Grade 10 Algebra Assessment

Question 1

Factorize the expression $$2x^2$$ - 5x - 3.

Accepted Answer

(2x + 1)(x - 3)

Answer

(2x - 6)(x + 1)

Answer

(2x + 3)(x - 1)

Answer

(2x - 1)(x + 3)

Question 2

Factorize the expression $$x^2$$ + 6x + 9.

Accepted Answer

(x + 3)(x + 3)

Answer

(x - 3)(x - 3)

Answer

(x - 3)(x + 3)

Answer

(x + 3)(x - 3)

Question 3

Factorize the expression $$4x^2$$ + 16.

Accepted Answer

4(x + 2)(x -2)

Answer

4(x + 4)(x - 4)

Answer

4(x - 4)(x - 4)

Answer

4(x - 4)(x + 4)

Question 4

Factorise the expression $$3x^2$$ - 6x - 9.

Accepted Answer

(3x + 3)(x - 3)

Answer

(3x + 1)(x + 3)

Answer

(3x - 1)(x - 3)

Answer

(3x - 1)(x + 3)

Question 5

Factorise the expression $$x^2$$ - 5x + 6.

Accepted Answer

(x - 3)(x - 2)

Answer

(x + 3)(x - 2)

Answer

(x - 3)(x + 2)

Answer

(x + 3)(x + 2)

Question 6

Factorise the expression $$2x^2$$ + 5x + 3.

Accepted Answer

(2x + 3)(x + 1)

Answer

(2x - 3)(x + 1)

Answer

(2x + 1)(x + 3)

Answer

(2x - 1)(x + 3)

Question 7

What is the simplified form of ($$5x^2$$ - 3x + 2) + (-$$2x^2$$ + 4x - 1)?

Accepted Answer

$$3x^2$$ + x + 1

Answer

$$3x^2$$ + x + 3

Answer

$$3x^2$$ + x - 1

Answer

$$3x^2$$ - x + 1

Question 8

What is the simplified form of 6(3x + 4) - (2x - 1)?

Accepted Answer

16x+25

Answer

20x + 23

Answer

16x + 6

Answer

18x + 5

Question 9

What is the simplified form of ($$2a^2$$ - 3ab + $$4b^2)$$(a - b)?

Accepted Answer

$$2a^3$$ - $$5a^2b$$ + $$7ab^2$$ - $$4b^3$$

Answer

$$2a^3$$ - $$4a^2b$$ + $$b^3$$

Answer

$$2a^3$$ - $$5ab^2$$ - $$4b^2$$

Answer

$$2a^3$$ - $$3a^2b$$ + $$7ab^2$$ - $$4b^3$$

Question 10

What is the simplified form of 4x/8 - 2x/6?

Accepted Answer

x/6

Answer

x/16

Answer

x/12

Answer

x/24

Question 11

What is the simplified form of ($$3x^2$$ + 4x - 8) - ($$x^2$$ - 2x + 1)?

Accepted Answer

$$2x^2$$ + 6x - 9

Answer

$$2x^2$$ + 6x - 7

Answer

$$2x^2$$ + 2x - 7

Answer

$$2x^2$$ + 2x - 9

Question 12

What is the simplified form of $$9a^2b$$^3 / 3ab?

Accepted Answer

$$3ab^2$$

Answer

$$3a^2b$$

Answer

$$6ab^2$$

Answer

$$3a^2b$$^2

Question 13

Which of the following is the solution to the equation 3x + 5 = 17?

Accepted Answer

x = 4

Answer

x = 3

Answer

x = 6

Answer

x = 9

Question 14

What is the value of x in the equation 2(x - 3) = 10?

Accepted Answer

x = 8

Answer

x = -1

Answer

x = 0

Answer

x = 5

Question 15

Which of the following is the solution to the equation 4(x + 3) = 28?

Accepted Answer

x = 4

Answer

x = -1

Answer

x = 2

Answer

x = 7

Question 16

What is the solution to the equation 2(3x - 1) + 3(2x + 1) = 11?

Accepted Answer

x = 5/6

Answer

x = -2

Answer

x = -1

Answer

x = 1

Question 17

What is the value of x in the equation (x/2) + 3 = 7?

Accepted Answer

x = 8

Answer

x = -2

Answer

x = 2

Answer

x = 12

Question 18

Which of the following is the solution to the equation 7 - 2(3x + 2) = 1?

Accepted Answer

x = 1/3

Answer

x = 0

Answer

x = 1

Answer

x = 2

Question 19

Solve the inequality 3x + 5 > 10.

Accepted Answer

x > 1

Answer

x < 1

Answer

x < 5

Answer

x > 5

Question 20

Which of the following is a solution for the inequality 2x - 3 < 9?

