Algebra I
Write an equation, in slope-intercept form, of a line that passes through the point (6,3）and has a slope of 2/3 ?
y = 2/3x - 1
The value of t in the equation 9t -1 = 276 - t is ？
（1）3.5 ； （3）8
（2）19/5 ； （4）4
（4）
Which regular polygon would carry onto itself after a rotation of 60° about its center?
hexagon
The graph of 7x + 2y = -31 in the -plane has an -intercept at (a,0） and a y-intercept at (0, b), where a and b are constants. What is the value of b/a?
7/2
There are 8 cards with the numbers 1,2, 3,4, 5,6, 7, and 8 written on them. What is the probability that a card drawn randomly has a number that is a multiple of 4?
25% or 1/4 or 0.25
Solve the equation for x :
14x = 3(1 + 2x) - 4x
3/4
Factor the expression completely:
(x - 1)2 + 5(x - 1) - 6
(x - 2)(x + 5)
Line k is represented by the equation 4y + 3 = 7x. What equation represents a line that is perpendicular to line k and passes through the point (-5,2）？
(A)y + 2 = 4/7（x - 5）; (C)y + 2 = -4/7(x - 5)
(B)y - 2 = 4/7（x + 5）;（D）y -2 = -4/7（x + 5）
y -2 = -4/7（x + 5）or (D)
The cost of renting a carpet cleaner is $52 for the first day and $26 for each additional day. Which of the following functions gives the cost C(d), in dollars, of renting the carpet cleaner for d days, where d is a positive integer?
C (d） = 26d + 26
calculate：（1/4）-1 - 81/3 +∣−5∣
7
Students were asked to write a polynomial given the following conditions:
(1)the degree of the expression is 3
(2)the leading coefficient is 2
(3)the constant term is 26
What expression satisfies all three conditions?
(1)4x - 6 + 3x2 (3)4 - 6x + 2x3
(2)3x2 - 6x + 4 (4)4x3 + 2x3 - 6
(3)
Consider the system of equations below. (x + 1)2 + (y - 4)2 = 9 and x = 2.The x-value and y-value of the solution of the system are:
(1) one rational and one imaginary (3) one rational and one irrational
(2) both rational (4) both irrational
(4)
Triangle ABC has a right angle at C. If AC = 7.7 and m angle = 24°, what is AB, to the nearest tenth?
(1)18.9 ; (3)8.4
(2)17.3 ; (4)3.1
(3) or 8.4
Line P is defined by 4y + 8x = 6. Line R is perpendicular to line P in the xy-plane. What is the slope of line R?
0.5 or 1/2
What is m of value?
（x + 2）4 = x4 + mx3 + 24x2 + 32x + 16
8
When f(x) = |4x + 2| and g(x) = 3x + 5 are graphed on the same set of axes, for which value of x is f(x) = g(x)?
(1) 1 (3) 3
(2) 2 (4) 14
(3)
Given f(x)=2/3x + 6, write the equation of f-1(x).
f-1= 3/2(x - 6）
In a right triangle, the acute angles have the relationship cos(5x + 7)° = sin(3x 1 3)°. Which equation is always true?
(A)5x+ 7 = 3x + 3 ; （C) 5x + 7 + 3x + 3 = 180
(B)5x+ 7 + 3x+ 3 = 90 ; (D) 5x + 7 + 3x + 3 + x = 180
(B)
The graph of x2 + x + y2 + y = 199/2 in the xy-plane is a circle. What is the length of the circle’s radius?
10
There are six cards labeled with the numbers 1, 2, 3, 4, 5, and 6. Cards labeled with the numbers 1, 4, and 5 are in player A's hand, and cards labeled with the numbers 2, 3, and 6 are in player B's hand. If each player randomly draws a card, the probability that player A's card has a higher number than player B's is ________.
4/9
Determine the product of （2x + 3） and (-6x2 + 5x -1）. Express the product in standard form.
-12x3 + 4x2 + 7x - 3
Solve 3.8e1.5t = 16 algebraically for t to the nearest hundredth.
0.96
Joan wants to fill an empty 75-liter fish tank with water. She uses a cylindrical bucket with a diameter of 20 cm. Determine and state the maximum number of buckets of water, filled to an exact height of 26cm, Joan can put into the fish tank before it overflows.
[1000 cm3 = 1 liter]
9 buckets
The floor of a ballroom has an area of 600 square meters. An architect creates a scale model of the floor of the ballroom, where the length of each side of the model is 1/10 times the length of the corresponding side of the actual floor of the ballroom. What is the area, in square meters, of the scale model?
6
Given the inverse proportional function ( y = -7/x), which of the following statements is correct? ( )
A. The graph of the function lies in the first and third quadrants.
B. y decreases as x increases.
C. The graph of the function lies in the second and fourth quadrants.
D. y increases as x increases.
C