Practice sheet

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Solve $x^2 = 100$ . Enter all solutions.
Solve $(x - 7)^2 = 64$ . Enter all solutions.
Solve $3x^2 - 3 = 0$ . Enter all solutions.
Solve $x(x - 3) = 0$ . Enter all solutions.
Solve $(4x - 6)(x + 8) = 0$ . Enter all solutions.
To solve $(x - 3)(x + 7) = 4$ , Ana writes “ $x - 3 = 4$ or $x + 7 = 4$ ”. Is that right?
1. No: the zero product property only works when the product is 0
2. Yes: set each factor equal to 4
3. Only the first factor can equal 4
To solve $(x - 7)(x + 6) = 17$ , Ana writes “ $x - 7 = 17$ or $x + 6 = 17$ ”. Is that right?
1. No: the zero product property only works when the product is 0
2. Yes: set each factor equal to 17
3. Only the first factor can equal 17
To solve $(x - 9)(x + 4) = 9$ , Ana writes “ $x - 9 = 9$ or $x + 4 = 9$ ”. Is that right?
1. No: the zero product property only works when the product is 0
2. Yes: set each factor equal to 9
3. Only the first factor can equal 9
To solve $(x - 1)(x + 8) = 16$ , Ana writes “ $x - 1 = 16$ or $x + 8 = 16$ ”. Is that right?
1. No: the zero product property only works when the product is 0
2. Yes: set each factor equal to 16
3. Only the first factor can equal 16
To solve $(x - 9)(x + 8) = 13$ , Ana writes “ $x - 9 = 13$ or $x + 8 = 13$ ”. Is that right?
1. No: the zero product property only works when the product is 0
2. Yes: set each factor equal to 13
3. Only the first factor can equal 13
To solve $(x - 9)(x + 6) = 18$ , Ana writes “ $x - 9 = 18$ or $x + 6 = 18$ ”. Is that right?
1. No: the zero product property only works when the product is 0
2. Yes: set each factor equal to 18
3. Only the first factor can equal 18
To solve $(x - 9)(x + 3) = 17$ , Ana writes “ $x - 9 = 17$ or $x + 3 = 17$ ”. Is that right?
1. No: the zero product property only works when the product is 0
2. Yes: set each factor equal to 17
3. Only the first factor can equal 17
To solve $(x - 6)(x + 6) = 14$ , Ana writes “ $x - 6 = 14$ or $x + 6 = 14$ ”. Is that right?
1. No: the zero product property only works when the product is 0
2. Yes: set each factor equal to 14
3. Only the first factor can equal 14
To solve $(x - 8)(x + 6) = 6$ , Ana writes “ $x - 8 = 6$ or $x + 6 = 6$ ”. Is that right?
1. No: the zero product property only works when the product is 0
2. Yes: set each factor equal to 6
3. Only the first factor can equal 6
To solve $(x - 6)(x + 4) = 19$ , Ana writes “ $x - 6 = 19$ or $x + 4 = 19$ ”. Is that right?
1. No: the zero product property only works when the product is 0
2. Yes: set each factor equal to 19
3. Only the first factor can equal 19
To solve $(x - 3)(x + 4) = 14$ , Ana writes “ $x - 3 = 14$ or $x + 4 = 14$ ”. Is that right?
1. No: the zero product property only works when the product is 0
2. Yes: set each factor equal to 14
3. Only the first factor can equal 14
To solve $(x - 4)(x + 1) = 20$ , Ana writes “ $x - 4 = 20$ or $x + 1 = 20$ ”. Is that right?
1. No: the zero product property only works when the product is 0
2. Yes: set each factor equal to 20
3. Only the first factor can equal 20
To solve $(x - 7)(x + 6) = 9$ , Ana writes “ $x - 7 = 9$ or $x + 6 = 9$ ”. Is that right?
1. No: the zero product property only works when the product is 0
2. Yes: set each factor equal to 9
3. Only the first factor can equal 9
To solve $(x - 4)(x + 1) = 12$ , Ana writes “ $x - 4 = 12$ or $x + 1 = 12$ ”. Is that right?
