About this preparation
Math diagnostic test, Year 11: Algebraic Substitution and Core Algebra Skills. 10 questions with answers and explanations. Topics: Substitution in algebra, Evaluating expressions, Solving linear equations, Simplifying algebraic expressions, Systems of equations. Duration: 55 min.
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.
