Lesson test: Equations and the quadratic

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Equations and the quadratic

1.[2p]
Solve $5 x - 7 = 3 (x + 1)$ .

CorrectNot quite: 5

2.[2p]
Reducing an equation leaves $6 = 5$ , with the unknown gone. What does that mean?

The equation has no solution

Correct

Every number is a solution

The answer is: The equation has no solution

The equation has exactly one solution, $x = 1$

The answer is: The equation has no solution

An arithmetic slip must have been made, since the unknown cannot vanish

The answer is: The equation has no solution

3.[2p]
Why must every candidate be checked in the original equation after squaring both sides?

Squaring can create solutions the original equation does not have

Correct

Squaring can destroy solutions the original equation does have

The answer is: Squaring can create solutions the original equation does not have

Because square roots are irrational

The answer is: Squaring can create solutions the original equation does not have

Because squaring is not distributive

The answer is: Squaring can create solutions the original equation does not have

4.[2p]
Completing the square on $x^{2} - 8 x$ gives $(x - p)^{2} - q$ . Give $p$ and $q$ as "p, q".

CorrectNot quite: 4, 16

5.[2p]
The larger solution of $2 x^{2} + 5 x - 12 = 0$ .

CorrectNot quite: 1.5

6.[2p]
The discriminant of $3 x^{2} - 5 x + 4 = 0$ .

CorrectNot quite: -23

7.[1p]
A quadratic with a negative discriminant has no solution among the real numbers.

True

Correct

False

The answer is: True

8.[3p]
Put the steps of completing the square on $a x^{2} + b x + c = 0$ in order.

Rewrite the first two terms as a square minus $b^{2} / 4 a^{2}$
Take the square root of both sides, keeping both signs
Divide through by $a$
Move the constants to the right-hand side

Show the answer

a, b, c, d

9.[3p]
A stone thrown from a cliff has height $h = 40 + 15 t - 4.9 t^{2}$ metres. At what time in seconds does it hit the water?

CorrectNot quite: 4.77

1.[2p] Solve 5x-7=3(x+1).

2.[2p] Reducing an equation leaves 6=5, with the unknown gone. What does that mean?

3.[2p] Why must every candidate be checked in the original equation after squaring both sides?

4.[2p] Completing the square on x2-8x gives (x-p)2-q. Give p and q as "p, q".

5.[2p] The larger solution of 2x2+5x-12=0.

6.[2p] The discriminant of 3x2-5x+4=0.

7.[1p] A quadratic with a negative discriminant has no solution among the real numbers.

8.[3p] Put the steps of completing the square on ax2+bx+c=0 in order.

9.[3p] A stone thrown from a cliff has height h=40+15t-4.9t2 metres. At what time in seconds does it hit the water?

1.[2p]
Solve $5 x - 7 = 3 (x + 1)$ .

2.[2p]
Reducing an equation leaves $6 = 5$ , with the unknown gone. What does that mean?

3.[2p]
Why must every candidate be checked in the original equation after squaring both sides?

4.[2p]
Completing the square on $x^{2} - 8 x$ gives $(x - p)^{2} - q$ . Give $p$ and $q$ as "p, q".

5.[2p]
The larger solution of $2 x^{2} + 5 x - 12 = 0$ .

6.[2p]
The discriminant of $3 x^{2} - 5 x + 4 = 0$ .

7.[1p]
A quadratic with a negative discriminant has no solution among the real numbers.

8.[3p]
Put the steps of completing the square on $a x^{2} + b x + c = 0$ in order.

9.[3p]
A stone thrown from a cliff has height $h = 40 + 15 t - 4.9 t^{2}$ metres. At what time in seconds does it hit the water?