# HSPT Math

## 32 terms · Provides guidance on math principles that are used in HSPT Math

### What is the next number in this sequence? 4,6,8,10

Principle: Arithmetic Progression

N+C where C is a constant

So 4 + C = 6

C=2

10+2= 12, Answer is 12.

### What is the next number in this sequence? 2, -6, 18, -48?

Principle: Geometric Progression
N*C where C is a constant

So 2*C=-6

C=-3

-48 * -3 = 144, Answer is 144

### What is the next number in this sequence? * 4, 11, 32, 95?

Principle: Combination of Arithmetic and Geometric Progression

At first this looks geometric but the ratio of the next number to the first changes

So you look at the ratio of differences:

7 ((11-4)
21 (32 - 11)
63 (95-11)

And you see the ratio of the difference is 3 so one factor is 3 or 3N +/- C applying it to the first one 4 *3 is 12, subtract 1 to get 11

So the next number is 95 * 3 -1 or 284

### What is the circumference of circle with a diameter of 3 and is it greater or smaller than the perimeter of square that has a diameter of 3?

Principle: Perimeter or length of lines defining a shape and the constant ∏ and base formulas for each:

Circle perimeter is ∏ or 3.14 times diameter
Diameter is two times the radius defined as the distance from the outer edge of the circle to the center

So in this cash diameter of 3 times 3.14 or 9.42 is the perimeter of the circle

Square permiter is 4 times the length of one side as all side are equal so the square perimeter is 4 times 3 or 12.

*Note that the diameter of circle is the same as on the sides so the circle fits inside of square and touches all four sides

### What is the perimeter of box with one side equal to 4 inches and the other side equal to 6 inches?

Principle: Perimeter of a rectangle

P = 2l + 2w or 2(l + w)

P = 2(4+6) or 2(10) or 20

### What is the perimeter of a square with one side equal to 7

Principle: Perimeter of a square

P = 4s

P = 4 x 7 or P=28

Also, add 7 + 7 + 7 + 7

### What is the area of triangle with a base of 3 and height of 4

Principle: Area of a triangle
A = (1/2)bh
A = 1/2 x 3 x 4 or A = 6

Note a triangle doubled equals a square with area = S2 multiplying by 1/2 gives the area.

### What is the area of rectangle that has a base of 7 and a height of 6

Principle: Area of a rectangle
A = bh or lw
A= 7 x 6 or 32

### What is the area of square with one side equal to 6

Principle: Area of a square
A = Sx2
A = 6 x 6
A=36

### What is the volume of box that is is 6 x 5 x 7?

Principle: Volume of rectangular solids
V = lwh
V = 6 x 5 x7
V = 210

### What is the length of the hypotenuse of a right triangle with a 6 and 7 side?

Principle: Pythagorean theorem
For right triangles (with 90°)
a2 + b2 = c2
(6 x 6) + (7 x 7) = c2
36 + 49 = 85
c2 = 85
c = Square root of 85 (more than 9 and less than 10)

90°

180°

360°

90°

180°

12

3

100

1,000

16

8

2

### 1 quart = ? pints or ? cups

2 pints or 4 cups

4

1,000

### Order of operations

Parentheses, Exponents, Multiplication, Division, Addition, Subtraction

### What are the definitions of the following mathematical equation? 12 / 5 = 2 r 2

Principle: Division
12 is the dividend, the number being divided
5 is the divisor, the number the dividend will be divided by
2 is the quotient, number times the divisor will go into the dividend
2 is the remainder, the number remaining that is too small for the divisor to go into

### What are the definitions of the following mathematical equation? 12 x 5 = 60

Principle: Multiplication

12 and 5 are the factors being multiplied

60 is the product which is the result

### What are the definitions of the following mathematical equation? 4 + 8 = 12

4 and 8 are addends

12 is the sum

### What are the definitions of the following mathematical equation? 12 -4 = 8

Principle: Substraction

12 is the minuend, the the number being subtracted or lowered

4 is the subtrahend, the number used to reduce the minuend

8 is the difference

### What is the area of this geometric form?

Principle: Area of a trapezoid
A= 1/2H(B1-B2)

Where H is the height and b1 and b2 are the length of each base