 ## Full Length ISEE Upper Level Mathematics Practice Test

If you want to prepare for the ISEE Upper Level Mathematics Practice Test? It’s time to taking a Full-length ISEE Upper Level Mathematics Practice Test. It is the best way to simulate test day. To challenge your skills and simulate the full length ISEE Upper Level Mathematics Practice Test day experience, score your tests using the answer keys.

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## ISEE Upper Level Mathematics Practice Test 1

• 47 questions
• Total time for this section: 40 Minutes
• Calculators are not allowed at the test.
1- Which of the following graphs represents the compound inequality $$3 \ \leq \ 2 \ x \ - \ 3 \ < \ 13$$?
(A) (B) (C) (D) 2- Which graph shows a non-proportional linear relationship between $$x$$ and $$y$$?
(A) (B) (C) (D) 3- A girl $$162$$ cm tall, stands $$270$$ cm from a lamp post at night. Her shadow from the light is $$100$$ cm long. How high is the lamp post? (A) $$800$$ cm
(B) $$650$$ cm
(C) $$576$$ cm
(D) $$317$$ cm
4- Find all values of $$x$$ for which $$2 \ x^2 \ + \ 15 \ x \ + \ 7= 0$$
(A) $$- \ 7, - \ \frac{1}{3}$$
(B) $$8, \frac{1}{2}$$
(C) $$- \ 7, - \ \frac{1}{2}$$
(D) $$- \ \frac{3}{5}, - \ \frac{1}{2}$$
5- Solve.
$$|1 \ – \ (12 \ ÷ \ | 1 \ - \ 5 |) | =$$?
(A) $$2$$
(B) $$- \ 2$$
(C) $$- \ 5$$
(D) $$5$$
6- The ratio of boys to girls in a school is $$7:4$$. If there are $$550$$ students in a school, how many boys are in the school?
(A) $$350$$
(B) $$250$$
(C) $$200$$
(D) $$400$$
7- The rectangle on the coordinate grid is translated $$5$$ units down and $$4$$ units to the left.
Which of the following describes this transformation? (A) $$(x,y) ⇒ (x \ - \ 4, y \ + \ 5)$$
(B) $$(x,y) ⇒ (x \ - \ 4, y \ - \ 5)$$
(C) $$(x,y) ⇒ (x \ + \ 4, y \ + \ 5)$$
(D) $$(x,y) ⇒ (x \ + \ 4, y \ - \ 5)$$
8- How is this number written in scientific notation?
$$0.0000007685$$
(A)  $$7.685 \ × \ 10^{–7}$$
(B)  $$76.85 \ × \ 10^{–9}$$
(C)  $$7.685 \ × \ 10^{4}$$
(D)  $$0.0007685 \ × \ 10^{- \ 8}$$
9- $$(x \ - \ 9) \ (x \ + \ 3) =$$
(A) $$x^2 \ + \ 8 \ x \ - \ 22$$
(B) $$2 \ x \ + \ 32 \ x \ - \ 27$$
(C) $$- \ x^2 \ - \ 6 \ x \ + \ 27$$
(D) $$x^2 \ - \ 6 \ x \ - \ 27$$
10- Which value of $$x$$ makes the following inequality true?
$$\frac{2}{25} \ ≤ \ x \ < \ 25\%$$
(A) $$0.27$$
(B)  $$\frac{7}{48}$$
(C)  $$\sqrt{0.169}$$
(D)  $$0.2981$$
11- Use the diagram below to answer the question.
Given the lengths of the base and diagonal of the rectangle below, what is the length of height $$h$$, in terms of $$s$$? (A) $$2 \ s \ \sqrt{5}$$
(B) $$2 \ s^2$$
(C) $$s \ \sqrt{15}$$
(D) $$4 \ s$$
12- If the area of trapezoid is $$168$$ cm$$^2$$, what is the perimeter of the trapezoid? (A) $$40 \ + \ 4 \ \sqrt{ 10 }$$ cm
(B) $$4 \ \sqrt{ 13 }$$ cm
(C) $$10 \ \sqrt{ 3}$$ cm
(D) $$10 \ + \ 4 \ \sqrt{ 10}$$ cm
13- Find the area of a rectangle with a length of $$145$$ feet and a width of $$68$$ feet.
(A) $$10,340$$ sq. ft.
(B) $$12,602$$ sq. ft.
(C) $$9,860$$ sq. ft.
(D) $$8,540$$ sq. ft.
14- Emily and Daniel have taken the same number of photos on their school trip. Emily has taken $$3$$ times as many as photos as Claire and Daniel has taken $$12$$ more photos than Claire. How many photos has Claire taken?
(A) $$6$$
(B) $$8$$
(C) $$4$$
(D) $$10$$
15- $$93 \ ÷ \ \frac{1}{5} =$$?
(A) $$512$$
(B) $$610$$
(C) $$46.5$$
(D) $$465$$
16- $$3 \ – \ 12 \ ÷ \ (5^2 \ ÷ \ 5) =$$ ___
(A) $$- \ 1$$
(B) $$4$$
(C) $$8$$
(D) $$- \ 3$$
17- Emily lives $$4 \ \frac{1}{5}$$ miles from where she works. When traveling to work, she walks to a bus stop $$\frac{1}{2}$$ of the way to catch a bus. How many miles away from her house is the bus stop?
(A) $$3 \ \frac{1}{5}$$ Miles
(B) $$2 \ \frac{1}{10}$$ Miles
(C) $$2 \ \frac{1}{5}$$ Miles
(D) $$4 \ \frac{1}{10}$$ Miles
18- $$\frac{8}{32}$$ is equals to:
(A) $$0.25$$
(B) $$2.15$$
(C) $$0.025$$
(D) $$1.025$$
19- Use the chart below to answer the question.
There are also purple marbles in the bag. Which of the following can NOT be the probability of randomly selecting a purple marble from the bag? (A) $$\frac{1}{10}$$
(B) $$\frac{1}{4}$$
(C) $$\frac{2}{5}$$
(D) $$\frac{7}{15}$$
20- If $$(3.2 \ + \ 3.6 \ + \ 3.8) \ x = x$$, then what is the value of $$x$$?
(A) $$10.6$$
(B) $$1$$
(C) $$0$$
(D) $$\frac{1}{10.6}$$
21- Two dice are thrown simultaneously, what is the probability of getting a sum of $$6$$ or $$9$$?
(A) $$\frac{1}{3}$$
(B) $$\frac{1}{4}$$
(C) $$\frac{1}{25}$$
(D) $$\frac{1}{12}$$
22- If a vehicle is driven $$25$$ miles on Monday, $$40$$ miles on Tuesday, and $$22$$ miles on Wednesday, what is the average number of miles driven each day?
(A) $$32$$ Miles
(B) $$31$$ Miles
(C) $$30$$ Miles
(D) $$29$$ Miles
23- In the following figure, AB is the diameter of the circle. What is the circumference of the circle? (A)  $$5 \ \pi$$
(B)  $$20 \ \pi$$
(C)  $$10 \ \pi$$
(D)  $$15 \ \pi$$
24- $$48.32 \ ÷ \ 0.05 =$$?
(A) $$900.45$$
(B) $$850.18$$
(C) $$966.4$$
(D) $$950.52$$
25- Solve for $$4 \ x^2 \ + \ 8 = 24$$
(A) $$± \ 4$$
(B) $$± \ 8$$
(C) $$± \ 16$$
(D) $$± \ 2$$
26- With an $$25\%$$ discount, Ella was able to save $$28.32$$ on a dress. What was the original price of the dress?
(A) $$113.28$$
(B) $$120.10$$
(C) $$112.94$$
(D) $$121.32$$
27- Use the following table to answer question below.
This table shows the data Daniel collects while watching birds for one week. How many raptors did Daniel see on Monday? (A) $$5$$
(B) $$10$$
(C) $$15$$
(D) $$20$$
28- A circle has a diameter of $$18$$ inches. What is its approximate area?
(A) $$254.34$$ in$$^2$$
(B) $$269.22$$ in$$^2$$
(C) $$310.93$$ in$$^2$$
(D) $$300.45$$ in$$^2$$
29- The sum of $$6$$ numbers is greater than $$240$$ and less than $$380$$. Which of the following could be the average (arithmetic mean) of the numbers?
(A) $$35$$
(B) $$75$$
(C) $$55$$
(D) $$25$$

