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.
   
   

   Solution to Question 1

   
   
2. Question
   Expand and simplify the expressions.
   
   

   Solution to Question 2

   
   
3. Question
   Factor completely the expressions.
   
   

   Solution to Question 3

   
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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).
   
   
   

   Solution to Question 5

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

   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.
   
   
   

   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 49^o. 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
    
    
    
    

    Solution to Question 15

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

    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.
    
    
    
    

    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.