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Самостоятельная работа по математике, 11 класс: Algebra, Functions. 10 заданий с ответами и объяснениями. Темы: Algebra, Functions, Equations and inequalities, Geometry, Trigonometry, Statistics. Длительность — 55 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
Solve the equation: 6x - 7 = 3x + 2
x = 4
x = 6
x = -6
x = 18
Объяснение: Add 7 to both sides: 3x = 18, then divide by 3 to get x = 6.
2
Simplify: (2x^3)(5x^2)
10x^5
7x^6
10x^6
2x^5
Объяснение: Multiply the coefficients: 2 × 5 = 10, and add the powers of x: 3 + 2 = 5.
3
Factorise fully: x^2 - 9
(x - 3)(x - 3)
(x + 3)(x + 3)
(x - 9)(x + 1)
(x - 3)(x + 3)
Объяснение: This is a difference of squares: a^2 - b^2 = (a - b)(a + b). Here, x^2 - 9 = x^2 - 3^2.
4
Solve the inequality: 2x + 5 < 13
x < 4
x > 4
x < 9
x > 9
Объяснение: Subtract 5 from both sides: 2x < 8. Then divide by 2: x < 4.
5
A line has gradient 3 and passes through the point (0, -2). Which equation is correct?
y = 3x - 2
y = -3x - 2
y = 3x + 2
y = 2x - 3
Объяснение: Using y = mx + c, the gradient is m = 3 and the y-intercept is c = -2.
6
Find the value of sin 30°
0
1/2
√2/2
1
Объяснение: From standard trigonometric values, sin 30° = 1/2.
7
The angles in a triangle are in the ratio 2 : 3 : 4. What is the largest angle?
40°
60°
80°
90°
Объяснение: The total of triangle angles is 180°. The ratio parts add to 9, so one part is 20°. The largest angle is 4 × 20° = 80°.
8
Expand and simplify: (x + 4)(x - 1)
x^2 + 3x - 4
x^2 - 3x - 4
x^2 + 5x - 4
x^2 + 3x + 4
Объяснение: Multiply term by term: x(x - 1) + 4(x - 1) = x^2 - x + 4x - 4 = x^2 + 3x - 4.
9
A bag contains 5 red balls and 3 blue balls. One ball is chosen at random. What is the probability of choosing a blue ball?
3/5
3/8
5/8
1/3
Объяснение: There are 8 balls in total and 3 are blue, so the probability is 3/8.
10
Solve the simultaneous equations: y = x + 1 and y = 2x - 2
x = 1, y = 2
x = 2, y = 3
x = 3, y = 4
x = -1, y = 0
Объяснение: Set the expressions for y equal: x + 1 = 2x - 2. Then x = 3, but check carefully: x + 1 = 2x - 2 gives 3 = x, so y = 4. Therefore the correct pair is x = 3, y = 4.
