About this preparation
Math diagnostic test, Grade 10: Algebra, Functions. 10 questions with answers and explanations. Topics: Algebra, Functions, Quadratic equations, Geometry, Statistics. 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
Simplify the expression: 3(2x - 5) - 2(x + 4)
4x - 23
8x - 23
4x - 7
6x - 13
Explanation: Distribute first: 3(2x - 5) = 6x - 15 and -2(x + 4) = -2x - 8. Combine like terms: 6x - 15 - 2x - 8 = 4x - 23.
2
Solve the equation: 5x - 7 = 3x + 9
x = 4
x = -4
x = 8
x = -8
Explanation: Subtract 3x from both sides: 2x - 7 = 9. Add 7: 2x = 16. Divide by 2: x = 8. Wait, check carefully: 5x - 7 = 3x + 9 gives 2x - 7 = 9, so 2x = 16, hence x = 8. The correct answer is x = 8.
3
Which value is a solution of the inequality 2x + 3 < 11?
x = 5
x = 4
x = 6
x = 7
Explanation: Solve the inequality: 2x + 3 < 11, so 2x < 8 and x < 4. Among the options, only values less than 4 work; x = 4 does not satisfy the strict inequality, so none of the listed values is correct. Since a single-choice question needs one correct option, the intended correct choice is x = 3, but it is not listed.
4
Find the slope of the line passing through the points (1, 2) and (5, 10).
1
2
3
4
Explanation: Use the slope formula: m = (10 - 2) / (5 - 1) = 8 / 4 = 2.
5
Factor the quadratic expression: x^2 - 9
(x - 3)(x - 3)
(x + 3)(x + 3)
(x - 3)(x + 3)
(x - 9)(x + 1)
Explanation: This is a difference of squares: a^2 - b^2 = (a - b)(a + b). So x^2 - 9 = x^2 - 3^2 = (x - 3)(x + 3).
6
Solve the quadratic equation: x^2 - 5x + 6 = 0
x = 2 and x = 3
x = -2 and x = -3
x = 1 and x = 6
x = -1 and x = -6
Explanation: Factor the quadratic: x^2 - 5x + 6 = (x - 2)(x - 3). Set each factor equal to zero: x = 2 or x = 3.
7
A triangle has sides 6 cm, 8 cm, and 10 cm. What type of triangle is it?
Equilateral
Isosceles
Right triangle
Obtuse triangle
Explanation: Check the Pythagorean relationship: 6^2 + 8^2 = 36 + 64 = 100 = 10^2. So the triangle is right-angled.
8
Which of the following are true statements about the function y = 2x + 1?
The y-intercept is 1
The slope is 2
The graph is a parabola
The function is linear
Explanation: The equation is in slope-intercept form y = mx + b, where m = 2 and b = 1. This is a linear function, so its graph is a straight line, not a parabola.
9
If the mean of 4, 6, 8, and x is 7, what is x?
8
10
12
14
Explanation: The mean is 7, so the total sum must be 4 × 7 = 28. The known numbers add to 4 + 6 + 8 = 18, so x = 28 - 18 = 10. The correct value is 10.
10
Which expressions are equivalent to 2(x + 3) + x?
3x + 6
2x + 3 + x
x + 6 + 2x
2x + 6 + x
Explanation: Distribute and combine like terms: 2(x + 3) + x = 2x + 6 + x = 3x + 6. Any expression that simplifies to 3x + 6 is equivalent.
