About this preparation
Math diagnostic test, Grade 10: Math for Grade 10. 11 questions with answers and explanations. Topics: Linear equations and inequalities, Quadratic expressions and equations, Functions and graphs, Systems of equations, Geometry and trigonometry, Statistics and probability. 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 = 2
Explanation: Add 7 to both sides to get 3x = 18, then divide by 3. So x = 6.
2
Which value of x satisfies the inequality 2x + 5 < 13?
x = 3
x = 4
x = 5
x = 6
Explanation: Subtract 5 from both sides: 2x < 8. Divide by 2: x < 4, so 3 works.
3
Factor the quadratic expression x^2 - 9.
(x - 3)(x - 3)
(x + 9)(x - 1)
(x - 9)(x + 1)
(x - 3)(x + 3)
Explanation: This is a difference of squares: a^2 - b^2 = (a - b)(a + b). Here, x^2 - 9 = x^2 - 3^2.
4
Find the roots of the equation x^2 - 5x + 6 = 0.
x = 1 and x = 6
x = 2 and x = 3
x = -2 and x = -3
x = 0 and x = 6
Explanation: Find two numbers that multiply to 6 and add to -5: -2 and -3. So the equation factors as (x - 2)(x - 3) = 0.
5
If f(x) = 2x + 1, what is f(4)?
7
8
9
10
Explanation: Substitute x = 4 into the function: f(4) = 2(4) + 1 = 9.
6
Which point lies on the graph of y = -x + 3?
(0, 3)
(3, 0)
(1, 4)
(2, 5)
Explanation: When x = 0, y = 3. So the point (0, 3) is on the graph.
7
Solve the system of equations: x + y = 10 and x - y = 2.
x = 4, y = 6
x = 6, y = 4
x = 5, y = 5
x = 8, y = 2
Explanation: Add the equations: 2x = 12, so x = 6. Then substitute into x + y = 10 to get y = 4.
8
A triangle has angles 50°, 60°, and x°. What is x?
60°
70°
80°
90°
Explanation: The angles in a triangle add up to 180°. So x = 180 - 50 - 60 = 70°.
9
In a right triangle, one acute angle is 35°. What is the other acute angle?
45°
50°
55°
65°
Explanation: The two acute angles in a right triangle add up to 90°. So the other angle is 90 - 35 = 55°.
10
A data set has the values 2, 5, 5, 8, 10. What is the median?
5
6
7
8
Explanation: The numbers are already in order. The middle value of five numbers is the median, which is 5.
11
A bag contains 3 red balls and 2 blue balls. What is the probability of choosing a blue ball?
2/3
2/5
3/5
1/2
Explanation: There are 2 blue balls out of 5 total balls, so the probability is 2/5.
