GRADE 10 EXAM PREP
1. Determine the number of solutions that this system has.
-3x - 2y = 6 6x + 4y = 12
2. Factor a) m2 – 5m – 14 b) 2c² + 3c – 20
c) t² - 49 d) 4x2y3 + 2xy2
3. The endpoints of the line segment TU are T( 10, -5 ) and U( 14, 1 ).
a) Find the midpoint. b) Find the length of TU.
4. Expand and simplify. a) ( 3a + 2 )( 5a - 4 ) b) 2(y - 3)²
5. Solve this system of equations x + 2y = 0 y = 3x + 7 by graphing and algebracically using elimination
6. State the vertex for the quadratic function y = ( x + 6 )2 + .
7. What kind of roots does the function y = x2 + x - 2 have?
8. Which are the exact roots for 5m2 – 2m – 2 = 0
9. State the zeroes for (m – 2)(m + 5) = 0. Find the coordinates of the vertex and express the relation in standard form.
10. Given that D CAE is similar to D CBD, find
the length of x.
11. Calculate angle A to 1 decimal place.
12. Evaluate to 4 decimal places.
a) sin54° b) tan 67°
13. Find the angle to 1 decimal place.
a) tan x = 0.5241 b) cosT = 0.3426
14.
a) State the discriminant for this quadratic solution.
b) How many real roots will there be?
15. Given the parabola defined by ,
a) State the coordinates of the vertex.
b) State the equation of the axis of symmetry.
c) Does the function have a maximum or minimum point?
d) State the maximum/minimum value.
e) State the y-intercept.
f) Sketch the graph. Be sure to show 5 points.
16. State the equation of the parabolaafter undergoing the
following transformations (each part is a separate case).
a) A horizontal shift of 2 units right.
b) Vertical stretch of factor 3 & vertical shift 2 units down.
c) A reflection in the x-axis and horizontal shift of 4 units left.
17. Write the equation y = x2 – 2x + 4 in the form y = a( x – h )2 + k.
18. Use the sine law to find side c, to the nearest tenth of a centimetre.
19. Find the equation of a parabola in vertex form if the parabola has a vertex of (-3, -9) and passes through the point (-7, -1)
20. Find the roots of 2x2 - 5x + 1 = 0 by using the quadratic formula
21. If ΔABC has vertices A(12, 4), B(-6, 2) and C(-4, -2), find the equation of the median from B.
22. A triangle has vertices at P(-2, 2), Q(-1, -3) and R(4, 1). Show that this is NOT a right triangle.
23. Solve for each:
a) A b) B
58º 28
20 25 15
C a B
A 23 C