Download Equations – normal - Grade 9 Math Semester 2

Math 9
Review for April 2010 Cumulative Assessment
1) Solve the following equations:
a) 13x + 7 = 29 + 2x
b) 5(-4 – x) = -2(3x + 2)
x x x
  1
2 5 4
x3 x2

d)
5
3
c)
2) Solve and check the following equations.
a) 2(x – 2) = 3x – 14
3) Rearrange for u:
a) v = u + at
b) w = uv – z
b)
3x
2
+
3
4
=2
c) v = 2 ut2
3
4) A board (4.2 m) is cut into two pieces. One piece is to be three times as long as the other. What will
be the length of the longer piece?
5) Dan has 18 coins, composed of quarters and dimes. If he has $2.40, how many quarters and dimes
does he have?
6) Emily is 2 years older than her sister Sarah. Eight years ago, she was twice as old as Sarah. How old
are the two sisters right now?
7) Four consecutive even numbers have a sum of 212. Find the numbers.
8) Jack has 37 animals: chickens and sheep. How many sheep does he have if the 37 animals have a
total of 106 legs?
9) The perimeter of a rectangle is 32m. The length of the rectangle is two times more than the width plus
1m. What are the dimensions of the rectangle?
10) Solve the following inequalities:
a) 3n – 2 < 7
b) 5a+ 2 ≥ -2a -5
c) 8(3x - 5) < -4x + 2
d)
c3
 4
2
11) Solve, give the set notation, AND graph your solution set:
a) 7n – 6 > 22
b)
c) 9x – 3  3(x – 5)
12) Write the equation of each line for each graph.
1st – find the slope
2nd – find the y intercept
3rd – place in y = mx + b format
13) Find the equation of the line with slope -4 and passing through (-2, 5).
14) Find the equation of a line that passes through:
a. G(-4, 7) and H(1,0)
b. C(-2,8) and D(1, -1).
15) Rearrange the following into y=mx+b form:
i. 3x – 4y = 12
ii. 4x + 6y – 24 = 0
iii. 5x – 2y + 10 = 0
16) Find the x and y intercepts for the following equations:
i. y = 2x – 5
ii. 4x + 6y – 12 = 0
iii. 3x – 4y = 12
iv.
y
2
x6
3
ANSWERS:
1. a) x = 2
b) x = 16
2. a) x = 10
b) x 
16
9
3. a) u = v – at
b) u 
w z
v
d) x = ½
c) x = 20
c) u 
3v
2t 2
4. The longer piece will be 3.15m.
5. He has 4 quarters and 10 dimes.
6. Emily is 12 and Sarah is 10.
7. The numbers are 50, 52, 54, 56.
8. There are 16 sheep and 21 chickens.
9. The rectangle has a width of 5m and a length of 11m.
b) a ≥ -1
10. a) n < 3
11.
c) x 
3
2
d) c < 5
a) n > 4
{ n | n > 4, n  R }
graph with open dot on 4, arrow to the right
b) x ≤ -2
{ x | x ≤ -2, x  R }
graph with closed dot on -2, arrow to the left
c) x ≤ -2
{ x | x ≤ -2, x  R }
graph with closed dot on -2, arrow to the left
5
5
x 1
; b = 1; y 
4
4
4
4
b) m = ; b = 0 ; y  x
3
3
1
1
c) m = ; b = -2; y  x  2
3
3
12. a) m =
13. y  4 x  3
14. a) y 
15. i) y 
7
7
x
5
5
b) y  3 x  2
3
x3
4
16. i) y-int: 5 and x-int:
ii) y 
5
2
2
x4
3
ii) y-int: 2 and x-int: 3
iii) y 
5
x5
2
iii) y-int: -3 and x-int: 4 iv) y-int: 6 and x-int: -9