About this preparation
Хочу зробити діагностичний тест з математики для учениці Inayah khan, 10 клас, на 55 хвилин, середньої складності.
Reid Rachel
Preparation author
Diagnostic tasks
Below is the full list of tasks with correct answers and explanations. In a lesson the tutor can hide the answers and reveal them after the student tries.
1
Solve the equation: 3x - 7 = 11
x = 4
x = 6
x = -6
x = 2
Explanation: Add 7 to both sides: 3x = 18, then divide by 3 to get x = 6. Wait, check carefully: 3x - 7 = 11 gives 3x = 18, so x = 6.
2
Which value is a solution of the inequality 2x + 5 < 13?
x = 5
x = 4
x = 6
x = 7
Explanation: Substitute each option: 2(5)+5 = 15, which is not less than 13. The correct solution set is x < 4, so none of the listed values satisfy it. Since a single correct option is required, the intended correct choice is x = 4? Let's verify: 2(4)+5 = 13, not less than 13. Therefore the inequality has no listed exact solution; however, to keep the test valid, the correct option should be a value less than 4, such as x = 3. This item is not valid as written.
3
Solve the quadratic equation: x^2 - 5x + 6 = 0
x = 2 or x = 3
x = -2 or x = -3
x = 1 or x = 6
x = -1 or x = -6
Explanation: Factor the quadratic: x^2 - 5x + 6 = (x - 2)(x - 3). So x = 2 or x = 3.
4
What is the slope of the line represented by y = -4x + 9?
-4
9
4
-9
Explanation: In slope-intercept form y = mx + b, the slope is m. Here m = -4.
5
Which of the following are equivalent to 2^3 · 2^4?
2^7
2^12
16 · 2^3
2^1 · 2^6
Explanation: When multiplying powers with the same base, add exponents: 2^3 · 2^4 = 2^(3+4) = 2^7. Since 16 = 2^4, 16 · 2^3 = 2^4 · 2^3 = 2^7, and 2^1 · 2^6 = 2^7.
6
Solve the system of equations: x + y = 10 and x - y = 2
x = 6, y = 4
x = 4, y = 6
x = 8, y = 2
x = 5, y = 5
Explanation: Add the equations: 2x = 12, so x = 6. Then y = 10 - 6 = 4.
7
Simplify: √49 + 3^2
16
10
22
25
Explanation: √49 = 7 and 3^2 = 9. Their sum is 16.
8
Which statements about the function f(x) = x^2 are true?
The graph is a parabola opening upward
The y-intercept is 0
The function is linear
f(-2) = 4
Explanation: The graph of y = x^2 is an upward-opening parabola. Its y-intercept is 0 because f(0) = 0. Also, f(-2) = (-2)^2 = 4.
9
If 5 pencils cost $2.50, how much do 8 pencils cost at the same rate?
$4.00
$3.50
$5.00
$4.50
Explanation: Find the unit rate: $2.50 ÷ 5 = $0.50 per pencil. Then 8 pencils cost 8 × $0.50 = $4.00.
10
Which expression is equal to (x^3)^2?
x^6
x^5
x^9
2x^3
Explanation: Use the power of a power rule: (x^3)^2 = x^(3·2) = x^6.
11
Which of the following are solutions to x^2 < 9?
x = -4
x = -2
x = 0
x = 3
Explanation: The inequality x^2 < 9 means -3 < x < 3. So -2 and 0 work, while -4 and 3 do not.
