Free Printable Algebra Gym M5G

1.

$64^x=8^{3x+1\ }$

a)

1

b)

-1

c)

$\frac{1}{5}$

d)

$-\frac{1}{5}$

2.

$f\left(x\right)=10\left(1.05\right)^x$ For this function, what is the percent rate of change? Also, is this exponential growth or decay?

a)

5%, growth

b)

5%, decay

c)

10%, growth

d)

10%, decay

3.

A cyclist rides over a hill that can be described by the equation $y=-x^2+2x+24$ , where y is the height in meters and x is the vertical distance in meters. How far is the start position from the end position in a straight line?

a)

10

b)

24

c)

2

d)

5

4.

$f\left(x\right)=4\left(x-1\right)^2$

Jeremy is working with the Fundamental Theorem of Algebra, and thinks he's found an exception. Looking at , this will result in only one root, x=1. Therefore, despite this being a second degree polynomial, there is only one root. Is this correct?

a)

Yes, this is a known exception

b)

No, this is not a polynomial, it is a quadratic function.

c)

No, if the quadratic formula is used, the other root is found.

d)

No, this root has multiplicity of 2, which means it counts as two roots.

5.

$2^x=64$ is equivalent to which of the following?

a)

$\log_{64}x=2$

b)

$\log_264=x$

c)

$\log_xx=64$

d)

$\log_x64=2$

6.

a)

f(x) is linear, because the difference of y-values over equal intervals is constant.

b)

f(x) is linear, because the difference of x-values is constantly 2 units

c)

f(x) is exponential, because the ratio of y-values over equal intervals is constant

d)

It cannot be determined whether f(x) is linear or exponential, because there are no intervals of only one unit in the table.

7.

What is the domain and range of the graphed function?

a)

Domain and range are all real numbers.

b)

Domain is all real numbers less than zero and range is all real numbers

c)

Domain is all real numbers and range is all real numbers equal to or less than zero.

d)

None of the above

8.

$16^{\left(x-2\right)\ }=64^{\left(2x-2\right)}$

Solve for

a)

$-\frac{1}{2}$

b)

2

c)

$-\frac{5}{2}$

d)

$\frac{1}{2}$

9.

$\left(3x^3y^{-4}\right)^{-2}$

What is the simplified form of Exponent ,answers must have positive exponents in them.

a)

$\frac{y^8}{6x^{-2}}$

b)

$\frac{9y^8}{x^6}$

c)

$\frac{y^8}{9x^6}$

d)

$\frac{y^8}{9x^{-6}}$

10.

What is the domain of the function? Assume 1 unit intervals for both axes.

a)

All real numbers

b)

$\left(-\infty,0\right)$

c)

$\left(0,\infty\right)$

d)

$\left(-\infty,\infty\right)$

11.

$\left(\frac{1}{27}\right)^{-\frac{2}{3}}$

Evaluate

a)

-3

b)

9

c)

$\frac{1}{3}$

d)

$-\frac{1}{9}$

12.

$y=4x+3$ $y=-x-2$

Solve the system

a)

(1,1)

b)

(-1,-1)

c)

(-1,1)

d)

(1,-1)

13.

$-3x+2y=8$ $x+2y=-8$

What is the solution to the system?

a)

(-4,-2)

b)

(4,2)

c)

(-2,-4)

d)

(2,4)

14.

$81-9k^2$

a)

(3k-9)(3k-9)

b)

(9+3k)(9-3k)

c)

(3k+9)(3k-9)

d)

(9+3k)(9+3k)

15.

Factorize 6xy - 8x + 15y - 20

a)

(3y + 4)(2x - 5)

b)

(3y - 4)(2x + 5)

c)

(2y - 4)(3x + 5)

d)

(2y + 5)(2y - 4)

16.

Solve by factoring

a)

x = {-5,-3}

b)

x = {-5,-3}

c)

x = {-5,3}

d)

x = {5,3}

17.

The annual gym subscription for a single member is

R1 000, while an annual family membership is

R1 500. The gym is considering increasing all membership fees by the same amount. If this is done then a single membership would cost 5/7 of a family membership. Determine the amount of the proposed increase.

a)

100

b)

150

c)

200

d)

250

18.

A group of friends is buying lunch together. The group buys

2 waffles and

4 hotdogs. Here are some facts about their lunch:

the total cost for the 2 waffles and 4 hotdogs is R160 a waffle costs R5 more than a hotdog

What is the price for one waffle and the price for one hotdog?

a)

R20 and R30

b)

R25 and R35

c)

R30 and R25

d)

R30 and R20

Algebra Gym M5G

Total questions: 18

Worksheet time: 18mins

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