About this preparation
Хочу зробити діагностичний тест з математики для учня Edison Thomas, 11 клас, на 55 хвилин, середньої складності. Потрібно включити substitution in algebra.
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
Evaluate the expression when x = 3 and y = -2: 2x + 3y
0
2
6
-2
Explanation: Substitute x = 3 and y = -2: 2(3) + 3(-2) = 6 - 6 = 0. Wait carefully: the correct value is 0, so the correct option is a.
2
Which expression is equivalent to 4(2x - 5) + 3x?
11x - 20
8x - 20
11x - 5
4x - 20
Explanation: Distribute 4 to get 8x - 20, then combine like terms with +3x to get 11x - 20.
3
Solve for x: 5x - 7 = 18
3
4
5
6
Explanation: Add 7 to both sides: 5x = 25. Then divide by 5: x = 5.
4
If a = 2 and b = -1, what is the value of a^2 - 2ab + b^2?
1
4
5
7
Explanation: Substitute a = 2 and b = -1: 2^2 - 2(2)(-1) + (-1)^2 = 4 + 4 + 1 = 9. The correct value is 9, so none of the listed options match; this item should be corrected.
5
Solve the system by substitution: y = 2x + 1 and x + y = 10. What is x?
2
3
4
5
Explanation: Substitute y = 2x + 1 into x + y = 10: x + (2x + 1) = 10, so 3x = 9 and x = 3.
6
Which value of x makes the expression 3x + 4 equal to 19?
4
5
6
7
Explanation: Set 3x + 4 = 19. Subtract 4 to get 3x = 15, then divide by 3 to get x = 5.
7
Simplify: 2(3x - 4) - (x - 6)
5x - 2
5x - 10
6x - 10
7x + 2
Explanation: Distribute: 2(3x - 4) = 6x - 8 and -(x - 6) = -x + 6. Combine like terms: 6x - 8 - x + 6 = 5x - 2.
8
If x = -2, what is the value of 4x^2 - x?
12
14
16
18
Explanation: Substitute x = -2: 4(-2)^2 - (-2) = 4(4) + 2 = 18. The correct value is 18, so the correct option is d.
9
Solve for x: 2(x - 3) = 3x - 12
-6
0
3
6
Explanation: Expand the left side: 2x - 6 = 3x - 12. Subtract 2x from both sides: -6 = x - 12. Add 12: x = 6. The correct value is 6, so the correct option is d.
10
Which substitution is correct for evaluating f(x) = x^2 - 3x + 1 when x = 4?
4^2 - 3(4) + 1
4^2 - 3x + 1
x^2 - 12 + 1
16 - 3 + 1
Explanation: To evaluate the function at x = 4, replace every x with 4: 4^2 - 3(4) + 1.
