Algebra
Differentiation
Integration
Functions
Logarithms & Exponentials
100
Factorise
x^2-3x-28
(x+4)(x-7)
100
Differentiate
y=2x^3+6x+10
dy/dx=6x^2+6
100
Integrate:
int\ 2x\ dx
x^2 + C
100
Evaluate f(2) given,
f(x)=2x^2−3x+1
3
100
Evaluate:
log_2 32
5
200
Simplify - answer with positive indices.
a^-3/a^-8\times(a^2b^-3)/b^-5
a^7b^3
200
Differentiate:
y=x^2(x^2-10x)
dy/dx=4x^3-30x^2
200
Find the integral:
int\ 4x^3+3\ dx
x^4+3x+C
200
State the domain of:
f(x)=sqrt(x-5)
x>=5
200
Solve for x:
3^x=81
x=4
300
Expand and simplify.
(sqrt(3)+sqrt(5))(sqrt(3)-sqrt(5))
-2
300
Differentiate:
f(x)=(2x)/x^4
f'(x)=-6/x^(2)
300
Find the integral:
int\ 6x^2 +2x-1 dx
2x^3+x^2-x
300
Find f(g(2)) when
f(x)=x+3 and g(x)=x^2
7
300
Write as a single number:
log_5 20-log_5 4
1
400
Rationalise the denominator:
1/(x-sqrt(2))
(x+sqrt(2))/(x^2-2)
400
Find the derivate:
f(x)=(2x-1)^4
f'(x)=8(2x-1)^3
400
Evaluate:
int_{1}^{3}\ (3x^2 - 2x)\ dx
18
400
f(x) is an odd function. Find f(-6) when
f(6)=-10
10
400
.
p + q
500
Solve for x by completing the square.
x^2-4x+1
x=2+-sqrt(3)
500
Differentiate:
y=(2x+1)/(2x-1)
4/((2x-1)^2
500
Find the indefinate integral:
int_{-4}^{4}\ x^3\ dx
0
500
The function f(x) has an inverse, and the point (4,11) lies on the graph of y = f(x).
What point must lie on the graph of:
y=f^(−1)(x)
(11, 4)
500
y=0