Quiz about Methods in algebra multiple-choice quiz

Question 1

What is the expression $$5-3\left(x+1\right)$$ equal to?

Accepted Answer

$$2-3x$$

Answer

$$2x-2$$

Answer

$$8-3x$$

Answer

$$2x+2$$

Question 2

What is the expansion of $$\left(a+\frac{1}{a}\right)^2$$ ?

Accepted Answer

$$a^2+2+\frac{1}{a^2}$$

Answer

$$a^2+1+\frac{1}{a^2}$$

Answer

$$a^2+\frac{1}{a^2}$$

Answer

$$a^2+2a+\frac{1}{a^2}$$

Question 3

What is the factorisation of $$2x^2-3x-5\ ?$$

Accepted Answer

$$\left(2x-5\right)\left(x+1\right)$$

Answer

$$\left(2x-1\right)\left(x+5\right)$$

Answer

$$x\left(2x-3\right)-5$$

Answer

$$\left(2x+1\right)\left(x-5\right)$$

Question 4

What is the factorisation of $$2y^2-18\ ?$$

Accepted Answer

$$2\left(y+3\right)\left(y-3\right)$$

Answer

$$2\left(y-3\right)^2$$

Answer

$$\left(2y-3\right)\left(y+6\right)$$

Answer

$$2\left(y+3\right)^2$$

Question 5

What is the fraction $$\frac{x^2+x}{x^2-1}$$ equivalent to?

Accepted Answer

$$\frac{x}{x-1}$$

Answer

$$\frac{x-1}{x+1}$$

Answer

$$\frac{x+1}{x-1}$$

Answer

$$-x$$

Question 6

What is the factorisation of $$n^3+125\ ?$$

Accepted Answer

$$\left(n+5\right)\left(n^2-5n+25\right)$$

Answer

$$\left(n+5\right)\left(n^2-10n+25\right)$$

Answer

$$\left(n-5\right)\left(n^2+5n+25\right)$$

Answer

$$\left(n-5\right)\left(n^2+10n+25\right)$$

Question 7

What is the solution of the linear equation $$\frac{x+2}{3}-\frac{x-3}{2}=1\ ?$$

Accepted Answer

$$x=7$$

Answer

$$x=-6$$

Answer

$$x=-11$$

Answer

$$x=12$$

Question 8

What are the solutions of the quadratic equation $$4x^2+2x-1=0\ ?$$

Accepted Answer

$$\frac{-1\pm\ \sqrt[]{5}}{4}$$

Answer

$$\frac{1\pm2\ \sqrt[]{5}}{4}$$

Answer

$$\frac{-1\pm2\ \sqrt[]{5}}{4}$$

Answer

$$\frac{1\pm\ \sqrt[]{5}}{4}$$

Question 9

What is the simultaneous solution of the equations $$2x+3y=5$$ and $$5x-3y=23\ ?$$

Accepted Answer

$$x=4$$ and $$y=-1$$

Answer

$$x=7$$ and $$y=-3$$

Answer

$$x=6$$ and $$y=-\frac{7}{3}$$

Answer

$$x=5$$ and $$y=-\frac{5}{3}$$

Question 10

What must be added to $$x^2-30x$$ to create a perfect square?

Accepted Answer

$$225$$

Answer

$$900$$

Answer

$$-900$$

Answer

$$-225$$

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