This document contains a quiz with math problems of varying difficulty levels: easy, average, and difficult. The easy problems are worth 1 point each and cover topics like the intersection of lines, factoring, algebraic expressions, evaluating expressions, and identifying quadrants and graphs. The average problems are worth 3 points each and involve factoring quadratics, simplifying expressions, and operations with monomials. The difficult problems are worth 5 points each and require solving systems of equations, finding areas of rectangles, identifying mathematicians, and identifying perfect square trinomials. An answer key is provided with the solutions.

1. Grade 8

2. EASY
1. What is the intersection of two distinct lines?
a. Point
b. Line
c. Plane
d. space

3. EASY
2. It is the reverse process of multiplication.
a. Factoring
b. Subtracting
c. Adding
d. Simplifying

4. EASY
3. An algebraic expression that is made up of three or
more terms.
a. Monomial
b. Binomial
c. Trinomial
d. Multinomial

5. EASY
4. Which of the following can be factored using the
difference of two squares?
a. 3x2 – 4x4
b. a4 – 64b3
c. x2 – 81
d. 9b2 – 144c3

6. EASY
5. Which of the following does not belong to the
group?
a. -
3
−5
b.
−3
−5
c.
3
5
d. -
−3
−5

7. EASY
6. Evaluate 8x0
a. 0
b. 1
c. 8
d. x

8. EASY
7. What is the value of 𝜋?
a. 4
b. 3.41
c. 3.1416
d. 3

9. EASY
8. In which quadrant can we found the ordered pair
(10, -2)?
a. Quadrant 1
b. Quadrant II
c. Quadrant III
d. Quadrant IV

10. EASY
9. If the graph of a linear function points downward
to the right, the function is said to be __________.
a. Increasing
b. decreasing
c. Constant
d. Not defined

11. EASY
10. The graph of a linear equation in two variables is
_________.
a. A point
b. A line
c. A ray
d. A segment

12. AVERAGE
1. Which of the following factors gives a product of
x2 + 5x + 4?
a. (x + 1) (x + 4)
b. (x + 2) (x + 2)
c. (x + 5) (x – 1)
d. (x + 2)2

13. AVERAGE
2. What is the least common denominator of
1
2𝑥3
, -
3
6𝑥2
, and
𝑥+1
9𝑥
?
a. 9x6
b. 18x3
c. 54x
d. 108

14. AVERAGE
3. Simplify 4x3 – 3x2 – x3 + 5x2
a. 3x3 + 2x2
b. 3x3 – 2x2
c. 5x3 + 2x2
d. 3x3 – 8x2

15. AVERAGE
4. Multiply the monomials 3xy2 and 5y.
a. 15xy3
b. 15xy2
c. 15x2y2
d. 8xy3

16. AVERAGE
5. If the reciprocal of x3 is 27, what is the value of x?
a. 1/9
b. 1/3
c. 3
d. 9

17. DIFFICULT
1. If (a + b)2 = 81, and a2 + b2 = 41,
what is ab?

18. DIFFICULT
2. A rectangle is 3x + 1 units long and
2x – 3 units wide. Find its area.

19. DIFFICULT
3. Who was the French
mathematician and philosopher who
invented the rectangular coordinate
system?

20. DIFFICULT
4. What is the possible value of b so
that 4x2 + bxy + 36y2 would be a
perfect square trinomial?

21. DIFFICULT
5. The length of a rectangle is 2 more
than twice its width. If the area of
the rectangle is 24 sq meters, find its
dimensions.

22. ANSWER KEY
Easy – 1 point
1. a 6. c
2. a 7. c
3. d 8. d
4. c 9. b
5. d 10. b

23. AVERAGE
3 points each
1. A
2. B
3. A
4. A
5. B

24. DIFFICULT
5 POINTS EACH
1. 20
2. 6X2 – 7X – 3
3. Rene Descartes
4. 24
5. L = 8, w = 3