7 grade
Write the number using scientific notation: 0.000657
6,57*10-4
Estimate:
sin45∘tan45∘cos45∘cot45∘=
1/2
Evaluate:
tan(3π+a)+tan(п-a)=
0
... is a statement that is accepted as true without proof and serves as a basis for building a theory
An axiom
The ratio of two adjacent (supplementary) angles is 12:18. Find these angles.
72∘ and 108∘
Mark rides his bike 9 km south and then 12 km east. How far is he from his starting point?
15 km
The first term of an arithmetic progression is 5 and the common difference is 3. What is the 10th term?
32
... is a natural number greater than 1 that has exactly two divisors: 1 and itself.
A prime number
Calculate:
(52)3⋅125/254
5
A rectangle has a length that is 3 meters longer than its width. If the area of the rectangle is 70 m², find the dimensions of the rectangle
7 and 10
Solve the system of equations:
y=x2+7x+3
y=9x+2
x=1
y=11
... is a mapping between two sets, in which each element of the first set corresponds to exactly one element of the second set
A function
A volleyball tournament involves 10 teams.
Each team must play one match against every other team.
How many matches will be played in total during the tournament?
45
Find the roots of the quadratic equation:
2025x2+x-2026=0
x=1 and x=2026/2025
A Coach wants to choose 5 students from a group of 9 to form a basketball team . How many different ways can she choose the students?
126
... is a closed plane figure formed by three or more line segments connected in sequence, where each segment intersects only with its adjacent segments.
A polygon
Expand the brackets:
(a+b)4=
a4+4a3b+6a2b2+4ab3+b4
Completing the square:
2x2+8x-5=
2(x+2)2−13
Find the coordinates of the center and the radius:
y2+4x-20-2y+x2=0
Center: (−2,1)
r=5
The basic elements in geometry, from which all other geometric figures are constructed, are:
Point, Line, Plane