Free Printable Rising Geometry Summer Math Practice

1.

15c + 12 - 9 - 11c =43

a)

c =-8

b)

c= 9

c)

c = 10

d)

c = -9

2.

What is the solution to the equation $-3\left(3x-8\right)=27$ ?

a)

$-\frac{1}{3}$

b)

$-5\ \frac{2}{3}$

c)

$5\ \frac{2}{3}$

d)

$12\ \frac{2}{3}$

3.

-11 + 3(b + 5) = 7

a)

1

b)

-1

c)

3

d)

-3

4.

Solve for x:

a)

x = yb - v

b)

x = by - v

c)

x = by + v

5.

$Given\ ax-b=c,\ solve\ for\ x.\$

a)

$x\ =\ \frac{c+b}{a}$

b)

$x\ =\ \frac{c-b}{a}$

c)

$x\ =\ \frac{a+b}{c}$

d)

$x\ =\ \frac{c+a}{b}$

6.

$Given\ d=rt,\ solve\ for\ r.\$

a)

$r=\frac{t}{d}$

b)

$t\ =\ \frac{d}{r}$

c)

$d=\frac{r}{t}$

d)

$r=\frac{d}{t}$

7.

$Given\ V=lwh,\ solve\ for\ l.$

a)

$l=\frac{Vw}{h}$

b)

$l=\frac{V}{wh}$

c)

$l=\frac{Vh}{w}$

d)

$l=\frac{wh}{V}$

8.

In the equation y=mx+b, what does the m represent?

a)

slope

b)

y-intercept

c)

linear

d)

point-slope

9.

What is the slope of the equation?
y = -3x + 4

a)

-3

b)

4

c)

-4

d)

3

10.

Find the slope of the line.

a)

-5/4

b)

5/4

c)

-4/5

d)

4/5

11.

At what rate did the rain fall?

a)

2 cm per hour

b)

¹/₄ cm per hour

c)

¹/₂ cm per hour

d)

4 cm per hour

12.

Find the slope of the line.

a)

1/2

b)

-1/2

c)

2

d)

-2

13.

Find the slope:

(9, 2), (7, -3)

a)

$\frac{-5}{2}$

b)

$\frac{5}{2}$

c)

$-\frac{1}{16}$

d)

$\frac{1}{16}$

14.

Find the slope:

(10, -2), (12, -3)

a)

$\frac{1}{2}$

b)

$-\frac{5}{22}$

c)

$-\frac{1}{2}$

d)

$\frac{8}{9}$

15.

Find the slope:

(4, -2) (4, 0)

a)

$\frac{2}{0}$ or undefined

b)

$\frac{0}{2}$ or 0

c)

$\frac{2}{4}$ or $\frac{1}{2}$

d)

$-\frac{1}{4}$

16.

Rate of Change is the same as Slope.

a)

True

b)

Sometimes

c)

False

17.

Find the unit rate of 624 calories in 3 servings.

a)

1,872 calories per serving

b)

208 calories per serving

c)

624 calories per serving

d)

621 calories per serving

18.

Look at the graph. Write down the equation for the line.

a)

y = - x + 3

b)

y = 4x + 3

c)

y = ¹/₄x + 3

d)

y = - 4x + 3

19.

Which equation represents the line shown on the coordinate plane?

a)

$𝑦=\frac{2}{5}𝑥−2$

b)

$𝑦=\frac{2}{5}𝑥+5$

c)

$y=-\frac{2}{5}𝑥+5$

d)

$𝑦=−\frac{2}{5}𝑥−2$

20.

Which equation is being represented by this line?

a)

y = -1x + 2

b)

y = 1/2x + 2

c)

y = 3x -4

d)

y = -3x +2

21.

If a system of equations has no solution, what does the graph look like?

a)

intersecting lines

b)

parallel lines

c)

skew lines

d)

intersecting lines

22.

What is the solution?

a)

(1, -1)

b)

(-1, 1)

c)

(0, -2)

d)

(0, 1)

23.

Solve for x and y
3x + 2y = 16
7x + y = 19

a)

(-2,5)

b)

(-2,-5)

c)

(2,-5)

d)

(2,5)

24.

Solve for x and y
y = 2x + 1
y = 4x - 1

a)

(1,3)

b)

(-1,-3)

c)

(-1,3)

d)

(3,1)

25.

A college student completed some courses worth 3 credits and some courses worth 4 credits. The student earned a total of 59 credits after completing 18 courses.