1. No: the zero product property only works when the product is 0
2. Yes: set each factor equal to 12
3. Only the first factor can equal 12
To solve $(x - 8)(x + 6) = 4$ , Ana writes “ $x - 8 = 4$ or $x + 6 = 4$ ”. Is that right?
1. No: the zero product property only works when the product is 0
2. Yes: set each factor equal to 4
3. Only the first factor can equal 4
To solve $(x - 2)(x + 1) = 20$ , Ana writes “ $x - 2 = 20$ or $x + 1 = 20$ ”. Is that right?
1. No: the zero product property only works when the product is 0
2. Yes: set each factor equal to 20
3. Only the first factor can equal 20
To solve $(x - 3)(x + 1) = 13$ , Ana writes “ $x - 3 = 13$ or $x + 1 = 13$ ”. Is that right?
1. No: the zero product property only works when the product is 0
2. Yes: set each factor equal to 13
3. Only the first factor can equal 13
To solve $(x - 9)(x + 5) = 18$ , Ana writes “ $x - 9 = 18$ or $x + 5 = 18$ ”. Is that right?
1. No: the zero product property only works when the product is 0
2. Yes: set each factor equal to 18
3. Only the first factor can equal 18
To solve $(x - 5)(x + 1) = 8$ , Ana writes “ $x - 5 = 8$ or $x + 1 = 8$ ”. Is that right?
1. No: the zero product property only works when the product is 0
2. Yes: set each factor equal to 8
3. Only the first factor can equal 8
To solve $(x - 7)(x + 2) = 4$ , Ana writes “ $x - 7 = 4$ or $x + 2 = 4$ ”. Is that right?
1. No: the zero product property only works when the product is 0
2. Yes: set each factor equal to 4
3. Only the first factor can equal 4
To solve $(x - 7)(x + 2) = 11$ , Ana writes “ $x - 7 = 11$ or $x + 2 = 11$ ”. Is that right?
1. No: the zero product property only works when the product is 0
2. Yes: set each factor equal to 11
3. Only the first factor can equal 11
To solve $(x - 2)(x + 2) = 5$ , Ana writes “ $x - 2 = 5$ or $x + 2 = 5$ ”. Is that right?
1. No: the zero product property only works when the product is 0
2. Yes: set each factor equal to 5
3. Only the first factor can equal 5
To solve $(x - 7)(x + 9) = 8$ , Ana writes “ $x - 7 = 8$ or $x + 9 = 8$ ”. Is that right?
1. No: the zero product property only works when the product is 0
2. Yes: set each factor equal to 8
3. Only the first factor can equal 8
To solve $(x - 6)(x + 4) = 2$ , Ana writes “ $x - 6 = 2$ or $x + 4 = 2$ ”. Is that right?
1. No: the zero product property only works when the product is 0
2. Yes: set each factor equal to 2
3. Only the first factor can equal 2
To solve $(x - 5)(x + 5) = 13$ , Ana writes “ $x - 5 = 13$ or $x + 5 = 13$ ”. Is that right?
1. No: the zero product property only works when the product is 0
2. Yes: set each factor equal to 13
3. Only the first factor can equal 13
To solve $(x - 8)(x + 6) = 16$ , Ana writes “ $x - 8 = 16$ or $x + 6 = 16$ ”. Is that right?
1. No: the zero product property only works when the product is 0
2. Yes: set each factor equal to 16
3. Only the first factor can equal 16
To solve $(x - 2)(x + 5) = 16$ , Ana writes “ $x - 2 = 16$ or $x + 5 = 16$ ”. Is that right?
1. No: the zero product property only works when the product is 0
2. Yes: set each factor equal to 16
3. Only the first factor can equal 16
To solve $(x - 6)(x + 6) = 15$ , Ana writes “ $x - 6 = 15$ or $x + 6 = 15$ ”. Is that right?
1. No: the zero product property only works when the product is 0
2. Yes: set each factor equal to 15
3. Only the first factor can equal 15
To solve $(x - 6)(x + 6) = 4$ , Ana writes “ $x - 6 = 4$ or $x + 6 = 4$ ”. Is that right?
