Grade 9 Math Review

Rational Numbers and Algebra

100

2x - 4 = 7

11/2

200

2/7 - (3/4)

-13/28

300

3x/(x + 17) - 3/(2x - 5) = ?

3/4

400

3/5 / 4/6

9/10

500

1.5 + 3/5 - 2/3 + 0.4 x 2

67/30

Exponents

100

2³ +3²

17

200

2² x 2³ x 2^-4

2^{2 = 4}

300

(a³b³)² / (a^-1b²)

a⁷b⁴

400

((2b)^-1 x (a²b³)⁶ ) / (5²a^-1b³)

a¹³b¹⁴/50

500

(a²a^-3b⁴c²d²)^-1 / (ab²c²c^-2d³d^-5)

1/b⁶c²

Linear Relations

100

What are the slope and y-intercept of the line y = -2x+3?

-2, 3

200

Where will the two lines cross? (Give the x value)

y = 2x - 4

y = -1/2x +3

x = -4/10

300

Write a linear equation to represent the following problem: A candle is 8 inches tall, and it melts at a rate of 1/2 inch per hour. Define your variables.

y = 1/2x +8 

y = height of the candle

x = number of hours

400

Write an equation for a horizontal line with a y-intercept of 1.5.

y = 1.5

500

The temperature is 15^o at 5:00 am and is rising by 2^o each hour. At what time will it reach 26^o?

10:30 am 

Polynomials

100

Combine like terms: 8x³ + 11x² + 3 - x² - 5 + 3x²

8x³ + 13x² -2

200

2(x² - y² - 4) + 4(x² - y² - 3)

6x² - 6y² - 20 

300

2x(4x³ - x² - x + 4) + (2x)² - 3(x² - x³ - 1)

8x⁴ + x³ - x² +8x +3

400

(x² - x) - (2x³ - x²)^-1 + (3x³ - (2x)(-4x)) - x²

x³ + 9x² - x - 1

500

((2x² -x²) - (x³ - 2x⁵ - x⁰) + x³ - 2x⁵ - (-3x²) - 3x + 1)/ x

4x - 3

Surface Area

100

A triangle has a hypotenuse of 10cm and one side of length 8cm. What is the length of the missing side?

6cm

200

Calculate the surface area of a cylinder with a diameter of 6m and a height of 3m.

113.1m²

300

Calculate the surface area of a rectangular prism with a length of 2.5m, a width of 4m and a height of 3m.

59m²

400

Calculate the surface area of a triangular prism with a base of 3, a height of 4 and a length of 6.

58.15 units squared

500

A cake with 3 layers - the height of each layer is 4 inches, the diameter of the smallest layer is 3 inches, the middle is 5, and the biggest is 7. Calculate the surface area.

84.5 pi or 226.98 inches²