How many courses worth 3 credits did the student complete?

a)

13

b)

5

c)

20

d)

39

26.

A customer at a store paid $64 for 3 large candles and 4 small candles. At the same store, a second customer paid $4 more than the first customer for 1 large candle and 8 small candles. The price of each large candle is the same, and the price of each small candle is the same.

Which system of equations can be used to find the price in dollars of each large candle, x, and each small candle, y?

a)

4y = 3x + 64

8y = x + 68

b)

4y = 3x + 64

8y = x + 60

c)

3x + 4y = 64

x + 8y = 68

d)

3x + 4y = 64

x + 8y = 60

27.

Anything raised to a power of zero is always:

a)

0

b)

1

c)

itself

d)

negative

28.

Simplify the following expression:

$\frac{x^{18}y^{15}}{x^6y^3}$

a)

x³y⁵

b)

x¹²y¹²

c)

x²⁴y¹⁸

d)

x¹⁰⁸y⁴⁵

29.

Which expression is NOT equivalent to $3^8$ ?

a)

$\left(3^6\right)\left(3^2\right)$

b)

$\left(3^4\right)^2$

c)

$\left(3^4\right)\left(3^4\right)$

d)

$\left(3^4\right)^4$

30.

Simplify: $x^{-5}$

a)

$\frac{1}{x^5}$

b)

$x^5$

c)

$\frac{1}{x^{-5}}$

d)

not possible

31.

$\left(\frac{2x^5y^4}{3z^2}\right)^3$

a)

$\frac{6x^{15}y^{12}}{9z^6}$

b)

$\frac{8x^8y^7}{27x^5}$

c)

$\frac{8x^{15}y^{12}}{27z^6}$

d)

$\frac{2x^{15}y^{12}}{3z^6}$

32.

Which expression is equivalent to $\left(x^9yz^4\right)^5$

a)

$x^{14}y^6z^9$

b)

$x^{14}y^5z^9$

c)

$x^{45}yz^{20}$

d)

$x^{45}y^5z^{20}$

33.

Simplify the expression using exponential notation:

$a^2\cdot a^4$

a)

$a^6$

b)

$a^8$

c)

$a^2$

d)

$a^{24}$

34.

Simplify the expression using exponential notation:

$\left(y^8\right)^5$

a)

$y^{13}$

b)

$y^{40}$

c)

$y^3$

d)

$y^{85}$

35.

Simplify each expression using exponential notation:

$\frac{6^3k^{15}}{6^7k^{19}}$

a)

$k^46^4$

b)

$\frac{k^4}{6^4}$

c)

$6^4k^4$

d)

$\frac{6^4}{k^4}$

36.

Add the following polynomials:
(6n²- 7n⁴+8) + (6 + 8n + 4n⁴)

a)

-3n⁴+ 6n²+8n+14

b)

-n⁴-2n²+8n+7

c)

-n⁴ + 6n²+8n+7

d)

-3n⁴+ 6n²+8n+7

37.

Subtract the following polynomials:
(a³ - 2a²) - (-4a³ + 4a²)

a)

-5a⁶- 5a⁴

b)

5a³ - 2a²

c)

-2a³ - 6a²

d)

5a³ - 6a²

38.

Find the product:
5xy(6x - y)

a)

11x² - y²

b)

30x² + y²

c)

30x²y - 5xy²

d)

11x²y + 5x²y²

39.

Use the FOIL method to multiply:
(x-7)²

a)

x²-49

b)

x²+49

c)

x²-14x+49

d)

x²-14x-49

40.

(3x - 2)(6x + 1)

a)

21x²

b)

18x² + 9x + 2

c)

9x² - 9x - 2

d)

18x² - 9x - 2

41.

Divide

$\frac{-4a^{7\ }-\ 6a^5}{2a^3}$

a)

$2a^{4\ }+3a^2$

b)

$4a^{4\ }-\ 4a^2$

c)

$-2a^{7\ }-\ 3a^5$

d)

$-2a^{4\ }-3a^2$

42.

Divide

$\frac{-12a^{4\ }+\ 6a^3}{6a^3}$

a)

$2a$

b)

$-2a+1$

c)

$2a\ +1$

d)

$-2a\ +\ 1a$

43.

Divide

$\frac{8x^2-4x+12}{2x}$

a)

4x + 2

b)

4x - 2

c)

$4x\ -\ 2\ +\ \frac{6}{x}$

d)

$4x\ -2\ +\frac{12}{x}$

44.

