ACT 1 Alg: Solve quadratics equations - One Minute Per Question

Welcome to your ACT 1 Alg: Solve quadratics equations

$Q_{1}:$ For what values of $x$ is $x^{2} − 3x − 10 = 0$?

$ x = 5$ and $x = −2$

$ x = -5$ and $x = 2$

$ x = 5$

$x = −2$

$Q_{2}:$ If $3x^{2}-\frac{1}{2}x=0$ and $x > 0$, what is the value of $x$?

$\frac{1}{6}$

$\frac{1}{2}$

$\frac{3}{2}$

$6$

$Q_{3}:$ How many roots larger than $5$ does $x^{2} − 3x + 2$ have?

None

One

Two

Cannot be determined from the given information

$Q_{4}:$ Solve $6x^{2}-2x− 7$

$x=\frac{1\pm \sqrt{43}}{6}$

$x=\frac{2 \pm \sqrt{43}}{3}$

$x=\frac{2 \pm 3\sqrt{37}}{5}$

$x=\frac{1\pm 3\sqrt{37}}{2}$

$Q_{5}:$ Solve $x^{2}-18$

$x=\pm \sqrt{9}$

$x=\pm \sqrt{14}$

$x=\pm \sqrt{18}$

$x=3 \sqrt{2}$

$Q_{6}:$ Factor $3x^{2}+4x+1$.

$(2x+1)(x+2)$

$(3x-1)(x-1)$

$(2x-1)(x-2)$

$(3x+1)(x+1)$

$Q_{7}:$ Given $f(x)=-(x+2)(x-4)$ , find the $x$-intercepts.

$-2,4$

$-2,-4$

$-2$

$1$

$Q_{8}:$ Which of the following is an equivalent form of the equation of the graph shown

$y=-(x+1)(x-5)$

$y=x(x-6)+5$

$y=(x+1)(x+5)$

$y=(x-1)(x-5)$

$Q_{9}:$Which of the following is solution of $3x^2-48=-21$

$3$

$-9$

$-3,3$

$9$

$Q_{10}:$ If r and s are two solutions of the equation $x^{2}-3x=28$, which of the following is the value of $r+s$?

$-3$

$3$

$6$

$9$

$Q_{11}:$ Solve $2x^{2}-6x-7=0$

$x=\frac{3}{2} \pm \frac{\sqrt{23} }{2}$

$x=\frac{3}{2} + \frac{\sqrt{23} }{2}$

$x=\frac{3}{2} - \frac{\sqrt{23} }{2}$

$x=\frac{-3}{2} \pm \frac{\sqrt{23} }{2}$

$Q_{12}:$ 1 If $x^{2}-10 x=75$ and $x < 0$ , what is the value of $x + 5$ ?

$-10$

$-20$

$0$

$-15$

$Q_{13}:$ In the quadratic equation $x^{2}-rx=\frac{k^{2}}{4}$, $k$ and $r$ are are constants. What are the solutions for $x $?

$x=\frac{r}{4} \pm \frac{\sqrt{k^{2}+2r^{2}}}{4}$

$x=\frac{r}{2} \pm \frac{\sqrt{k^{2}+8r^{2}}}{4}$

$x=\frac{r}{4} \pm \frac{\sqrt{k^{2}+r^{2}}}{4}$

$x=\frac{r}{2} \pm \frac{\sqrt{k^{2}+r^{2}}}{4}$

$Q_{14}:$ Which of the following equations has no real solution?

$5x^{2}-10x=6$

$4x^{2}+8x+4=0$

$3x^{2}-5x=-3$

$-\frac{x^{2}}{3} +2x-2=0$

$Q_{15}:$ For which of the following quadratic equations is the sum of its roots equal to the product of its roots?

$x^{2}+ 5x + 5 = 0$

$x^{2}- 5x + 5 = 0$

$2x^{2}-3x + 6= 0$

$2x^{2}-6x + 6= 0$

$Q_{16}:$ What is the greatest integer k for which the equation $x^{2} + 5x + k = 0$ has real solutions?

$4$

$6$

$7$

$12$

$Q_{17}:$ The product of the roots of a quadratic equation is $−15$ and their sum is $−2$. Which of the following could be the quadratic equation?

$x^{2} − 2x −15 = 0$

$x^{2} + 2x −15 = 0$

$x^{2} − 2x +15 = 0$

$x^{2} +15x −2 = 0$

$Q_{18}:$ If the sum of two numbers is equal to 17 and their product is equal to 60, what are the numbers?

$12,5$

$12,-5$

$-12,5$

$-12,-5$

$Q_{19}:$ If the area of a rectangle is 46 square units and its longest side is 12 units longer than its shortest side, what are the lengths of the sides?

$4, 16$

$-14, -16$

$-4, -16$

$4, -16$

$Q_{20}:$ The difference between the squares of two consecutive odd numbers is equal to 40. Find both numbers.

$9,11$

$11,13$

$10,12$

none

$Q_{21}:$ Find two numbers such that their sum equals $15$ and their product equals $36$

$9,6$

$11,4$

$3,12$

$13,2$

$Q_{22}:$Which of the following is solution of $x^2+2x=-2$

$-1$

$1$

$-3$

No real solution

$Q_{23}:$ Jon jumped off a cliff into the ocean while vacationing with some friends. His height as a function of time could be modeled by the function $h(s) = -16s^{2} + 16s + 480 $, where $s$ is the time in seconds and $h$ is the height in feet. Jon hit the water after how many seconds?

$6$

$-5$

$0$

$5$

$Q_{24}:$ If a toy rocket is launched vertically upward from ground level with an initial velocity of $128$ feet per second, then its height $h$ after $t$ seconds is given by the equations $h(t) = -16t^{2} + 128t$ (if air resistance is neglected). How long will it take for the rocket to return to the ground?

$4$

$16$

$7$

$8$

$Q_{25}:$ Find the value of $k$ for which the quadratic equation $2x^{2}-kx+1=0$ has equal roots.

$\sqrt{8}$

$\sqrt{-8}$

$\sqrt{4}$

$\sqrt{6}$

Please fill in the comment box below.

Name

Email

Leave a Reply Cancel reply