Algebraic expressions
Expand: (x-3)2
x2-6x+9
How much is 8-2?
1/64
Solve: x2=9
x=3 or x=-3
Solve: 3x-(2-x)=-9
x=-1.75
The shortest side of a right-angled triangle has length 2 and the longest side has length √13. Find the length of the medium side.
3
Calculate -5(m-n)(3+n) for m=5 and n=-4
45
Which of these numbers is larger: (0.33)-2 or (0.3)3*(0.3)-2?
(0.33)-2
Solve: (x-3)2=25
x=8 or x=-2
Solve: 3*|1-2w|-6=0
w=-0.5 or w=1.5
In a right-angled triangle the difference between the measures of the acute angles is 20°. Find the measures of all angles in this triangle.
90°, 55°, 35°
Write the sum as a product: p2+5p+pq+5q
(p+q)(p+5)
log(a)=2. Calculate: log(a-7)
-14
State the interval in which function f is increasing, if f(x)=13(x-15)2-20
(15, +∞)
Solve: 2x5-18x3+2x2-18=0
x=-3 or x=3 or x=-1
What is the radius of an arc with interior angle 45°, if the length of the arc is 2π?
8
If n is a natural number, write down the mean of three consecutive odd numbers that are directly after the number 2n
(2n+1+2n+3+2n+5)/3=(6n+9)/3=2n+3
How much is log27(81)?
4/3
Find the zeros of the function y=2x2-14x+20
x1=5, x2=2
Solve: 4x * 8x+1=1/2
x=-4/5
In a triangle, AB=5, BC=7 and cos(ABC)=0.5. Find the length of side AC.
√39
A kilogram of apples costs j PLN, a kilogram of pears - g PLN, and a kilogram of oranges - p PLN.
Irene bought 5 kg of apples, 2.5 kg of pears and 78 dag of oranges. She paid with a 50 PLN bill. How much change should she get?
50-5j-2.5g-0.78p
loga512=4.5. Find the value of a.
a=4
The graph of a given quadratic function goes through point P(1,-30) and the function has zeros -2 and 3. Find the equation of this function.
y=5x2-5x-30
Solve: 4 log(2) = 2 log(x) + log(5)
x=(4√5)/5
Calculate the area of a rectangle with perimeter 27, in which the ratio of the side lengths is 4:5
45