1. No: the zero product property only works when the product is 0
2. Yes: set each factor equal to 4
3. Only the first factor can equal 4
To solve $(x - 6)(x + 5) = 9$ , Ana writes “ $x - 6 = 9$ or $x + 5 = 9$ ”. Is that right?
1. No: the zero product property only works when the product is 0
2. Yes: set each factor equal to 9
3. Only the first factor can equal 9
To solve $(x - 6)(x + 3) = 9$ , Ana writes “ $x - 6 = 9$ or $x + 3 = 9$ ”. Is that right?
1. No: the zero product property only works when the product is 0
2. Yes: set each factor equal to 9
3. Only the first factor can equal 9
To solve $(x - 3)(x + 9) = 20$ , Ana writes “ $x - 3 = 20$ or $x + 9 = 20$ ”. Is that right?
1. No: the zero product property only works when the product is 0
2. Yes: set each factor equal to 20
3. Only the first factor can equal 20
To solve $(x - 1)(x + 4) = 13$ , Ana writes “ $x - 1 = 13$ or $x + 4 = 13$ ”. Is that right?
1. No: the zero product property only works when the product is 0
2. Yes: set each factor equal to 13
3. Only the first factor can equal 13
To solve $(x - 8)(x + 9) = 15$ , Ana writes “ $x - 8 = 15$ or $x + 9 = 15$ ”. Is that right?
1. No: the zero product property only works when the product is 0
2. Yes: set each factor equal to 15
3. Only the first factor can equal 15
To solve $(x - 2)(x + 1) = 17$ , Ana writes “ $x - 2 = 17$ or $x + 1 = 17$ ”. Is that right?
1. No: the zero product property only works when the product is 0
2. Yes: set each factor equal to 17
3. Only the first factor can equal 17
To solve $(x - 6)(x + 1) = 11$ , Ana writes “ $x - 6 = 11$ or $x + 1 = 11$ ”. Is that right?
1. No: the zero product property only works when the product is 0
2. Yes: set each factor equal to 11
3. Only the first factor can equal 11
To solve $(x - 5)(x + 8) = 5$ , Ana writes “ $x - 5 = 5$ or $x + 8 = 5$ ”. Is that right?
1. No: the zero product property only works when the product is 0
2. Yes: set each factor equal to 5
3. Only the first factor can equal 5
To solve $(x - 6)(x + 3) = 16$ , Ana writes “ $x - 6 = 16$ or $x + 3 = 16$ ”. Is that right?
1. No: the zero product property only works when the product is 0
2. Yes: set each factor equal to 16
3. Only the first factor can equal 16
To solve $(x - 6)(x + 1) = 12$ , Ana writes “ $x - 6 = 12$ or $x + 1 = 12$ ”. Is that right?
1. No: the zero product property only works when the product is 0
2. Yes: set each factor equal to 12
3. Only the first factor can equal 12
To solve $(x - 8)(x + 8) = 19$ , Ana writes “ $x - 8 = 19$ or $x + 8 = 19$ ”. Is that right?
1. No: the zero product property only works when the product is 0
2. Yes: set each factor equal to 19
3. Only the first factor can equal 19
To solve $(x - 3)(x + 5) = 12$ , Ana writes “ $x - 3 = 12$ or $x + 5 = 12$ ”. Is that right?
1. No: the zero product property only works when the product is 0
2. Yes: set each factor equal to 12
3. Only the first factor can equal 12
To solve $(x - 3)(x + 7) = 9$ , Ana writes “ $x - 3 = 9$ or $x + 7 = 9$ ”. Is that right?
1. No: the zero product property only works when the product is 0
2. Yes: set each factor equal to 9
3. Only the first factor can equal 9
To solve $(x - 5)(x + 2) = 3$ , Ana writes “ $x - 5 = 3$ or $x + 2 = 3$ ”. Is that right?
