SAT Practice Test - Bluesilvers Consulting - Training, Data Analysis, Projects

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Welcome to your Practice Questions| SAT Quadratic Equations

1. \( Solve for \,\,x: 𝑥^2 − 5 𝑥 + 6 = 0 \)

𝑥 = 1 and 6

x = 2 and 3

x = 3 and 5

x = 1 and 5

None

2. \( Solve for \,\,x: 𝑥^2 + 7 𝑥 + 12 = 0 \)

x = - 3 and - 4

x = - 2 and - 6

x = - 4 and - 7

x = - 1 and - 12

None

3. \( Solve for \,\,𝑥: 2 𝑥 ^2 − 8 𝑥 + 6 = 0 \)

x = 1 and 3

x = 2 and 3

x = 1 and 4

x = 3 and 4

None

4. \(Solve for \,\,𝑥 : 𝑥^2 − 3 𝑥 − 10 = 0 \)

x = -2 and 5

x = 2 and -5

x = 1 and -10

x = 3 and -3

None

5. \(Solve for \,\,𝑥: 3 𝑥^2 − 12 𝑥 + 9 = 0 \)

1 and 3

3 and 4

2 and 3

3 twice

None

6. \(Solve for \,\,𝑥: 4 𝑥^2 − 4 𝑥 − 8 = 0 \)

-2 and 2

1 and -2

2 and -1

-4 and 4

None

7. \(Solve for \,\,𝑥: 𝑥 ^2 − 4 𝑥 − 5 = 0 \)

x=2± √9

x=2± √13

x=2± √25

x=2± √5

None

8. \(Solve for \,\,𝑥: 𝑥^2 + 7 𝑥 + 10 = 0 \)

\(x = \frac{−7± √29}{2}\)

\(x = \frac{−7± √39}{2}\)

\(x = \frac{−7± √49}{2}\)

\(x = \frac{−7± √9}{2}\)

None

9. \(Solve for \,\,𝑥 : 2 𝑥 ^2 + 3 𝑥 − 2 = 0 \)

\(x = \frac{−3± √17}{4}\)

\(x = \frac{−3± √13}{4}\)

\(x = \frac{−3± √29}{4}\)

\(x = \frac{−3± √9}{4}\)

None

10. \(Solve for \,\,𝑥 : 3 𝑥 ^2 − 6 𝑥 + 2 = 0 \)

\(x = \frac{3± √12}{6}\)

\(x = \frac{3± √24}{6}\)

\(x = \frac{1± √6}{3}\)

\(x = \frac{1± √12}{3}\)

None

1. \(If the roots of 𝑥^2 + 𝑘𝑥 + 16 = 0 are 4 and −4 what is 𝑘? \)

0

8

- 8

16

None

What is the sum of the roots of 2 𝑥 ^2 − 7 𝑥 + 3 = 0?

\(x = \frac{−7}{2}\)

\(x = \frac{7}{2}\)

−3

3

None

\( If 𝑝 ( 𝑥 ) = 𝑥 ^2 − 2 𝑥 − 8, for what value of 𝑥 is 𝑝 ( 𝑥 ) = 0 ? \)

-2 and 4

2 and - 4

4 and - 2

0 and - 8

None

\( Find the roots of 𝑥^2 − 6 𝑥 + 10 = 0.\)

𝑥 = 3 ± √2

𝑥 = 3 ± i√1

𝑥 = 3 ± i√2

𝑥 = 3 ± i√4

None

\(A rectangle has a length of (x+2) and a width of (x−3). If the area is 35, what is the value of x? \)

5

3

7

4

None

\(The height h (in meters) of a ball thrown into the air is given by h(t)=−5t^2+20t+2, where t is time in seconds. When does the ball reach its maximum height? \)

4 seconds

3 seconds

2 seconds

1 second

None

\(A product's revenue R is modeled by R(x) = -2x^2 + 16x + 20, where x represents the price in dollars. What price maximizes revenue? \)

2

4

5

6

None

\(Which of the following is the vertex of y = x^2 - 6x + 8? \)

(3, - 1)

(2, 0)

(-1, 8)

(-3, -1)

None

\(The parabola y = -x^2 + 4x - 3 opens: \)

Upwards

Downwards

Sideways

Neither

None

\(Find the axis of symmetry for y = 2x^2 + 4x - 1. \)

x = 2

x = 1

x = 0

x = - 1

None

1. \(How many real solutions does x^2 - 4x + 8 = 0 have?\)

0

1

2

Infinite

None

2. \(How many real solutions does 2x^2 - 6x + 10 = 0 have?\)

No solution

One solution

Two solutions

Infinitely many solutions

None

3. \(How many real solutions does 2x^2 - 9x + 13 = 0 have?\)

Complex solution

One solution

Two solutions

Infinitely many solutions

None

4. \(The sum of two numbers is 10, and their product is 21. What are the numbers? \)

2, 8

3, 7

4, 6

5, 5

None

5. \(A projectile is launched from a height of 10 feet with an initial velocity of 32 feet per second. Its height is given by h(t) = -16t^2 + 32t + 10. How long until it hits the ground? \)

t = 1 second

t = 2 seconds

t = 3 seconds

t = 4 seconds

None

6. \(The cost C of producing x items is modeled by C(x) = 5x^2 - 20x + 100. What is the minimum cost? \)

$50

$60

$80

$100

None

7. \(Solve: x^2 - 3x - 10 > 0. \)

x 5

− 2 < 𝑥 < 5

x>−2

. 𝑥 < 5

None

8. \(Which of the following represents the solution to 2x^2 + 4x ≤ 0? \)

−2 ≤ x ≤0

x ≥−2

x ≤ 0

𝑥 ≥ 0

None

9. \(If \frac{m^2}{4}\= 2m, then m equals \)

0 and -2

0 and -6

1 and 4

0 and 8

None

None

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