Al-Hussan Model Schools

International Section
2022-2023
Math review grade 10

1
Q1. Describe the interval shown using an inequality, set notation, and interval
notation.
1. 2.

Inequality: _________________ Inequality: _________________

Set Notation: _________________ Set Notation: _________________

Interval Notation: _________________ Interval Notation: _________________

Describe the domain and range of the graph using an inequality, set notation, and
interval notation. Then describe its end behavior.

3. Graph of f ( x ) = − x 2 + 3 : Domain:
Inequality: _________________

Set Notation: _________________

Interval Notation: _________________

Range:
Inequality: _________________

Set Notation: _________________

Interval Notation: _________________

End Behavior:
_______________________________________

Draw the graph of the function with its given domain. Then determine the range
using interval notation.
4. g ( x ) = −3 x + 2 with domain ( −1, 2] :

Range: _________________

2
Q2: Use the graph to answer Problems 1–4.
1. On which intervals is the function increasing and
decreasing?

_________________________________________________

_________________________________________________

2. What are the local maximum and minimum values?

_________________________________________________

_________________________________________________

3. What are the zeros of the function?

_________________________________________________

4. What is the domain and range?

_________________________________________________

_________________________________________________

Q3: Let g(x) be the transformation of f(x). Write the rule for g(x) using the change
described.
___________________
1. reflection across the y-axis followed by a vertical shift 3 units up

2. horizontal stretch by a factor of 5 followed by a horizontal shift right

___________________
2 units

1
3. vertical compression by a factor of followed by a vertical shift
8
___________________
down 6 units

4. reflection across the x-axis followed by a vertical stretch by a factor

___________________
of 2, a horizontal shift 7 units left, and a vertical shift 5 units down

3
Q4: Find the inverse of each function.

1. f ( x ) = 10 − 4x _____________________________________

2. g ( x ) = 15x − 10 _____________________________________

x − 12
3. h ( x ) = _____________________________________
4
3x + 1
4. j ( x ) = _____________________________________
6

Q5: Use composition to determine whether each pair of functions

are inverses.

7 2 10
1. g ( x ) = −5 − x and f ( x ) = − x − _____________________________________
2 7 7

1 7
2. s ( x ) = 7 − 2x and t ( x ) = x+ _____________________________________
2 2
1
3. h ( x ) = x + 4 and j ( x ) = 3x − 12 _____________________________________
3

Q6. For each absolute value graph, identify the domain, the range, and the vertex.
The first one is started for you.
1. 2.

_______________________________________ _____________________________

4
Q7. For each absolute value function, identify the range and the vertex. Then graph the
function. The first one is started for you.

1. f ( x ) = x − 4 2. f ( x ) = x + 3

_______________________________________ ________________________________________

Q8.Solve.
1. How many solutions does the equation x + 7 = 1 have? _________________________

2. How many solutions does the equation x + 7 = 0 have? _________________________

3. How many solutions does the equation x + 7 = −1 have? _________________________

Solve each equation algebraically.

1
4. x = 12 5. x = 6. x − 6 = 4
2

_______________________ _______________________ _______________________

7. 5 + x = 14 8. 3 x = 24 9. x + 3 = 10

_______________________ _______________________ _______________________

Solve each equation graphically.

10. x − 1 = 2 11. 4 x − 5 = 12

5
Q9. Solve each inequality and graph the solutions.
1. x − 7  − 4 2. x − 3 + 0.7  2.7

_______________________________________ ________________________________________

1
3. x+2 1 4. x − 5 − 3  1
3

_______________________________________ ________________________________________

1
5. 5 x  15 6. x + −22
2

_______________________________________ ________________________________________

7. x − 2 + 7  3 8. 4 x − 6  − 8

_______________________________________ ________________________________________

Q10 . Find the square of each imaginary number.

3i 21
1. −21i 2. 2i 97 3. −
5

_______________________ _______________________ ________________________

Q11. Determine whether each equation has real or imaginary solutions by solving.

1.
1 2
3
x + 15 = −21 2. −15 x 2 + 44 = 2 ( ) (
3. 6 3 x 2 − 1 = 3 5 x 2 − 7 )
_______________________ _______________________ ________________________

_______________________ _______________________ ________________________

6
Q12. Solve.
The length of a rectangular garden is 4 times its width. The area is
102 square feet. What are the dimensions of the garden? __________________________________

Q13.

Write each expression as an imaginary number.

1. −25 2. 3 −49 3. − −81

_______________________ _______________________ ________________________

For each complex number, identify the real part.

4. 2i 5. −3 + 3 − 2i

_______________________________________ ________________________________________

For each complex number, identify the imaginary part.

1 1
6. i− 7. − 5 + (1 − 2)i
2 3

_______________________________________ ________________________________________

Simplify each expression. Write your answer as a complex number.

8. (4i) + (2 + 8i)

9. (2 − 7i) – (5 − 3i)

10. (3 + i)(1 − 4i)

7
Q14.

Solve using the quadratic formula.

1. x2 + 10x = −9 2. x2 + 2x = −4

_______________________________________ ________________________________________

3. x2 + 5x = 3 4. 2x2 + 7x + 10 = 0

_______________________________________ ________________________________________

Find the discriminant of each equation. Then determine the number of real or
nonreal solutions.
5. x2 − 3x = −8 6. x2 + 4x = −3 7. 2x2 − 12x = −18

_______________________ _______________________ ________________________

Solve each equation by completing the square.

8. x2 + 2x = 3 9. 2x2 =  + 

_______________________________________ ________________________________________

10. −3x2 + 18x = −30 11. 4x2 = −12x + 4

_______________________________________ ________________________________________

8
Q15.
Write the equation of each circle.
1. Center (8, 9) and radius r = 10 2. Center (−1, 5) and containing the
point (23, −2)

_______________________________________ ________________________________________

3. Center (2, 2) and containing the 4. Center (3, −5) and containing the
point (−1, 6) point (−7, 11)

_______________________________________ ________________________________________

5. Center (−3, 0) and radius r = 6 6. Center (6, −1) and radius r = 8

_______________________________________ ________________________________________

Graph each circle by rewriting the equations in standard form.

7. x2 + y2 + 4x − 4y − 1 = 0 8. x2 + y2 + 2x + 4y + 1 = 0

___________________________________________ ________________________________________

9
Q16

Write the equation in standard form for each parabola.

1. Vertex (0, 0), directrix y = −2 2. Vertex (0, 0), focus (9, 0)

_______________________________________ ________________________________________

3. Focus (−6, 0), directrix x = 6 4. Vertex (0, 0), focus (0, −3)

_______________________________________ ________________________________________

Q17. Solve each system algebraically.

 x 2 + y 2 = 101
1. 
10 x + y = 0

3 y = 4 x
2.  2
 x − y = −63
2

10
  x 2 + y 2 = 34
3. 
3 x − 3 y = 6

 x + y + 2z = −7

4.  −5z = 25
3 x − 3 y − 6z = 3


 20 x + 20 y = 46

5.  50 x + 20z = 126
60 x + 10 y + 50z = 263


11
Q17. Calculate the reference points for each transformation of the parent function
f ( x ) = x 3 . Then graph the transformation. (The graph of the parent function is
shown.)
1. g ( x ) = ( x − 3 ) + 2
3
2. g ( x ) = −3( x + 2)3 − 2

Write the equation of the cubic function whose graph is shown.

3. 4.

_______________________________________ ________________________________________

12