level A
Solve the equation.
2/5 • b = 12/5
6
Simplify (-a2b3)2(c2)0
a4b6
Simplify Exponents and Radicals
Evaluate the following expression: ∛2 ∛(32)
4
Order from greatest to least
a) 25100
b) 2300
c) 3400
d) 4200
e) 2600
3400 , 2600, 25100 , 4200 , 2300
Add & Subtract Polynomials (answer should be a polynomial in standard form).
G=3t2−5t+6
P=−8t2+7t−9
What is the answer for G + P?
−5t2+2t−3
Complete the statement using < , > or =.
82/3 - 71/4 ____ 1
>
If (x2 - y2) = 10 and (x + y) = 2, find x and y.
x = 7/2 (or 3.5) , y = -3/2 (or -1.5)
Use the table below to find the following if possible (example needs to be shown):
f -1(- 4)
6
When divided by x - 1, the polynomial P(x) = x5 + 2x3 +Ax + B, where A and B are constants, the remainder is equal to 2. When P(x) is divided by x + 3, the remainder is equal -314. Find A and B.
A = 4 and B = -5 : solve the above systems of equations.
Solution:
P(1) = 15 + 2(13) +A*(1) + B = 2 : remainder theorem
P(-3) = (-3)5 + 2(-3)3 +A*(-3) + B = -314
2x4+4x3-30x2=?
2x2(x+5)(x-3)
At 10:00 A.M., Archie leaves the house at a rate of 60 mi/h. At the same time, Luna leaves the same house at a rate of 50 mi/h in the opposite direction. At what time will the two be 330 miles apart?
60t ± 50t = 330: 1:00 P.M.
The area of a rectangular field is equal to 300 square meters. Its perimeter is equal to 70 meters. Find the length and width of this rectangle.
W = 15 and L = 20
Find the domain of the function f(x)=√(−x2−4).
−x2−4≤0
f(x) is a function such that f(x) + 3f(8 - x) = x for all real numbers x. Find the value of f(2).
f(2) = 2
x2−2x+1
----------- = ?
x - 1
x−1
Kevin is cutting wood to build his closet that are to be 141/4 inches wide. If he has a piece that is 114 inches long, how many boards can he cut from this wood piece?
Kevin can cut 8 pieces from this wood.
In a right triangle ABC with angle A equal to 90°, find angle B and C so that sin(B) = cos(B).
Let b be the length of the side opposite angle B and c the length of the side opposite angle C and h the length of the hypotenuse.
sin(B) = b/h and cos(B) = c/h
sin(B) = cos(B) means b/h = c/h which gives c = b
The two sides are equal in length means that the triangle is isosceles and angles B and C are equal in size of 45°.
Find the x and y intercepts of the parabola with equation y = - x 2 + 2 x + 3?
x = 3 and x = -1
y = - (0)
The sum of the first three terms of a geometric sequence is equal to 42. The sum of the squares of the same terms is equal to 1092. Find the three terms of the sequence.
(r2 - r + 1) / (r2 + r + 1) = 1092 / 422
r = 4 , r = 1/4 : solve for r
a = 2 : substitute r = 4 and solve for a
a = 32 : substitute r = 1/4 and solve for a
a = 2 , ar = 8 , ar2 = 32 : find the three terms for r = 4
a = 32 , ar = 8 , ar2 = 2 : find the three terms for r = 1/4
Find the range of function f(x)=x−1 / 2−3x
f−1(x)=y=2x+13x+1.
The domian of f−1 is the set of all real numbers except −13. Hence the range of f is the set of all real numbers except −13 which may be written in interval form as
(−∞,−13)∪(−13,+∞)
Find the x and y intercepts of the line with equation
3y - 6 = 3?
(0 , 3)
The lengths of side AB and side BC of a scalene triangle ABC are 12 cm and 8 cm respectively. The size of angle C is 59°. Find the length of side AC (rounded to one decimal place).
x = 14.0
Find the equation y = a x2 + x of the parabola that is tangent to the line with equation y = 3 x + 1.
y = -x2 + x
Solve the trigonometric equation given by
sin(x) + sin(x/2) = 0 for 0 ≤ x ≤ 2 pi
x = 0, x = 4pi/3 and x = 2pi
Find the inverse of function f(x)=ln(2x−3)+2
f−1(x)=1/2(ex−2+3)