# Grade 10 Math Practice Test Questions

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

- Question

Solve the systems of equations.

- Question

Expand and simplify the expressions.

- Question

Factor completely the expressions.

\( \)\( \)\( \)\( \) - 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).

- Question

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

- Question

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

- Question

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

- Question

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

- 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.

- 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 \( y = 3 \).

- 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?

- 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 ?

- 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 \( AC\).

- 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 ?

- Question

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

- Question

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

- 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.

## More References and links

- Factor Polynomials by Common Factor Questions With Solutions .
- Factor Polynomials by Grouping .
- Vertex and Intercepts of Quadratic Functions .
- Complete the Square .
- Pythagorean Theorem .
- Similar Triangles .
- Sine Law .
- Cosine Law .
- Kite Problems .
- Angles in Parallel Lines and Transversals .
- Pyramid Problems .
- More High School Math including grade 10 math.