1. No: the zero product property only works when the product is 0
2. Yes: set each factor equal to 3
3. Only the first factor can equal 3
To solve $(x - 1)(x + 1) = 15$ , Ana writes “ $x - 1 = 15$ or $x + 1 = 15$ ”. Is that right?
1. No: the zero product property only works when the product is 0
2. Yes: set each factor equal to 15
3. Only the first factor can equal 15
To solve $(x - 3)(x + 8) = 3$ , Ana writes “ $x - 3 = 3$ or $x + 8 = 3$ ”. Is that right?
1. No: the zero product property only works when the product is 0
2. Yes: set each factor equal to 3
3. Only the first factor can equal 3
To solve $(x - 1)(x + 6) = 6$ , Ana writes “ $x - 1 = 6$ or $x + 6 = 6$ ”. Is that right?
1. No: the zero product property only works when the product is 0
2. Yes: set each factor equal to 6
3. Only the first factor can equal 6
To solve $(x - 2)(x + 7) = 16$ , Ana writes “ $x - 2 = 16$ or $x + 7 = 16$ ”. Is that right?
1. No: the zero product property only works when the product is 0
2. Yes: set each factor equal to 16
3. Only the first factor can equal 16
To solve $(x - 3)(x + 2) = 20$ , Ana writes “ $x - 3 = 20$ or $x + 2 = 20$ ”. Is that right?
1. No: the zero product property only works when the product is 0
2. Yes: set each factor equal to 20
3. Only the first factor can equal 20
To solve $(x - 2)(x + 1) = 2$ , Ana writes “ $x - 2 = 2$ or $x + 1 = 2$ ”. Is that right?
1. No: the zero product property only works when the product is 0
2. Yes: set each factor equal to 2
3. Only the first factor can equal 2
To solve $(x - 6)(x + 9) = 19$ , Ana writes “ $x - 6 = 19$ or $x + 9 = 19$ ”. Is that right?
1. No: the zero product property only works when the product is 0
2. Yes: set each factor equal to 19
3. Only the first factor can equal 19
$x^2 + 8x + 15 = (x + 3)(x + \;?)$
Solve $x^2 - 9x + 14 = 0$ by factoring. Enter all solutions.
Solve $x^2 + 8x - 9 = 0$ by factoring. Enter all solutions.
What number makes $x^2 + 10x + \;?$ a perfect square?
Solve $x^2 + 6x = 8$ by completing the square. Enter all solutions (use sqrt).
$x^2 + 12x + 22 = (x + 6)^2 + \;?$
How many real solutions has $x^2 + 7x + 49 = 0$ ?
1. None
2. Two
3. One
How many real solutions has $x^2 + 4x + 16 = 0$ ?
1. None
2. Two
3. One
How many real solutions has $x^2 + 6x + 36 = 0$ ?
1. None
2. Two
3. One
How many real solutions has $x^2 + 3x + 9 = 0$ ?
1. None
2. Two
3. One
How many real solutions has $x^2 + 8x + 64 = 0$ ?
1. None
2. Two
3. One
How many real solutions has $x^2 + 5x + 25 = 0$ ?
1. None
2. Two
3. One
How many real solutions has $x^2 + 2x + 4 = 0$ ?
1. None
2. Two
3. One
How many real solutions has $x^2 + 1x + 1 = 0$ ?
1. None
2. Two
3. One
How many real solutions has $x^2 + 9x + 81 = 0$ ?
1. None
2. Two
3. One
Solve $2x^2 + 5x - 1 = 0$ with the quadratic formula. Enter all solutions (use sqrt).
Find the discriminant $b^2 - 4ac$ of $1x^2 + 12x + 2 = 0$ .
A rectangular garden is 6 m longer than it is wide. Its area is 216 m². Write and solve an equation for the width w. What is the width, in meters?
A ball is kicked upward. Its height after t seconds is h = −5t² + 35t meters. After how many seconds does it land?
The product of two consecutive whole numbers is 240. Which equation models this, with x the smaller number?
1. x(x + 1) = 240
2. x + (x + 1) = 240
3. x² + 1 = 240
The product of two consecutive whole numbers is 210. Which equation models this, with x the smaller number?
