Grade 10 Math Practice Test Questions

Grade 10 math practice test questions including algera, trigonmetry and geometry are presented along with their detailed solutions

  1. Question
    Solve the systems of equations.
    System of Equations

    Solution to Question 1


  2. Question
    Expand and simplify the expressions.
    Expressions

    Solution to Question 2


  3. Question
    Factor completely the expressions.
    Expressions

    Solution to Question 3


    \( \)\( \)\( \)\( \)
  4. Question

    Given \( f(x) = -2 x^2 - 2 x + 4 \), find
    a) the vertex of the graph of \( f \),
    b) The x and y intercepts of the graph of function \( f(x) = -2 x^2 - 2 x + 4 \),
    c) The axis of symmetry of the graph of \( f \).
    d) Use a calculator to graph \( f \) and check the answers to parts a) , b) and c).

    Solution to Question 4


  5. Question
    Use proportionality to complete, if possible, the tables of values in a), b) and c).
    Tables of Values

    Solution to Question 5


  6. Question
    Find all unknown sides and angles in the right triangle below.
    Right Triangle

    Solution to Question 6


  7. Question
    Angle \( \alpha \) is an acute angle such that \( \sin \alpha = 0.6 \). Find \( \cos \alpha\) and \( \tan \alpha\)

    Solution to Question 7


  8. Question
    In the figure below, BE is parallel to CD. Find the lengths \( x \) and \( y \) of the segments CD and DE respectively.
    Similar Triangles

    Solution to Question 8


  9. Question
    The lengths of side AB and side BC of a triangle ABC are 14 cm and 10 cm respectively. The size of angle C is 49o. Find all unknown angles and all unknown sides of the triangle.

    Solution to Question 9


  10. Question
    Find the values of \( A \) and \( B \) if the line with equation \( A x + By = 1 \) passes through the points \( (1,5) \) and has a y-intercept at \( y = 3 \).

    Solution to Question 10


  11. Question
    A chemist needs to make 5 L of 45%, by volume, of sulfuric acid solution. He has 20% and 55%, by volume, of sulfuric acid solutions available. He decides to mix the 20% and 55% solutions to make the 45% solution. How many liters of each solution must be mixed?

    Solution to Question 11


  12. Question
    A family drove 1000 km from Paris to Prague in 10 hours. They drove part of the distance at an average speed of 80 km/h, and the rest at an average speed of 120 km/h. What distance did they drive at each speed ?

    Solution to Question 12


  13. Question
    Triangle ABC has vertices at the points \( A(2,3) \), \( B(-3 , 4) \) and \( C \) located on the vertical line \( x = -1\). Find all possible coordinates of point \( C \) so that \( ABC \) is a right triangle with hypotenuse \( AC\).

    Solution to Question 13


  14. Question
    Linda spends \( 70\% \) of her monthly budget on housing and food and spends \( \$ 500 \) more on housing than on food. She spends \( 5\% \) of her budget and that is \( \$ 200 \) to pay for a monthly membrship at a yoga club.
    How much does she spend on food and housing separately ?

    Solution to Question 14


  15. Question
    Find the area of the kite shown below given that \( \overline {CD} = 10 \) cm

    Kite

    Solution to Question 15


  16. Question
    m and n are parallel lines. Show that lines m and r are perpendicular.

    Parallel Lines and Intersecting Lines

    Solution to Question 16


  17. Question
    Find the length of the height AM of the right square pyramid if its volume is 1500 cubic centimeters and the length of the diagonal CE of its base is equal to 10 centimeters.

    Right Pyramid with Square Base

    Solution to Question 17




More References and links

  1. Factor Polynomials by Common Factor Questions With Solutions .
  2. Factor Polynomials by Grouping .
  3. Vertex and Intercepts of Quadratic Functions .
  4. Complete the Square .
  5. Pythagorean Theorem .
  6. Similar Triangles .
  7. Sine Law .
  8. Cosine Law .
  9. Kite Problems .
  10. Angles in Parallel Lines and Transversals .
  11. Pyramid Problems .
  12. More High School Math including grade 10 math.

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