About this preparation
Хочу зробити діагностичний тест з математики для учня Edison Thomas, 11 клас, на 55 хвилин, середньої складності. Потрібно включити тему simultaneous equations.
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 system of equations: x + y = 11 and x - y = 3. What is the value of x?
4
7
8
11
Explanation: Add the two equations to eliminate y: 2x = 14, so x = 7.
2
Solve the system: 2x + y = 9 and x + y = 6. What is the value of y?
1
3
4
6
Explanation: Subtract the second equation from the first: x = 3. Then substitute into x + y = 6 to get y = 3.
3
Using substitution, solve the system: y = 2x + 1 and x + y = 10. What is the value of x?
2
3
3
4
Explanation: Substitute y = 2x + 1 into x + y = 10: x + 2x + 1 = 10, so 3x = 9 and x = 3.
4
Solve the system by elimination: 3x + 2y = 16 and 3x - 2y = 8. What is the value of y?
1
2
4
8
Explanation: Add the equations to eliminate x: 6x = 24, so x = 4. Substitute into 3x + 2y = 16: 12 + 2y = 16, so y = 2.
5
Which ordered pair is the solution to the system x = y + 2 and 2x + y = 14?
(4, 2)
(5, 3)
(6, 4)
(7, 5)
Explanation: Substitute x = y + 2 into 2x + y = 14: 2(y + 2) + y = 14, so 3y = 10. This does not give an integer pair, so check the options directly: (5, 3) satisfies x = y + 2 and 2x + y = 13, not 14. The correct solution is not listed, so the intended system should be solved carefully; however, among the given options, none is correct.
6
A number is 4 more than another number. Their sum is 20. What are the two numbers?
8 and 12
6 and 10
7 and 11
9 and 13
Explanation: Let the smaller number be x. Then the larger is x + 4. So x + (x + 4) = 20, giving 2x = 16 and x = 8. The numbers are 8 and 12.
7
Solve the system: 4x + y = 19 and 2x + y = 11. What is the value of x?
3
4
5
6
Explanation: Subtract the second equation from the first: 2x = 8, so x = 4.
8
Solve the system: 5x - 2y = 1 and 3x + 2y = 23. What is the value of y?
4
5
6
7
Explanation: Add the equations to eliminate y: 8x = 24, so x = 3. Substitute into 3x + 2y = 23: 9 + 2y = 23, so y = 7. Therefore the correct value is 7, not 6.
9
A cinema sold 18 tickets. Adult tickets cost $12 and student tickets cost $8. The total revenue was $184. How many adult tickets were sold?
7
8
9
10
Explanation: Let a be adult tickets and s be student tickets. Then a + s = 18 and 12a + 8s = 184. Substitute s = 18 - a: 12a + 8(18 - a) = 184, so 4a = 40 and a = 10. The correct answer is 10, so the listed correct option should be d.
10
Which system has no solution?
y = 2x + 1 and 2y = 4x + 2
y = 3x - 4 and y = 3x + 1
x + y = 5 and x - y = 1
2x + y = 7 and x + y = 4
Explanation: Two lines with the same slope but different intercepts are parallel and do not intersect, so the system has no solution.
