I. PART 1
QUESTION 01
\(2 \sqrt{12} - 3 \sqrt{6} : \sqrt{18} = \bbox[10px, border: 2px solid red]{(1)}\).
QUESTION 02
\(\dfrac {x^2 - x - 6}{x^2 + x - 2} - \dfrac{2x - 4}{x - 1} = \bbox[10px, border: 2px solid red]{(1)}\).
QUESTION 03
When \(\alpha + \beta = 2\) and \(\alpha \beta = 4\), then \(\alpha^2 + \beta^2 = \bbox[10px, border: 2px solid red]{(1)}\) and \(a^3 = \bbox[10px, border: 2px solid red]{(2)}\).
QUESTION 04
The smallest solutions of equation \(x^4 - 13x^2 + 36 = 0\) is \(\bbox[10px, border: 2px solid red]{(1)}\).
QUESTION 05
The solutions of equation \(\sin^2 x - \cos x + 1 = 0\) where \(0^{\text{o}} \leq x < 360^{\text{o}}\) is \(\bbox[10px, border: 2px solid red]{(1)}\).
QUESTION 06
The solutions of equation \(2 \log_{10} (x - 4) - \log_{10} 4(x - 1) = 0\) is \(\bbox[10px, border: 2px solid red]{(1)}\)
QUESTION 07
The area of the common region expressed by two inequalities \(x^2 + y^2 \leq 4\) and \(x + y \leq -2\) is \(\bbox[10px, border: 2px solid red]{(1)}\). Circular constant: \(\pi\).
QUESTION 08
There are five boys and five girls.
(i) How many ways can three be chosen from ten? The answer is \(\bbox[10px, border: 2px solid red]{(1)}\)
(ii) How many ways can three boys and two girls be chosen from the ten? The answer is \(\bbox[10px, border: 2px solid red]{(2)}\)
QUESTION 09
If sequence \(a_1 = 1, a_2 = 4, a_3 = 7, a_4= 10, \dotso\) then \(a_{30} = \bbox[10px, border: 2px solid red]{(1)}\).
QUESTION 10
Let vector \(\overrightarrow a = (2,3)\) and \(\overrightarrow b = (x,2)\). When \(\overrightarrow a\) and \(\overrightarrow b\) are vertical, \(x = \bbox[10px, border: 2px solid red]{(1)}\). When \(\overrightarrow a\) and \(\overrightarrow b\) are parallel, \(x = \bbox[10px, border: 2px solid red]{(2)}\)
QUESTION 11
Let \(f(x) = x^3 - 6x^2 + 9x\)
(i) \(f'(x) = \bbox[10px, border: 2px solid red]{(1)}\) and when \(x = \bbox[10px, border: 2px solid red]{(2)}\), the graph of \(y = f(x)\) has a maximum value.
(ii) The area enclosed by \(y = f(x)\) and x axis is \(x = \bbox[10px, border: 2px solid red]{(3)}\).
II. PART 2
On the plane \(xy\), there are three points: \(0(0,0), A(2,4), C(3,0)\).
QUESTION 01
Taking point D in the fourth quadrant and when the quadrilateral ODBA is parallelogram, the coordinates of point D is \(\left( \: \bbox[10px, border: 2px solid red]{(1)}, \bbox[10px, border: 2px solid red]{(2)} \: \right)\)
QUESTION 02
When a straight line \(x = p\) bisects the area of \(\Delta OAB\), \(p = \bbox[10px, border: 2px solid red]{(1)}\)
QUESTION 03
When a straight line \(y = q\) bisects the area of \(\Delta OAB\), \(q = \bbox[10px, border: 2px solid red]{(1)}\)
QUESTION 04
When the straight line L drawn from point B bisects the area of \(\Delta OAB\). the equation of the straight line L is \(y = \bbox[10px, border: 2px solid red]{(1)}\)
QUESTION 05
The equation of a parabola which passes three points: O, A and B is \(y = \bbox[10px, border: 2px solid red]{(1)}\)
III. Part 3
QUESTION 01
Given ten functions, (1) to (10) and five properties of function, (a) to (e).
Which properties does each function have?
Functions:
\(| x |\)
\(\bbox[10px, border: 2px solid red]{(1)}\)
\( x \)
\(\bbox[10px, border: 2px solid red]{(2)}\)
\(x^2 \)
\(\bbox[10px, border: 2px solid red]{(3)}\)
\(x^3\)
\(\bbox[10px, border: 2px solid red]{(4)}\)
\(x - \dfrac 1x\)
\(\bbox[10px, border: 2px solid red]{(5)}\)
\(\sin x\)
\(\bbox[10px, border: 2px solid red]{(6)}\)
\(\cos x\)
\(\bbox[10px, border: 2px solid red]{(7)}\)
\(2^x \)
\(\bbox[10px, border: 2px solid red]{(8)}\)
\(2^{-x}\)
\(\bbox[10px, border: 2px solid red]{(9)}\)
\(\log_2 x\)
\(\bbox[10px, border: 2px solid red]{(10)}\)
Choose one or two properties and write the appropriate answer in the box.
(a) \(f(-x) = - f(x)\)
(b) \(f(-x) = f(x)\)
(c) \(f \left(\dfrac 1x \right) = - f(x)\)
(d) \(f(kx) = k f(x)\)
(e) \(f(x) \:.\: f(y) = f(x + y)\)