A runner can run 10 miles in 3 hours. How far can he run in 4 hours?
13 1/3 miles.
100
The scale factor from one side of a smaller triangle to the corresponding side of a larger triangle is 6. If the perimeter of the smaller triangle is 3, what is the perimeter of the larger triangle?
The scale factor for the perimeter is the same as the scale factor of the sides.
6 * 3 = 18.
100
Given the side lengths below, say whether or not those sides could be a triangle, and if so, what kind of triangle would it be?
1, 2, 12
It cannot be a triangle.
1+2 = 3 < 12 (triangle inequality)
100
The two legs of a right triangle are lengths 3 and 4. How long is the hypotenuse?
The hypotenuse is length 5.
3^2 + 4^2 = 9 + 16 = 25. SQRT(25) = 5.
100
Do not use a calculator for this question!
Estimate the square root of 144.
12
200
A deli sandwich uses a pound of meat and 1/4 of a pound of bread. If the sandwich is cut so that the bread now only weighs 1/16 of a pound, how much does the meat weigh?
1/4 of a pound
200
The scale factor from one side of a larger triangle to the corresponding side of a smaller triangle is 2/3. If the area of the larger triangle is 27, what is the area of the smaller triangle?
The area scale factor is the square of the side scale factor.
(2/3)^2 = 4/9
27 * (4/9) = 12
200
Given the side lengths below, say whether or not those sides could be a triangle, and if so, what kind of triangle would it be?
7, 8, 9
It is an acute triangle.
7+8 = 15 > 9 (triangle inequality)
49+64 = 113 > 81
200
The two legs of a right triangle are lengths 5 and 12. How long is the hypotenuse?
The hypotenuse is length 13.
5^2 + 12^2 = 25 + 144 = 169. SQRT(169) = 13.
200
Do not use a calculator for this question!
Estimate the square root of 80.
Approximately 8.9.
300
Is the following relationship proportional?
The side length of a square and the area of a square.
No - it does not form a straight line.
300
The scale factor from the area of a smaller triangle to the area of a larger triangle is 144. If the perimeter of the smaller triangle is 10, what is the perimeter of the larger triangle?
The perimeter scale factor is the square root of the area scale factor.
SQRT(144) = 12.
10 * 12 = 120.
300
Given the side lengths below, say whether or not those sides could be a triangle, and if so, what kind of triangle would it be?
6, 8, 10
It is a right triangle
6+8 = 14 > 10 (triangle inequality)
36+64 = 100 = 100
300
One leg of a right triangle is length 24, and the hypotenuse is length 25. What is the length of the other leg?
The other leg is length 7.
25^2 - 24^2 = 625 - 576 = 49. SQRT(49) = 7
300
Do not use a calculator for this question!
Estimate the square root of 110.
Approximately 10.488.
400
A chocolate chip cookie recipe calls for 12 oz of chocolate chips for every 2 1/4 cups of flour. If a baker wants to use 40 oz of chocolate chips, then how much flour does she need?
7.5 cups of flour
400
The scale factor from one side of a smaller triangle to the corresponding side of a larger triangle is 4. If the area of the larger triangle is 64, what is the area of the smaller triangle?
The area scale factor is the square of the side scale factor.
4^2 = 16.
64 / 16 = 4.
400
Given the side lengths below, say whether or not those sides could be a triangle, and if so, what kind of triangle would it be?
9, 9, 13
It is an obtuse triangle
9+9 = 18 > 13 (triangle inequality)
81+81 = 162 < 169
400
What is the distance from one corner to the opposite corner of a square whose sides have a length of 1?
SQRT(2) or about 1.4.
When you draw a line from one corner to the opposite corner of a triangle, you create a right triangle with legs which both have a length of 1 and the diagonal as the hypotenuse. At this point, you can use the pythagorean theorem.
1^2 + 1^2 = 1 + 1 = 2. SQRT(2) = 1.4...
400
Do not use a calculator for this question!
Estimate the square root of 2.25.
1.5
500
List the two qualities a relationship must have in order to be proportional.
- It must pass through (0,0) OR When one quantity is 0, the other must also be 0.
- It must be a straight line OR When you multiply one quantity by a given number the other quantity is multiplied by the same amount.
500
The scale factor from the area of a larger triangle to the area of a smaller triangle is .25. If the perimeter of the smaller triangle is 10, what is the perimeter of the larger triangle?
The perimeter scale factor is the square root of the area scale factor.
SQRT(.25) = .5
10 / .5 = 20
500
Two of the sides of a triangle are of lengths 7 and 12. What is the range of possibilities for the unknown side?
The side is between 5 and 19.
(5 < x < 19)
500
Two of the sides of a right triangle are 5 and 7. What value or values could the third side be?
The third side could either be the hypotenuse or one of the legs.
Hypotenuse: 5^2 + 7^2 = 25 + 49 = 74. SQRT(74) = 8.602
Leg: 7^2 - 5^2 = 49 - 25 = 24. SQRT(24) = 4.899
500
Do not use a calculator for this question!
Estimate the square root of -15.
You cannot take the square root of a negative number. (yet)