Numbers & Operations
Evaluate: 42 − 3 ⋅ 5 + 6
16 − 15 + 6 = 7
The sum of the interior angles of any triangle is always this many degrees.
180°
Solve for x: x+4=9
x=5
There are 16 pizza boxes, each pizza is cut into 8 slices. How many slices are there total?
There are 128 slices total.
The squares of these 3 consecutive integers add up to 365. What are the 3 integers?
10, 11, 12
A matcha farmer buys 3 mugs for $2 each and 2 spoons for $1.50 each. If they pay with a $20 bill, how much change do they get?
$11
What is the area of a right triangle with base 6 cm and height 8 cm?
A = 1/2bh
= 1/2(6)(8)
= 24 cm2
Factor: x2−9
(x−3)(x+3)
A tray has 8 cookies. If 3 friends each have 2 cookies, how any are left for the fourth friend?
2 cookies are left.
A + B = 67
A + A + B = 112
B + C = 49
A + C = 72
A, B, C = ?
A = 45
B = 22
C = 27
*use substitution
Three consecutive even numbers sum to 84.
Find the 3 numbers.
26, 28, 30
A right triangle has an angle of 30 degrees and a hypotenuse of 10. What is the length of the side opposite the 30 degree angle?
10sin(30)=5
Solve: 2x2−5x−3=0
x=-½, 3
For every 4 coffees you buy (priced at $5 each), the 4th cup is free. If you buy 15 coffees, how much money do you end up paying?
Your total is $60.
I am a 2 digit number equal to 3 times the sum of my digits. What number am I?
27
The product of two consecutive positive integers is 506.
Find the integers
22 and 23.
What is the distance between the points (3,4) and (7,1)?
d= √[(x2−x1)2 + (y2−y1)2]
d = √[(7-3)2 + (1-4)2]
= √[16+9]
d = 5
Solve for x: 5x=625
x=4
A pack of socks has a total of 12 pairs. If you take 1/3 of the socks and your sibling takes half of what remains, how many individual socks are left?
8 socks left (4 pairs)
Two Labubus are travelling.
The first one walks 6 km north, then 4 km east.
The second walks 10 km west, 4 km east, then 7 km south.
Determine how far each Labubu traveled from their starting point (2 decimal places).
Labubu 1: 7.21 km
Labubu 2: 9.22 km
*use the Pythagorean theorem*
A fraction has a denominator 4 more than its numerator. If both the numerator and denominator are increased by 6, the fraction becomes 3/4. Find the original fraction.
6/10 or 3/5
In a triangle, angle A=40, angle B=75, and side a=8 cm. Find the length of side b.
Use sine law to solve for side b.
b ≈ 12
Solve: e2x=7
x=(ln7)/2
A banana costs $0.25 each, but you can buy 5 bananas for $1. If you buy 20 bananas with the sale, how much money do you save compared to buying them without the sale?
You save 1 dollar.
John Pork needs help to find this number.
When multiplied by 3, then 7 is added, the result is a perfect square.
When multiplied by 3, then 16 is added, the result is ALSO a perfect square.
Help John Pork find the number!
ANWER: 3
3x + 7 = m2
3x + 16 = n2
Subtract the 2 equations to get 9, which is the difference between the two perfect squares.
- Can test different pairs (0,9), (1, 10), (4, 13), etc. to find the suitable pair and solve for x.