc 480◦.
[2] 25. Find the amplitude and period of f (x) = 2 cos(2x), then sketch two cycles of f (x).
