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SAT Test

This is a sample exercise SAT test.

Problem #1

What is the value of x(x³ - x²) if x = -2?

24

-24

18

-18

36

Problem #2

If A = (x₁, y₁) and B = (x₂, y₂), then what is the midpoint of segment AB?

$(\frac{x_1 - x_2}{2}, \frac{y_1 - y_2}{2})$

$(\frac{x_1 - x_2}{2}, \frac{y_1 + y_2}{2})$

$(\frac{x_1 + x_2}{2}, \frac{y_1 - y_2}{2})$

$(\frac{x_1 + x_2}{2}, \frac{y_1 + y_2}{2})$

None of them

Problem #3

ABCD is square and AB=1. Find the area of the black space.

ABCD is square and AB=1. Find the area of the black space.

$1 - \pi$

$1 - \frac{\pi}{2}$

$1 - \frac{\pi}{3}$

$1 - \frac{\pi}{4}$

$1 - \frac{\pi}{5}$

Problem #4

If a=c², b=c³ and c is an odd number, then which one is true?

2a + b + 1 is odd

2a + b + 1 is even

3a + b + 1 is even

3a + 2b + 1 is odd

2a + 3b + 1 is odd

Problem #5

If f(x) = x³ - x² - x + 1, then what is the value of f(-1)?

-2

-1

0

2

Problem #6

If a, b, c are positive consecutive integers, then which one is true?

$a = \frac{b+c}{2}$

$b = \frac{a+c}{2}$

$c = \frac{b+a}{2}$

$a = \frac{b-c}{2}$

$b = \frac{a-c}{2}$

Problem #7

If ABCD is a square and AB=1, then find the value of red area.

If <em>ABCD</em> is a square and <em>AB=1</em>, then find the value of red area.

$1 - \frac{\sqrt{3}}{3}$

$1 - \frac{\sqrt{2}}{2}$

$\frac{1}{2}$

$\frac{2}{3}$

$\frac{3}{4}$

Problem #8

If f(x)=x³ + 3x + 2 and f(a) = f(b) = 0, then find a + b.

3

-3

2

-2

Problem #9

If 4|a| - 3(-b)³ = 5|-c|, then what is the value of a in terms of b and c?

$a=\frac{5|c|-3b^3}{4}$

$a=-\frac{5|c|-3b^3}{4}$

$a=\pm\frac{5|c|-3b^3}{4}$

$a=\frac{-5|c|-3b^3}{4}$

$a=\frac{5|c|+3b^3}{4}$

Problem #10

Find the sum of the units digits of the first 10 terms of the below sequence.

1, 5, 9, ..., a_n = 4n - 3

150

160

170

180

190

Problem #11

If f(x)=3x³ + 2x² + x then find f(-2)

18

-18

16

-16

10

Problem #12

If a, b, c are positive consecutive odd integers and c < b < a, then what is the value of b² in terms of a and b?

(A) a² - 4c - 12

(B) c² + 4a - 12

(C) 2a² - 4c - 12

(D) 2c² + 4a - 12

(E) A and B

Problem #13

What is the value of y + x²y + xy², if x = 1 and y = -1?

1

2

0

-2

-1

Problem #14

Suppose A=(2, 3) and B=(x, y). Let C=(3, 4) be the midpoint of AB. Find (x, y).

(4, 5)

(-4, -5)

(-4, 5)

(4, -5)

None of them

Problem #15

What is the average of x² + 3x + 2 and x³ - x² - x + 1 for x = -1?

1

2

0

-2

-1

Problem #16

If f(x)=x² - 2x + 4 and g(x) = xf(x) then find f(2) + g(-2).

-20

20

16

-16

0

Problem #17

If f(3) = f(2) = 0 then which one is true?

f(x) = x² - 5x + 6

f(x) = x² + 5x + 6

f(x) = x² - 5x - 6

f(x) = x² + 5x - 6

f(x) = x² - 2x + 3

Problem #18

If A=(1, 1) and B=(2, 3), then what is the distance between A and B?

$\sqrt{3}$

$2$

$\sqrt{5}$

$\sqrt{6}$

$\sqrt{7}$

Problem #19

Find the value of the S = 1 + 2 + 3 + ...+ 100.

4040

5050

6060

7070

8080

Problem #20

According to the figure, which one is true?

According to the figure, which one is true?

$\angle B + \angle C = \angle1$

$\angle B + \angle C = \angle2$

$\angle B + \angle C = 90^{\circ}$

$\angle1 + \angle 2 = 90^{\circ}$

$\angle 2 + \angle B = 90^{\circ}$

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