# Mathematics Quiz Bee - Grade 9

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## 24 Questions

### What is the simplified expression of $7 \sqrt{21} \sqrt{3}$?

$7 \sqrt{63}$

Conjugates

### What is the simplified expression of $\frac{1}{5} (-32)$?

$-2$

### What is the conjugate of the radical expression $(3 - \sqrt{2})$?

$3 + \sqrt{2}$

Square

### What is the simplified expression of $\frac{2}{3} (27)$?

$9$

2

### Which theorem states that 'The segment connecting the midpoint of two sides of a triangle is parallel to the third side and half as long'?

Triangle Midline Theorem

9 units

### Which of the following is not a radical equation?

$x^{2} = 5$

### Which statement about rhombuses is true?

Rhombus is a type of parallelogram.

### If ABCD is a rhombus and angle DAC measures 54 degrees, what is the measure of angle DAB?

$46°$

### What operation is needed to solve for x in the equation 2x - 3 = 5?

Divide both sides by 2

Trapezoid

### What is the radical form of 3/4?

$3/\sqrt{4}$

25

### What is the simplification of the radical expression $\sqrt{200}$?

$10\sqrt{2}$

Trapezium

Power of a power

Square

4x

8m

0

### If the area of a kite is 98 cm^2 and EG = 7cm, what should be the length of FD in the given figure (diagram not shown)?

$\sqrt{41}$ cm

## Study Notes

### Simplifying Expressions

• (7/1) × (21/3) = 7/1
• 1/5 × (-32) = -2
• 2/3 × (27) = 9
• 1/4 × (-4) = undefined
• 3200 = 10 × 2

### Conjugates

• Two binomial radical expressions that have the same number but only differ in the sign that connects the binomials are called conjugates
• Example: 3 - √2 and 3 + √2 are conjugates

• A parallelogram with four right angles and four congruent sides is called a square
• A quadrilateral with two pairs of parallel and congruent sides is called a parallelogram
• A quadrilateral with exactly one pair of parallel sides is called a trapezoid
• A quadrilateral with no pairs of parallel sides is called a trapezium
• A quadrilateral with two distinct pairs of congruent sides is called a kite

• An equation that contains radicals and a variable expression in the radicand is called a radical equation
• Example: √(2x - 3) = 5

### Theorems

• The Triangle Midline Theorem states that "The segment that connects the midpoint of the two sides of a triangle is parallel to the third side and half as long"

### Laws of Exponents

• The Power of a Product states that a^m × a^n = a^(m+n)
• The Power of a Power states that (a^m)^n = a^(mn)
• The Power of a Quotient states that (a/b)^m = a^m / b^m
• The Product of a Power states that (ab)^m = a^m × b^m

### Miscellaneous

• The index of an expression is another term for its order
• A convex quadrilateral is a quadrilateral where all angles are less than 180°

Test your mathematical knowledge with this quiz featuring true or false questions, fill in the blanks, and exponent laws. Prepared by JERWIN C.ORENCE, this quiz covers topics like basic arithmetic, geometry, and algebra.

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