Integers & rational numbers and operations
Evaluate: −3^2+5
-9 + 5 = -4
Simplify: 4x−2x+7
2x + 7
What is the slope and y intercept of the equation
2y= -6x−2
slope = -3
y intercept =-1
Area of triangle: base 8, height 5
½ × 8 × 5 = 20
Mean of: 5, 7, 9, 11
32/4 = 8
A bank account starts at -$25. A deposit of $40 is made, then a withdrawal of $18. What is the final balance?
-25 + 40 = 15
15 - 18 = -3
Evaluate when x = -2: x^2−3x+1
4 + 6 + 1 = 11
Find slope between (3, -2) and (7, 6)
(6 + 2)/(7 - 3) = 8/4 = 2
Volume of cylinder: r = 2, h = 9 (π ≈ 3.14)
3.14 × 4 × 9 = 113.04
Median of: 12, 5, 8, 15, 10
Ordered: 5, 8, 10, 12, 15
→ 10
Evaluate: ∣−12∣−(−5+9)
12 - 4 = 8
Simplify: 3(2x−4)−2(x+5)
6x - 12 - 2x - 10
= 4x - 22
Write equation of a line with slope -3 passing through (2, 5)
y - 5 = -3(x - 2)
→ y = -3x + 11
A shape is enlarged by scale factor 3. If original area is 12, what is new area?
3² × 12 = 9 × 12 = 108
A bag has 4 red, 6 blue, 10 green. Probability of NOT blue?
(4 + 10)/20
= 14/20
= 7/10
A diver is at -45 m. He rises 18 m, descends 7 m, then rises twice as much as the first rise. Where is he now?
Start: -45
+18 = -27
-7 = -34
+36 = 2 meters
Rewrite in standard form:
5x−2=3x+10
5x - 3x = 10 + 2
→ 2x -12 = 0
Solve system:
y = 2x + 1
y = x + 7
2x + 1 = x + 7
x = 6, y = 13
(6, 13)
Surface area of cube with side 6
6 × 6² = 6 × 36 = 216
Two dice are rolled. Probability sum = 8?
(5 outcomes) / 36 = 5/36
Evaluate and simplify:
(−2)^3−4[3−(5−9)]
(-8) - 4[3 - (-4)]
= -8 - 4(7)
= -8 - 28
= -36
Simplify completely:
(2x^2y)(−3xy^2)
-6x³y³
A line passes through (1, 4) and a slope of -2. Find its equation.
Perpendicular slope = -2
y - 4 = -2(x - 1)
y = -2x + 6
Two similar solids have volume ratio 8:27. If smaller volume is 64, find larger volume.
Scale factor = 2:3
So volume ratio = 8:27
64 corresponds to 8 → multiply by 8
64 × 27/8 = 216
A class has scores: 10, 20, 20, 30, 40, 50. If one score is removed and the mean becomes 30, which score was removed?
Sum = 170
Mean 30 → 5 numbers → total 150
Removed = 170 - 150
= 20