About this preparation
Math diagnostic test, Grade 10: Linear equations, Quadratic equations. 10 questions with answers and explanations. Topics: Linear equations, Quadratic equations, Functions and graphs, Systems of equations, Exponents and radicals, Word problems. 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
Solve the equation: 3x - 7 = 11
x = 4
x = 6
x = -6
x = 18
Explanation: Add 7 to both sides to get 3x = 18, then divide by 3. So x = 6.
2
Which value is a solution of the equation x^2 - 5x + 6 = 0?
x = 1
x = 2
x = 5
x = -2
Explanation: Factor the quadratic: x^2 - 5x + 6 = (x - 2)(x - 3). The solutions are x = 2 and x = 3.
3
What is the slope of the line y = 4x - 9?
-9
4
9
-4
Explanation: In slope-intercept form y = mx + b, the slope is the coefficient of x. Here, m = 4.
4
Solve the system of equations: x + y = 10 and x - y = 2
x = 4, y = 6
x = 6, y = 4
x = 8, y = 2
x = 2, y = 8
Explanation: Add the equations: 2x = 12, so x = 6. Substitute into x + y = 10 to get y = 4.
5
Simplify: (2^3)(2^4)
2^7
2^12
2^1
4^7
Explanation: When multiplying powers with the same base, add the exponents: 3 + 4 = 7.
6
Which expression is equivalent to sqrt(50)?
5sqrt(2)
25sqrt(2)
10sqrt(5)
2sqrt(25)
Explanation: Since 50 = 25 × 2, sqrt(50) = sqrt(25)sqrt(2) = 5sqrt(2).
7
A rectangle has a length of 12 cm and a width of 5 cm. What is its area?
17 cm^2
30 cm^2
60 cm^2
24 cm^2
Explanation: Area of a rectangle is length × width. So 12 × 5 = 60 cm^2.
8
If f(x) = 2x + 1, what is f(3)?
5
6
7
9
Explanation: Substitute x = 3 into the function: f(3) = 2(3) + 1 = 7.
9
Which equation represents a line with y-intercept 3 and slope -2?
y = 3x - 2
y = -2x + 3
y = 2x - 3
y = -3x + 2
Explanation: Slope-intercept form is y = mx + b, where m is the slope and b is the y-intercept. Here m = -2 and b = 3.
10
A number increased by 8 is 23. Which equation can be used to find the number n?
n - 8 = 23
n + 8 = 23
8n = 23
23 - n = 8
Explanation: “Increased by 8” means add 8 to the number, so the equation is n + 8 = 23.
