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Maths 114 past papers with memos
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Voorletters en van Studentenr.: .................................... : ................
Initials and surname Studentno.
Omkring die naam van jou dosent:
Circle the name of your lecturer: Breuer | de Villiers | Nyabadza | Wagner
Wiskunde / Mathematics 114
Klastoets / Class Test
25 April 2012
Tyd / Time: 2h Volpunte / Full marks: 60
INSTRUKSIES: INSTRUCTIONS:
• Hierdie vraestel bestaan uit 9 genommerde This paper consists of 9 numbered pages.
bladsye.
• Vrae wat met ’n * gemerk is, is meer uitda- Questions marked with a * are more challenging.
gend.
• Skryf die antwoorde direk op die vraestel. Write your answers directly on the question paper.
• Geen sakrekenaars toegelaat nie. No calculators allowed.
• Indien die linkerbladsye anders as vir rofw- If the left hand pages are used for other than rough
erk gebruik word, moet dit duidelik aangedui work, this must be indicated clearly.
word.
AFDELING A SECTION A
Skryf slegs die antwoorde in die blokkies, of omkring Write only the answers in the boxes, or circle the
die korrekte antwoord(e). correct answer(s). [30]
π π
1. Skryf die hoek α = 10 in grade. Write the angle α = 10 in terms of degrees.
α= [2]
2. Los op vir x: / Solve for x:
|x + 2| = |2x + 1| x= [2]
3. Bepaal die vergelyking van die reguit lyn wat Determine the equation of the straight line that is
loodreg is op die lyn x + 4y = −3 en wat deur perpendicular to the line x + 4y = −3 and passes
die punt (−1, 3) gaan. through the point (−1, 3).
y= x+ [2]
4. Watter van die volgende bewerings is altyd Which of the following statements is always true, in-
waar, onafhanklik van die waarheidsgehalte dependent of the truth of A? (Circle the correct an-
van A? (Omkring die korrekte antwoord(e).) swer(s).)
A ∧ (¬A), ¬(A ∨ (¬A)), A ∨ (¬A), ¬(A ∧ A).
1
, [2]
5. Bepaal die definisieversameling van die vol- Find the domain of the following function.
gende funksie.
1
f (x) = √ Df = [2]
x2 − 16
6. Bepaal (g ◦ f )(0) indien Determine (g ◦ f )(0) if
1 √
f (x) = 2 , en / and g(x) = x+4 (g ◦ f )(0) = [2]
x −2
7. Bereken die volgende limiete. Compute the following limits.
√
1 − 1 − x2
(a) lim = [2]
x→0 x2
2 − x2
as / if 1 < x ≤ 2
(b) As / If g(x) = , dan is / then
x−3 as / if x > 2
lim g(x) = [1]
x→2−
lim g(x) = [1]
x→2+
8. Bereken die volgende afgeleides. Compute the following derivatives.
d x2 + 1
(a) = [2]
dx 3x − 1
d
(b) sin5 (3x2 ) = [2]
dx
d2 √
(c) cos2 ( x) = [2]
dx2 x= π4
2
d2012
(d*) cos(2x) = [2]
dx2012
9. Gebruik die volgende tabel van waardes van Use the following table of values of f, g, f 0 and g 0 to
f, g, f 0 en g 0 om h0 (1) te bepaal as h(x) = determine h0 (1) if h(x) = f (g(x)).
f (g(x)).
x f (x) g(x) f 0 (x) g 0 (x)
1 3 2 4 6
2 1 8 5 7
3 7 2 7 9
h0 (1) = [2]
10. Indien / If y 3 + y = x2 − 2 dan / then
y 00 |(x,y)=(2,1) = [2]
2
, 11. Vir For
f (x) = x4 − 8x2 + 17,
laat A die absolute maksimum en B die abso- let A be the absolute maximum and B the absolute
lute minimum van f (x) op [−1, 3] wees. Dan minimum of f (x) on [−1, 3]. Then
A= [1]
B= [1]
Blaai om, asseblief. Please turn the page.
3
, AFDELING B SECTION B
Wys alle bewerkings. Show all work. [32]
1. Vereenvoudig so ver as moontlik: Simplify as far as possible:
[4]
(tan2 x − sin2 x) cosec2 x cot2 x =
2. Los die ongelykheid op en skryf die oplossing Solve the inequality and write the solution in interval
in intervalnotasie. notation. [4]
x+2
> x.
x
4
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