Maths quiz 1
factor the trinomial: s^2-5s+6
(s-2)(s-3)
Perform the multiplication and simplify. (t^2 − t − 42/t^2 + 14t + 49) · (t + 7/t^2 − 36)
(t-7)/t^2+t-42
factor the trinomial: 2x^2-3x-27
(x+3)(2x-9)
factor out the common factor of: (x+3)^2-4(x+3)
(x+3)(x-1)
factor by grouping:x^3-x^2+8x-8
(x-1)(x^2+8)
Write the rational expression in simplest form. x^2 − 1/x^3 + x^2 + 16x + 16
(x-1)X^2+16
factor the trinomial: x^2-4x+4
(x-2)^2
write the quadratic function in standard form:x^2-4x+1
(x-2)^2-3
write the quadratic function in standard form: x^2-8
(x-4)^2-16
Write the rational expression in simplest form. x^2 + 2x − 48/x^2 + 11x + 24
(x-6)/(x+3)
what is the midpoint formula
(x1+x2/2, y1+y2/2)
Write the rational expression in simplest form. 5 + 4x − x^2/2x^2 − 9x − 5
-(x+1)/2x+1
Write the rational expression in simplest form. x2 − 25/5 − x
-(x+5)
Write the complex number in standard form. −9i + i^2
-1-9i
The imaginary unit i is defined as i = where i^2=
-1^0.5 -1
Perform the operation and write the result in standard form. (4 − 5i)(2 − 6i)
-22-34i
Perform the operation and write the result in standard form. (5 + 7i)2
-24+70i
Write the rational expression in simplest form. 6 − 3x/x − 2
-3
Use the Quadratic Formula to solve the quadratic equation. (Enter your answers as a comma-separated list.) x^2 + 6x + 10 = 0
-3+-i
Perform the operation and write the result in standard form. (3 + 2i) − (6 + 18i)
-3-16i
Solve the quadratic equation by completing the square. (Enter your answers as a comma-separated list. If an answer does not exist, enter DNE.) x^2 + 8x + 13 = 0
-4+-3^0.5
what is −0.000539 in scientific notation
-5.39 * 10^-4
what is 20(-2)^-3
-5/2
Solve the quadratic equation by factoring. (Enter your answers as a comma-separated list.) 15x^2 − 5x = 0
0,1/3
what is (3^2)^0
1
Write the complex conjugate of the complex number. 4 − 9i Multiply the number by its complex conjugate. (Simplify your answer completely.)
1) 4+9i 2)97
Use the Quadratic Formula to solve the quadratic equation. (Enter your answers as a comma-separated list.) x^2 − 2x + 2 = 0
1+-i
what is 7x^-2 when x=2
1.75
what is (z+2)^-8(z+2)^-4
1/(z+2)^12
what is 3^4/3^7
1/27
(5^-2)^2
1/625
Perform the operation and write the result in standard form. (16 − 2i) + (−5 + 5i)
11+3i
Write the quotient in standard form. 13/1 − i
13/2+13i/2
Perform the operation and write the result in standard form. 25 + (−10 + 18i) + 12i
15+30i
Perform the operation and write the result in standard form. (3^0.5 + 4i)(3^-.5 − 4i)
19
Factor the difference of two squares: 50-32z^2
2(5-4z)(5+4z)
what is 24,613.7 in scientific notation
2.46137 * 10^4
what is (5z)^2
25z^2
Write the rational expression in simplest form. 6y + 15y^2/10y + 4
3y/2
Find the average rate of change of the function from x1 to x2. Function: f(x) = x2 − 2x + 7 x-Values:x1 = 1, x2 = 5
4
Perform the operation and write the result in standard form. (8 + −12^0.5) − (4 + 2 3i^0.5)
4
what is (2x+2)^2
4x^2+8x+4
Write the complex number in standard form. 6 + −49^0.5
6+7i
Find the zeros of the function algebraically. (Enter your answers as a comma-separated list.) f(x) = 2x^2 − 7x − 30
6,-2.5
what is (x^-5y^7/5)^4
625x^20/7^28
factor out the common factor of: 7z^3-14z^2+21z
7z(z^2-2z+3)
what is 45(x+y)^5/10(x+y)
9(x+y)^4/2
Write the quotient in standard form. 11 − 17i/1 − 2i
9+i
Consider the following. f(−6) = −7, f(1) = 2 (a) Write the linear function f that has the given function values
9/7x+5/7
what is the other name for the rectangular coordinates system
Cartesian plane
f(x) = 3x − 6 (a) f(1) (b) f(−2)− (c) f(x + 4)
a)-3,b)-2,c)x+4
Evaluate the function for the given values. h(x) = [[x + 7]] (a) h(−6) (b) h1/2 (c) h(4.2) (d) h(−23.2)
a)1,b)7,c)11,d)-17
Find the function value, if possible. (If an answer is undefined, enter UNDEFINED.) f(x) = x + 8 + 2 (a) f(−8) (b) f(1) (c) f(x − 8)
a)2,b)5,c)x^0.5+2
Find real numbers a and b such that the equation is true. a + bi = 19 − 3i
a=19,b=-3
Find real numbers a and b such that the equation is true. (a + 3) + (b − 4)i = 5 + 8i
a=2,b=12
Match the function with its name. f(x) = |x|
absolute value function
Find the domain of the expression. 2x^2 - 8x + 3
all real numbers
Find the domain of the function. h(x) = 6x^2 − 4x
all real numbers except x = 0 and x = 4
Find the domain of the expression. √5 - x
all real numbers x satisfying x ≤ 5
Find the domain of the expression. x + 5/3x + 7
all real numbers x such that x ≠ -7/3
Find the domain of the function. g(y) = (y + 7)^.5
all real numbers y such that y ≥ −7
what is (a^-7/b^-7) * (b/a)^8
b^15/a^15
how do you find the slope between two points
change in y over change in x
The numbers a + bi and a − bi are called _________and their product is a real number a^2 + b^2.
