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WorksheetsG09 - MATH Q1 Reviewer
Total questions: 28
Worksheet time: 14mins
What is the standard form of a quadratic equation?
y = mx + b
𝑎𝑥2 + 𝑏𝑥 + 𝑐 = 0
𝑦 = 𝑎(𝑥 − ℎ)2 + 𝑘
y = kx
What is the number of real solutions for a quadratic equation with a discriminant is = 0?
One real solution
Two real solutions
No real solutions
It depends on the value of 'a'
What is the solution to the quadratic equation 𝑥2 = 25 when extracting square roots?
x = 5
x = 6
x = ±5
x = ±6
An airplane makes a trip f 2400 miles long into the wind and 2400 miles back with the same tail wind, maintaining the constant speed of 440 miles per hour relative to the air. The entire round trip takes 8 hours. What is the speed of the current?
30 m / h
20 mi/h
40 m / h
60 mi/h
The roots of a quadratic equation are 6 and -3. Which of the following quadratic equations has these roots?
𝑥2 − 3𝑥 − 18 = 0
𝑥2 − 3𝑥 + 18 = 0
𝑥2 + 3𝑥 + 18 = 0
𝑥2 + 3𝑥 − 18 = 0
After completing the square, what is the solution to the equation 𝑥2 − 4𝑥 − 5 = 0?
x = 2 ± √9
x = 2 ± 3
x = 4 ± √9
x = 3 ± 2
What is the discriminant of a quadratic equation in the form 𝑎𝑥2 + 𝑏𝑥 + 𝑐 = 0
Δ = 𝑏2 − 4𝑎𝑐
Δ = 𝑏2 + 4𝑎𝑐
Δ = 2𝑎𝑏2 − 𝑐
Δ = 𝑎2 + 𝑏2 − 𝑐
The sum of the roots of a quadratic equation is 5. If one of the roots is 1, which of the following is the quadratic equation?
𝑥2 + 5𝑥 − 4 = 0
𝑥2 − 5𝑥 + 4 = 0
𝑥2 + 5𝑥 + 4 = 0
𝑥2 − 5𝑥 − 4 = 0
Marie and Joy are planning to paint a house together. Marie thinks that she works alone, it will take her 5 hours more than the time Joy takes to paint the entire house. Working together, they can complete the job in 6 hours. How long will it take Marie to finish the job?
5 hours
10 hours
15 hours
20 hours
Which of the following discriminant values indicates that a quadratic equation has no real solutions?
Δ > 0
Δ = 0
Δ < 0
Δ = 1
Given the equation, 4𝑥2 + 9𝑥 − 13 = 0, which of the following is the nature of its roots?
The roots are real, rational and equal.
The roots are imaginary and unequal.
The roots are real, irrational and unequal.
The roots are real, rational and unequal.
Which of the following quadratic equations has rational, equal and real roots?
9 − 6𝑥 + 𝑥2 = 0
4𝑥2 + 4𝑥 − 21 = 0
𝑥2 + 2𝑥 + 2 = 0
4𝑥2 + 12𝑥 + 10 = 0
How many real roots does the quadratic equation 5𝑥2 − 8𝑥 + 6 = 0 have?
0
1
2
3
The product of the roots of a quadratic equation is 36. If one of the roots is 9. Which of the following could be the equation?
𝑥2 + 13𝑥 + 48 = 0
𝑥2 − 13𝑥 − 48 = 0
𝑥2 − 13𝑥 + 36 = 0
𝑥2 + 13𝑥 − 48 = 0
Which of the following is a quadratic equation that can be solved by extracting square roots?
2𝑥2 − 5𝑥 + 3 = 0
𝑥2 + 4𝑥 − 6 = 0
3𝑥2 + 2𝑥 + 1 = 0
𝑥3 − 2𝑥2 + 𝑥 − 1 = 0
If 2+√3 and 2−√3 are the roots, which of the following is the quadratic equation?
25𝑥2 − 20𝑥 + 1 = 0
25𝑥2 + 20𝑥 − 1 = 0
25𝑥2 − 20𝑥 − 1 = 0
25𝑥2 + 20𝑥 + 1 = 0
Which of the following is a quadratic equation that can be solved by factoring?
2𝑥2 − 5𝑥 + 3 = 0
3𝑥2 + 4𝑥 + 2 = 0
𝑥3 + 4𝑥2 − 6𝑥 − 9 = 0
5𝑥2 + 7𝑥 + 3 = 0
What is the first step when solving a quadratic equation by factoring?
Divide by the leading coefficient
Set the equation equal to zero
Expand and simplify the equation
Factor the quadratic expression
In the equation 𝑥3 − 9 = 0, how can you factor it to find the solutions?
(x - 3)(x + 3) = 0
(x - 9)(x + 9) = 0
(x + 3)(x + 3) = 0
(x - 3)(x - 3) = 0
In the quadratic formula, what do the variables 'a,' 'b,' and 'c' represent?
The roots of the equation
The coefficients of the quadratic equation
The solution values
The square roots of the discriminant
Find the values of x given the quadratic equation 𝑎2 + 2𝑎 − 48 = 0 by completing the square.
8; -6
6; -8
-7; 6
-6, 7
Find the values of x given the quadratic equation 𝑛2 + 7𝑛 + 15 = 5 by factoring.
-5; -2
5; 2
-2; 5
-5; 2
Find the values of x given the quadratic equation 4𝑟2 + 1 = 325 by extracting square roots.
9; -9
9; 9
8; -9
9; -8
Find the value of the discriminant of quadratic equation 6𝑝2 − 2𝑝 − 3 = 0.
76
54
67
45
Find the value of the discriminant of quadratic equation 5𝑏2 − 𝑏 − 2 = 0.
41
51
61
31
Solve each equation by completing the square 𝑝2 + 2𝑝 − 63 = 0.
7; -9
9; -7
8; -9
9; -8
Two faucets can fill a tank in 1 hour and 20 minutes. The first faucet takes more than two hours longer to fill the same tank when functioning without the second tap. How long does it take to fill the tank at first?
2 hours
6 hours
7 hours
4 hours
A motorboat makes a round trip on a river of 45 miles upstream and 45 miles downstream, maintaining the constant speed 12 miles per hour relative to the water. The entire round trip takes 8 hours. What is the speed of the current?
3 mi/h
2 mi/h
20 mi/h
60 mi/h