1. x(x + 1) = 210
2. x + (x + 1) = 210
3. x² + 1 = 210
The product of two consecutive whole numbers is 30. Which equation models this, with x the smaller number?
1. x(x + 1) = 30
2. x + (x + 1) = 30
3. x² + 1 = 30
The product of two consecutive whole numbers is 110. Which equation models this, with x the smaller number?
1. x(x + 1) = 110
2. x + (x + 1) = 110
3. x² + 1 = 110
The product of two consecutive whole numbers is 56. Which equation models this, with x the smaller number?
1. x(x + 1) = 56
2. x + (x + 1) = 56
3. x² + 1 = 56
The product of two consecutive whole numbers is 156. Which equation models this, with x the smaller number?
1. x(x + 1) = 156
2. x + (x + 1) = 156
3. x² + 1 = 156
The product of two consecutive whole numbers is 72. Which equation models this, with x the smaller number?
1. x(x + 1) = 72
2. x + (x + 1) = 72
3. x² + 1 = 72
The product of two consecutive whole numbers is 132. Which equation models this, with x the smaller number?
1. x(x + 1) = 132
2. x + (x + 1) = 132
3. x² + 1 = 132
The product of two consecutive whole numbers is 42. Which equation models this, with x the smaller number?
1. x(x + 1) = 42
2. x + (x + 1) = 42
3. x² + 1 = 42
The product of two consecutive whole numbers is 20. Which equation models this, with x the smaller number?
1. x(x + 1) = 20
2. x + (x + 1) = 20
3. x² + 1 = 20
The product of two consecutive whole numbers is 90. Which equation models this, with x the smaller number?
1. x(x + 1) = 90
2. x + (x + 1) = 90
3. x² + 1 = 90
The product of two consecutive whole numbers is 182. Which equation models this, with x the smaller number?
1. x(x + 1) = 182
2. x + (x + 1) = 182
3. x² + 1 = 182
Which number is irrational?
1. $\sqrt{ 2 }$
2. $\sqrt{ 4 }$
3. $0.\overline{ 1 }$
Which number is irrational?
1. $\sqrt{ 10 }$
2. $\sqrt{ 16 }$
3. $0.\overline{ 3 }$
Which number is irrational?
1. $\sqrt{ 37 }$
2. $\sqrt{ 49 }$
3. $0.\overline{ 6 }$
Which number is irrational?
1. $\sqrt{ 26 }$
2. $\sqrt{ 36 }$
3. $0.\overline{ 5 }$
Which number is irrational?
1. $\sqrt{ 5 }$
2. $\sqrt{ 9 }$
3. $0.\overline{ 2 }$
Which number is irrational?
1. $\sqrt{ 17 }$
2. $\sqrt{ 25 }$
3. $0.\overline{ 4 }$
Which number is irrational?
1. $\sqrt{ 65 }$
2. $\sqrt{ 81 }$
3. $0.\overline{ 8 }$
Which number is irrational?
1. $\sqrt{ 50 }$
2. $\sqrt{ 64 }$
3. $0.\overline{ 7 }$
Which number is irrational?
1. $\sqrt{ 82 }$
2. $\sqrt{ 100 }$
3. $0.\overline{ 9 }$
Write $0.\overline{ 1 }$ (the digit 1 repeating forever) as a fraction.
Write $0.\overline{ 48 }$ (the digits 48 repeating forever) as a fraction.
The circle $x^2 + y^2 = 169$ and the line $y = 12$ meet at two points. Give their $x$ -coordinates.
How many points do the circle $x^2 + y^2 = 16$ and the line $y = 11$ have in common?
1. None
2. One
3. Two
How many points do the circle $x^2 + y^2 = 16$ and the line $y = 12$ have in common?
1. None
2. One
3. Two
How many points do the circle $x^2 + y^2 = 25$ and the line $y = 9$ have in common?
1. None
2. One
3. Two
How many points do the circle $x^2 + y^2 = 25$ and the line $y = 10$ have in common?