conjugate pairs
Match the function with its name. f(x) = c
constant function
Match the function with its name. f(x) = x^3
cubic function
what is the degree and leading coefficient of -7x^5
degree=5, leading coefficient=-7
what is derived from the Pythagorean theorem
distance formula
what is the coordinate plane divided into
four quadrants
Match the function with its name. f(x) = [x]
greatest integer function
Match the function with its name. f(x) = x
identity function
Match the function with its name. f(x) = ax + b
linear function
When the graph of a quadratic function opens downward, its leading coefficient is ________ and the vertex of the graph is a ________.
negative, maximum
Determine whether the equation represents y as a function of x. x^2 + y^2 = 49
no
two lines are what, if their slopes are equal
parallel
who lines are what is their slopes are negative reciprocals of each other
perpendicular
A _______ function is a second degree polynomial function and it's graph is called a _________
quadratic, polynomial
Match the function with its name. f(x) = 1/x
reciprocal function
Match the function with its name. f(x) = x^0.5
square root function
what is the distance formula
square root of (x2-x1)^2 + (y2-y1)^2
Match the function with its name. f(x) = x2
squaring function
what is the ratio of change in y to the change in x of a line
the slope
what is the vertex, axis of symmetry, x intercept of the smaller value and larger value of (x-4)^2-16
vertex:4,-16, axis of symmetry:4, x intercept 1:0,0 , x intercept 2:8,0
What is the quadratic formula?
x = (-b ± √b^2 - 4ac)/2a (will get 2 answers)
solve the inequality: 7(x+1)<5x+6
x<-1/2
Solve the equation by extracting square roots. List both the exact solution and its approximation rounded to two decimal places. (x + 7)^2 = 24
x= +- 2x6^0.5-7
Solve the quadratic equation by factoring. (Enter your answers as a comma-separated list.) x^2 − 2x − 8 = 0
x=-2,4
Solve the quadratic equation by factoring. (Enter your answers as a comma-separated list.) 9x^2 + 30x + 25 = 0
x=-5/3
Find all real values of x for which f(x) = 0. (Enter your answers as a comma-separated list.) f(x) = 4x + 6
x=-6/4
Solve the equation and check your solution. (If there is no solution, enter NO SOLUTION.) 3/2x + 1 − 8x/2x − 1 = −4
x=-7/2
Find the zeros of the function algebraically. (Enter your answers as a comma-separated list.) f(x) = 3x + 27
x=-9
Solve the equation and check your solution. (If there is no solution, enter NO SOLUTION.) 1/x + 3/x − 2 = 0
x=1/2
Solve the equation and check your solution. (If an answer does not exist, enter DNE. If all real numbers are solutions, enter REALS.) 5x − 7 = 4x + 7
x=14
Solve the equation and check your solution. (If there is no solution, enter NO SOLUTION.) 4x − 6/4x + 7 = 2/3
x=8
Solve the equation and check your solution. (If there is no solution, enter NO SOLUTION.) 12/(x − 1)(x + 3) = (3/x − 1 )+ (5/x + 3)
x=No Solution
solve the inequality: 4x-2<3+9x
x>-1
solve the inequality: 4x+7<3+6x
x>2
What is point slope form?
y-y1=m(x-x1)
What is slope intercept form?
y=mx+b
Determine whether the equation represents y as a function of x. x^2 − y = 81
yes
