Grade 9 Review

Simplify or Solve

100

Simplify: -8(xy⁴)(-x³)

24x⁴y⁴

200

Solve for x: 

12(x-2)=5-3(2x-5)

x=22/9

300

Fill in the blank:

(?)/15x³y  = 4x²c/3y

? = 20cx⁵

400

Simplify:

(5a²c⁷)⁴

Ans: 625a⁸c²⁸

500

Solve for x:

0.5+0.02(3x+5)=2

Ans: 70/3

Linear Equations

100

What is the proper form of a Linear Equation?

y=mx+b

200

find the slope of the following line (5, 3) and (2, -7)

y₂-y₁ / x₂ - x₁ 

(-7 - 3) / (2 - 5)

-10 / -3

10/3

300

find the slope of the following line (1, -3) and (1, 9)

y₂-y₁ / x₂ - x₁ 

(9 - (-3)) / (1 - 1)

12 / 0

Undefined

400

Find the equation of a line given points (5,4) and (10,6)

Find slope: m=2/5

y=(2/5)x + b   Now find b by plugging in a point

use (5,4) --> (4)=(2/5)(5) + b

b=2

the equation is y=(2/5)x + 2

500

Determine the point of intersection of the following lines algebraically.

y=(1/2)x +1   and y=-x+4

(1/2)x + 1 = -x+4    (multiply both sides by 2)

x+2=-2x+8   (solve for x)

x=2     (use x to solve for y)

y=-(2)+4

y=2     therefore point of intersection is (2,2)

Geometry

100

What is the formula for pythagorean theorem?

a²+b²=c²

200

Two angles are complementary. One angle is 27^o. What is the measure of the other angle?

complimentary angles sum to 90^o

90^o-27^o=63^o

300

Two supplementary angles add to 180^o. One angle is twice the other. Find both angles.

x+2x = 180

180=3x

x=60

so 60^o and 120^o

400

In a triangle, two angles measure 35^o and 65^o

Find the third angle and classify the triangle by its angles (acute, right, or obtuse).

180 - 35 -65 = 80

All 3 angles are less than 90^o so it is acute

500

A large rectangle measures 8 cm by 6 cm. A smaller rectangle measuring 4 cm by 2 cm is cut out from one corner. What is the area of the remaining shape?

Area of large rectangle (A Large)= 8x6 = 48 cm²

Area of small rectangle (A Small) = 4x2 = 8 cm²

Area remaining = 48 - 8 

Answer: 40cm²

Mixed Questions

100

A hoodie originally costs $60. It goes on sale for 25% off. What is the sale price?

0.25 x 60 = 15

60-15 = 45

$45

200

A group of students recorded the number of hours they studied last week:

14, 7, 6, 6, 3, 12, 11, 9, 2, 8
Find the mean.

(14+ 7+ 6+ 6+ 3+ 12+ 11+ 9+ 2+ 8) / 10

Mean is 7.8 or 78/10

300

Explain the difference between gross income and net income.

Gross income = the total amount you earn before any deductions.

Net income = the money you actually take home after deductions (like taxes, CPP, EI, benefits, etc.).

400

Expand and Simplify: 

4x(3x − 5) − 7(x² + 2x)

5x² - 34x

500

^{18. Which of the following is a primary source of data?}

^{A) Looking up the NHL’s leading scorers on NHL.com}

^{B) Getting information about your stocks from the newspaper}

^{C) Surveying the students in your class to determine what the most popular type of music is}

^{D) Using data collected by Statistics Canada to determine what is the most popular sport in Canada}

C) Surveying your class → primary (data collected first hand)

Word Problems

100

A school music club offers to cover $50 of each student’s Spotify Premium subscription. If the club has $1000 in total funding, how many students can get their subscription covered?

1000÷50=20
20 students can receive help

200

A soccer stadium is building an accessible ramp  (90^o) from the locker room to the field. The ramp rises 6m and extends 11m across the ground.
How long is the ramp the athletes will walk up?

Pythagorean theorem:

a²+b²=c²

6²+11²=c²

c=sqrt(157) or 12.53m

300

Ralph is 21 and Aunt Lisa is 76. How many years ago was Aunt Lisa exactly 6 times as old as Ralph?

x=#of years ago.  Ralph: 21−x and Aunt Lisa: 76−x

76-x=6(21-x)

76-x=126-6x

5x=50

x=10  so Ralph was 21 - (10) =11 and Aunt Lisa was 76 - (10) = 66. 11x6 = 66 

400

The length of a rectangle is one less than 3 times the width. If the width is increased by 5 and the length decreased by 4, the new perimeter is 48 cm. Find the dimensions of the original rectangle.

W= width of original rectangle.  Length L=3w-1

New Width (NW)= w+5  New Length (NL)= L-4

NL = (3w-1) - 4  = 3w-5

Perimeter of New rectangle (48cm) = 2(NL+NW) so 48=2[(w+5) + (3w-5)] so now 48=2(4w) so 48=8w then w=6

Now in the original length L =3w-1 = 3(6)-1 = 18-1 = 17. SO L =17cm and W=6cm

500

A movie theatre charges $12 for an adult ticket and $8 for a student ticket. On a certain night, the theatre sold 150 tickets and collected $1,520 in total.
How many adult and how many student tickets were sold?

let a = # adult tickets and s = # student tickets sold

Total tickets sold is: a+s=150 and total money is: 12a+8s =$1520

substitute from first equation: s=150-a and plug into second equation: 

12a + 8(150-a)=1520. Distribute and combine like terms to get 4a+1200=1520.

4a = 320 so a = 80. Find s now: s=150-80 so s =70

therefore 80 adult tickets and 70 student tickets