Solve!

a)

x = 2

b)

x = 6

c)

x = 4

d)

x = 8

45.

a)

3/5

b)

3/4

c)

1/4

d)

4/5

46.

$\sqrt{50}$

a)

$5\sqrt{2}$

b)

$\sqrt{5}$

c)

$2\sqrt{5}$

d)

$25\sqrt{2}$

47.

$\sqrt{96}$

a)

$16\sqrt{6}$

b)

$2\sqrt{6}$

c)

$4\sqrt{6}$

d)

$\sqrt{2}$

48.

$\sqrt{45}$ =

a)

$3\sqrt{5}$

b)

$5\sqrt{3}$

c)

$9\sqrt{5}$

d)

$5\sqrt{9}$

49.

∛27 =

a)

6

b)

3

c)

9

d)

19,682

50.

a)

y²z¹⁰√xy

b)

20yz√xy

c)

xy²z¹⁰√y

d)

yz⁶√xy²z²

51.

$2\sqrt{3}\left(\sqrt{6}-\sqrt{3}\right)$

a)

$6\sqrt{2}-6$

b)

$3\sqrt{2}+3$

c)

$6-\sqrt{3}$

d)

$\sqrt{3}-\sqrt{2}$

52.

Solve

$\sqrt{x+4}=10$

a)

$x=6$

b)

$x=104$

c)

$x=96$

d)

$x=14$

e)

$No\ solution$

53.

a)

5

b)

4

c)

41

d)

82

54.

What is the vertex of y=x²+4x+3?

a)

(2,1)

b)

(-2,1)

c)

(0,0)

d)

(-2,-1)

55.

Find the vertex of

y=3\left(x-2\right)^2+3

a)

$\left(2,3\right)$

b)

$\left(-2,3\right)$

c)

$\left(2,-3\right)$

d)

$\left(-2,-3\right)$

56.

Find the vertex of
f(x) = -x²- 4x + 12.

a)

(-2, 16)

b)

(2, 0)

c)

(2, 4)

d)

(-2, 4)

57.

What is the green dashed line called?

a)

roots or x-intercepts

b)

parabola

c)

axis of symmetry

d)

y intercept

58.

Where is the axis of symmetry for this parabola?

a)

x = −1

b)

x = 0

c)

y = 3

d)

x = −3

59.

Which graph is a parabola?

a)

b)

c)

d)

60.

A fountain shoots water in an arc over a lake that can be modeled by the graph of the equation y= -0.4x² + 8x where x is the horizontal distance (in feet) from the fountain base and y is the height (in feet) above the river. How high does the water go?

a)

It goes 11.78 feet high

b)

It goes 20 feet high

c)

It goes 40 feet high

d)

It goes 10 feet high

61.

A raft is dropped from a helicopter 256 feet in the air above the ocean. Its approximate height, h, after t seconds is given by the function h(t) = -16t² + 256. How many seconds did it take the raft to hit the water?

a)

-4

b)

2

c)

4

d)

8

62.

What is the initial (starting) height of an object following this path? h(t) = -16t² +20t + 6

a)

-16 feet

b)

0 feet

c)

20 feet

d)

6 feet

63.

An object in launched directly upward at 64 feet per second (ft/s) from a platform 80 feet high. Its height is represented by the equation
s(t) = –16t² + 64t + 80.
What will be the object's maximum height?

a)

2 ft

b)

80 ft

c)

144 ft

d)

64 ft

64.

What is the correct name for the transformation from y=x² to y = -x²?

a)

Reflection

b)

Translation

c)

Dilation

d)

Transformer

65.

Which way does the graph move if the equation looks like y = (x - 3)²?

a)

Graph moves UP 3 units

b)

Graph moves to the RIGHT 3 units

c)

Graph moves DOWN 3 units

d)

Graph moves to the LEFT 3 units

66.

Which way does the graph move if the equation looks like y = (x + 4)² ?

a)

Graph moves UP 4 units

b)

Graph moves to the RIGHT 4 units

c)

Graph moves DOWN 4 units

d)

Graph moves to the LEFT 4 units

67.

What happens to the parabola when you multiply its equation by a number bigger than 1? Eg y = 3x²

a)

Graph moves UP

b)

Graph gets WIDER

c)

Graph moves DOWN

d)

Graph gets NARROWER

Rising Geometry Summer Math Practice

Total questions: 67

Worksheet time: 6hrs 35mins

Similar Resources on Wayground