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Самостоятельная работа по математике, 7 класс: Advanced Mathematics Readiness. 10 заданий с ответами и объяснениями. Темы: Algebraic expressions, Equations and inequalities, Functions and graphs, Geometry and measurement, Probability and statistics. Длительность — 80 мин.
Задания самостоятельной работы
Ниже — полный список заданий с правильными ответами и объяснениями. На занятии репетитор может скрыть ответы и открывать их после того, как ученик попробует ответить сам.
1
Simplify the expression: 3(2x - 5) - 2(x + 4).
4x - 23
x - 23
4x + 23
8x - 13
Объяснение: Distribute first: 3(2x - 5) = 6x - 15 and -2(x + 4) = -2x - 8. Combine like terms: 6x - 15 - 2x - 8 = 4x - 23.
2
Solve the equation: 5x - 7 = 3x + 9.
x = 1
x = 8
x = -8
x = 16
Объяснение: Subtract 3x from both sides: 2x - 7 = 9. Add 7: 2x = 16. Divide by 2: x = 8.
3
Which value of x satisfies the inequality 2x + 3 < 11?
x = 3
x = 4
x = 5
x = 6
Объяснение: Solve the inequality: 2x + 3 < 11, so 2x < 8 and x < 4. Among the choices, only 3 is less than 4.
4
A line has slope 3 and passes through the point (0, -2). What is its equation in slope-intercept form?
y = 3x - 2
y = -3x - 2
y = 2x - 3
y = 3x + 2
Объяснение: Slope-intercept form is y = mx + b. Here m = 3 and b = -2, so the equation is y = 3x - 2.
5
If f(x) = x^2 - 4x + 1, what is f(3)?
-2
2
4
10
Объяснение: Substitute x = 3: f(3) = 3^2 - 4(3) + 1 = 9 - 12 + 1 = -2.
6
A triangle has sides 6 cm, 8 cm, and 10 cm. What type of triangle is it?
Equilateral
Isosceles
Right
Obtuse
Объяснение: A 6-8-10 triangle satisfies the Pythagorean theorem: 6^2 + 8^2 = 36 + 64 = 100 = 10^2, so it is a right triangle.
7
Which of the following are equivalent to 2(x - 3) + x?
3x - 6
2x - 3
x + 6
3(x - 2)
Объяснение: Expand the expression: 2(x - 3) + x = 2x - 6 + x = 3x - 6. The expression 3(x - 2) also simplifies to 3x - 6.
8
A bag contains 3 red marbles, 2 blue marbles, and 5 green marbles. Which statements are true?
The probability of drawing a blue marble is 2/10.
The probability of drawing a red marble is 3/5
There are 10 marbles in total.
The probability of drawing a green marble is 1/2.
Объяснение: There are 3 + 2 + 5 = 10 marbles total. Blue probability is 2/10. Green probability is 5/10 = 1/2. Red probability is 3/10, not 3/5.
9
What is the area of a rectangle with length 12 cm and width 7 cm?
19 cm²
42 cm²
84 cm²
24 cm²
Объяснение: Area of a rectangle is length × width. So 12 × 7 = 84 cm². The correct option is 84 cm².
10
A number is increased by 20% and becomes 48. What was the original number?
36
38
40
44
Объяснение: If the original number is x, then 1.2x = 48. Divide by 1.2: x = 40. Wait, check carefully: 48 ÷ 1.2 = 40, so the correct answer is 40.
