Про цю підготовку
Діагностичний тест з математики, 10 клас: Algebraic expressions, Linear equations. 11 завдань з відповідями та поясненнями. Теми: Algebraic expressions, Linear equations, Quadratic equations, Functions and graphs, Geometry and measurement, Percentages and ratios, Statistics and probability. Тривалість — 55 хв.
Завдання діагностики
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) + 4x
10x - 15
6x - 15
10x - 5
6x - 5
Пояснення: Distribute 3: 3(2x - 5) = 6x - 15, then add 4x to get 10x - 15.
2
Solve the equation: 5x - 7 = 18
x = 3
x = 4
x = 5
x = 6
Пояснення: Add 7 to both sides: 5x = 25. Then divide by 5: x = 5. Wait, check carefully: 5x - 7 = 18 gives 5x = 25, so x = 5.
3
Which expression is equivalent to (x + 3)^2?
x^2 + 6x + 9
x^2 + 9
x^2 + 3x + 9
x^2 + 6x + 3
Пояснення: Use the identity (a + b)^2 = a^2 + 2ab + b^2.
4
A line has gradient 2 and passes through the point (0, -3). What is its equation?
y = 2x - 3
y = -2x - 3
y = 2x + 3
y = x - 3
Пояснення: Use slope-intercept form y = mx + c. Here m = 2 and c = -3.
5
Which of the following are solutions of the equation x^2 - 5x + 6 = 0?
x = 2
x = 3
x = -2
x = -3
Пояснення: Factor the quadratic: x^2 - 5x + 6 = (x - 2)(x - 3). So the solutions are x = 2 and x = 3.
6
A rectangle has length 12 cm and width 5 cm. What is its area?
17 cm^2
30 cm^2
60 cm^2
24 cm^2
Пояснення: Area of a rectangle = length × width = 12 × 5 = 30 cm^2.
7
A price of $80 is increased by 15%. What is the new price?
$92
$95
$96
$100
Пояснення: 15% of 80 is 12, and 80 + 12 = 92. Alternatively, multiply by 1.15.
8
Which statements about the data set 2, 4, 4, 6, 8 are true?
The mean is 4.8
The median is 4
The mode is 4
The range is 4
Пояснення: Mean = (2 + 4 + 4 + 6 + 8) / 5 = 24 / 5 = 4.8. Median is 4, mode is 4, and range is 8 - 2 = 6.
9
If f(x) = 2x + 1, what is f(3)?
5
6
7
8
Пояснення: Substitute x = 3 into the function: f(3) = 2(3) + 1 = 7? Check carefully: 2(3) + 1 = 7, so the correct answer is 7.
10
A triangle has angles 45° and 65°. What is the third angle?
70°
80°
90°
100°
Пояснення: The angles in a triangle add up to 180°. So 180 - 45 - 65 = 70°.
11
Which of the following are valid steps when solving 2(x - 4) = 10?
Divide both sides by 2 first
Expand the brackets to get 2x - 8 = 10
Add 4 to both sides to get x = 5
Subtract 10 from both sides first
Пояснення: Valid methods include expanding first or dividing both sides by 2 first. The correct solution is x = 9, so adding 4 to both sides is not a correct final step.