1. None
2. One
3. Two
How many points do the circle $x^2 + y^2 = 16$ and the line $y = 8$ have in common?
1. None
2. One
3. Two
How many points do the circle $x^2 + y^2 = 25$ and the line $y = 12$ have in common?
1. None
2. One
3. Two
How many points do the circle $x^2 + y^2 = 25$ and the line $y = 7$ have in common?
1. None
2. One
3. Two
How many points do the circle $x^2 + y^2 = 9$ and the line $y = 9$ have in common?
1. None
2. One
3. Two
How many points do the circle $x^2 + y^2 = 36$ and the line $y = 8$ have in common?
1. None
2. One
3. Two
How many points do the circle $x^2 + y^2 = 9$ and the line $y = 12$ have in common?
1. None
2. One
3. Two
How many points do the circle $x^2 + y^2 = 4$ and the line $y = 8$ have in common?
1. None
2. One
3. Two
How many points do the circle $x^2 + y^2 = 16$ and the line $y = 9$ have in common?
1. None
2. One
3. Two
How many points do the circle $x^2 + y^2 = 9$ and the line $y = 11$ have in common?
1. None
2. One
3. Two
How many points do the circle $x^2 + y^2 = 4$ and the line $y = 11$ have in common?
1. None
2. One
3. Two
How many points do the circle $x^2 + y^2 = 25$ and the line $y = 8$ have in common?
1. None
2. One
3. Two
How many points do the circle $x^2 + y^2 = 16$ and the line $y = 10$ have in common?
1. None
2. One
3. Two
How many points do the circle $x^2 + y^2 = 4$ and the line $y = 9$ have in common?
1. None
2. One
3. Two
How many points do the circle $x^2 + y^2 = 9$ and the line $y = 8$ have in common?
1. None
2. One
3. Two
How many points do the circle $x^2 + y^2 = 9$ and the line $y = 10$ have in common?
1. None
2. One
3. Two
How many points do the circle $x^2 + y^2 = 16$ and the line $y = 7$ have in common?
1. None
2. One
3. Two
How many points do the circle $x^2 + y^2 = 36$ and the line $y = 9$ have in common?
1. None
2. One
3. Two
How many points do the circle $x^2 + y^2 = 9$ and the line $y = 7$ have in common?
1. None
2. One
3. Two
How many points do the circle $x^2 + y^2 = 36$ and the line $y = 10$ have in common?
1. None
2. One
3. Two
How many points do the circle $x^2 + y^2 = 36$ and the line $y = 12$ have in common?
1. None
2. One
3. Two
How many points do the circle $x^2 + y^2 = 4$ and the line $y = 7$ have in common?
1. None
2. One
3. Two
How many points do the circle $x^2 + y^2 = 36$ and the line $y = 7$ have in common?
1. None
2. One
3. Two
How many points do the circle $x^2 + y^2 = 36$ and the line $y = 11$ have in common?
1. None
2. One
3. Two
How many points do the circle $x^2 + y^2 = 4$ and the line $y = 12$ have in common?
1. None
2. One
3. Two
How many points do the circle $x^2 + y^2 = 4$ and the line $y = 10$ have in common?
1. None
2. One
3. Two
How many points do the circle $x^2 + y^2 = 25$ and the line $y = 11$ have in common?
1. None
2. One
3. Two
Find the $x$ -coordinates of the points where $y = x^2$ meets $y = x + 6$ .

Answers

$10,\ -10$
$15,\ -1$
$1,\ -1$
$0,\ 3$
$\frac{3}{2},\ -8$
No: the zero product property only works when the product is 0
$5$
$7,\ 2$
$-9,\ 1$
$25$
$-3 + \sqrt{17},\ - \sqrt{17} - 3$
$-14$
None
$- \frac{5}{4} + \frac{\sqrt{33}}{4},\ - \frac{\sqrt{33}}{4} - \frac{5}{4}$
$136$
$12$
$7$
x(x + 1) = 240
$\sqrt{ 2 }$
$\frac{1}{9}$
$\frac{16}{33}$
$5,\ -5$
None
$3,\ -2$