Про цю підготовку
Самостійна робота з математики, 7 клас: Advanced Math Readiness. 10 завдань з відповідями та поясненнями. Теми: Algebraic expressions, Equations and inequalities, Functions, Geometry, Probability and statistics. Тривалість — 90 хв.
Завдання самостійної роботи
Нижче — повний перелік завдань із правильними відповідями та поясненнями. На занятті репетитор може приховати відповіді й відкривати їх після спроби учня.
1
Simplify the expression: 3(2x - 5) - 2(x + 4).
4x - 23
8x - 23
4x - 7
6x - 13
Пояснення: 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 = 4
x = 8
x = -8
Пояснення: 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
Пояснення: Solve the inequality: 2x + 3 < 11, so 2x < 8 and x < 4. Among the choices, only x = 3 works.
4
If f(x) = x^2 - 4x + 1, what is f(3)?
-2
1
4
10
Пояснення: Substitute x = 3: f(3) = 3^2 - 4(3) + 1 = 9 - 12 + 1 = -2.
5
A triangle has angles 45°, 65°, and x°. What is x?
60°
70°
80°
90°
Пояснення: The angles in a triangle add to 180°. So x = 180 - 45 - 65 = 70°.
6
Which of the following are equivalent to 2(x + 3) + x?
3x + 6
2x + 3 + x
x + 6
2x + 6 + x
Пояснення: Expand and combine: 2(x + 3) + x = 2x + 6 + x = 3x + 6. Options a, b, and d are equivalent forms.
7
A bag contains 3 red marbles, 5 blue marbles, and 2 green marbles. What is the probability of choosing a blue marble?
1/2
1/5
1/3
5/10
Пояснення: There are 10 marbles total and 5 are blue, so the probability is 5/10 = 1/2.
8
The line y = 2x - 1 is shifted up by 4 units. What is the new equation?
y = 2x + 3
y = 2x - 5
y = 6x - 1
y = 2x + 1
Пояснення: A vertical shift up by 4 adds 4 to the output: y = 2x - 1 + 4 = 2x + 3.
9
Solve the system of equations: x + y = 9 and x - y = 3.
x = 3, y = 6
x = 6, y = 3
x = 9, y = 0
x = 0, y = 9
Пояснення: Add the equations: 2x = 12, so x = 6. Then y = 9 - 6 = 3.
10
Which statements about a rectangle are true?
Opposite sides are equal
All angles are 90°
All sides are equal
Diagonals are always perpendicular
Пояснення: A rectangle has opposite sides equal and all angles right angles. Its sides are not all equal, and diagonals are not always perpendicular.