Accepted Answer

x < 6

Answer

x > 6

Answer

x > 3

Answer

x < 3

Question 21

Solve the inequality -4x + 9 &le; 5.

Accepted Answer

x &ge; 1

Answer

x &le; 1

Answer

x &ge; 2

Answer

x &le; 2

Question 22

Which of the following is a solution for the inequality 7x + 3 > 24?

Accepted Answer

x > 3

Answer

x < 3

Answer

x > 4

Answer

x < 4

Question 23

Solve the inequality 2(3x - 1) &le; 4x + 2.

Accepted Answer

x &le; 2

Answer

x &ge; -2

Answer

x &le; 2/3

Answer

x &ge; 2/3

Question 24

Which of the following is a solution for the inequality -2x + 7 < 9?

Accepted Answer

x > -1

Answer

x < -1

Answer

x > -2

Answer

x < -2

Question 25

1. Solve the following system of equations: 2x + 3y = 8 4x - y = 10

Accepted Answer

x = 19/7, y = 6/7

Answer

x = 3, y = -2

Answer

x = 1, y = 2

Answer

x = -1, y = 4

Grade 10 Algebra Assessment in Sep 2024

1. Factorize the expression 2x^2 - 5x - 3.

2. Factorize the expression x^2 + 6x + 9.

3. Factorize the expression 4x^2 + 16.

4. Factorise the expression 3x^2 - 6x - 9.

5. Factorise the expression x^2 - 5x + 6.

6. Factorise the expression 2x^2 + 5x + 3.

7. What is the simplified form of (5x^2 - 3x + 2) + (-2x^2 + 4x - 1)?

8. What is the simplified form of 6(3x + 4) - (2x - 1)?

9. What is the simplified form of (2a^2 - 3ab + 4b^2)(a - b)?

10. What is the simplified form of 4x/8 - 2x/6?

11. What is the simplified form of (3x^2 + 4x - 8) - (x^2 - 2x + 1)?

12. What is the simplified form of 9a^2b^3 / 3ab?

13. Which of the following is the solution to the equation 3x + 5 = 17?

14. What is the value of x in the equation 2(x - 3) = 10?

15. Which of the following is the solution to the equation 4(x + 3) = 28?

16. What is the solution to the equation 2(3x - 1) + 3(2x + 1) = 11?

17. What is the value of x in the equation (x/2) + 3 = 7?

18. Which of the following is the solution to the equation 7 - 2(3x + 2) = 1?

19. Solve the inequality 3x + 5 > 10.

20. Which of the following is a solution for the inequality 2x - 3 < 9?

21. Solve the inequality -4x + 9 ≤ 5.

22. Which of the following is a solution for the inequality 7x + 3 > 24?

23. Solve the inequality 2(3x - 1) ≤ 4x + 2.

24. Which of the following is a solution for the inequality -2x + 7 < 9?

25. 1. Solve the following system of equations: 2x + 3y = 8 4x - y = 10

26. 2. Solve the following system of equations: 3x + 2y = 13 2x - 4y = -6?

27. 3. Solve the following system of equations: 6x + 3y = 21 2x + y = 8

28. 4. Solve the following system of equations: 4x - 5y = -13 2x + 3y = 7

29. 5. Solve the following system of equations: 3x + 4y = 12 6x + 8y = 18

30. 6. Solve the following system of equations: 2x + 5y = 9 6x + 15y = 27

31. What is the next term in the sequence: 2, 5, 10, 17, 26, ?

32. What is the 10th term in the arithmetic sequence: 3, 7, 11, 15, ...?

33. What is the sum of the first 15 terms in the geometric sequence: 2, 6, 18, 54, ...?

34. Which term is missing in the following arithmetic sequence: 8, __, 20, 26, 32, 38?

35. What is the 7th term in the Fibonacci sequence: 1, 1, 2, 3, 5, 8, ...?

36. What is the common difference in the arithmetic sequence: 9, 16, 23, 30, ...?

37. What is the definition of a graph in mathematics?

38. Which of the following is a directed graph?

39. What is the slope of a vertical line on a graph?

40. What does the x-intercept represent on a graph?

41. Which type of graph is used to show the relationship between two variables?

42. In a line graph, what does the slope of the line indicate?

43. If the price of a shirt is $40 and it is reduced by 20%, what is the sale price?

44. A car is traveling at a speed of 60 km/hr. How far can it travel in 2.5 hours?

45. The length of a rectangle is 10 cm and its width is 5 cm. What is its area?

46. A notebook costs $8. If Sarah buys 3 notebooks, how much does she spend?

47. Sara borrowed $500 from a friend at an interest rate of 8% per year. How much interest will she have to pay after 2 years?

48. The ratio of boys to girls in a class is 3:5. If there are 24 boys in the class, how many girls are there?

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