### ISEE Upper Level Math for Beginners

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The Ultimate Step by Step Guide to Preparing for the ISEE Upper Level Math Test

30- Simplify $$\frac{\frac{1}{3} \ - \ \frac{x \ + \ 4}{2}}{\frac{x^2}{2} \ - \ \frac{3}{4}}$$
(A)  $$\frac{ - \ 6 \ x \ - \ 20}{6 \ x^2 \ - \ 9}$$
(B)  $$\frac{ - \ 3 \ x \ + \ 10}{6 \ x^2 \ + \ 6}$$
(C)  $$\frac{12 \ x \ + \ 10}{ \ x^2 \ - \ 9}$$
(D)  $$\frac{8 \ x \ - \ 12}{4 \ x^2 \ + \ 9}$$
31- The base of a right triangle is $$4$$ foot, and the interior angles are $$45-45-90$$. What is its area?
(A) $$16$$ square feet
(B) $$8$$ square feet
(C) $$4$$ square feet
(D) $$4.5$$ square feet
32- If $$5$$ garbage trucks can collect the trash of $$25$$ homes in a day. How many trucks are needed to collect in $$200$$ houses?
(A) $$30$$
(B) $$40$$
(C) $$25$$
(D) $$45$$
33- Which equation represents the statement twice the difference between $$4$$ times $$H$$ and $$2$$ gives $$25$$.
(A) $$3 \ (2 \ H \ - \ 4) = 25$$
(B) $$\frac{1}{2} \ (4 \ H \ + \ 2) = 25$$
(C) $$2 \ (4 \ H \ - \ 2) = 25$$
(D) $$4 \ (2 \ H \ - \ 25) = 2$$
34- A floppy disk shows $$840,128$$ bytes free and $$698,589$$ bytes used. If you delete a file of size $$552,129$$ bytes and create a new file of size $$439,566$$ bytes, how many free bytes will the floppy disk have?
(A) $$892,691$$
(B) $$1032,623$$
(C) $$983,123$$
(D) $$952,691$$
35- If $$4 \ + \ x^{\frac{1}{2)}}=20$$, then what is the value of $$15 \ × \ x$$?
(A) $$3,340$$
(B) $$3,840$$
(C) $$2,925$$
(D) $$3,125$$
36- The width of a box is one third of its length. The height of the box is one third of its width. If the length of the box is $$36$$ cm, what is the volume of the box?
(A) $$1,728$$ cm$$^3$$
(B) $$1,548$$ cm$$^3$$
(C) $$1,317$$ cm$$^3$$
(D) $$1,250$$ cm$$^3$$
37- Triangle ABC is graphed on a coordinate grid with vertices at A $$(- \ 3, - \ 2)$$, B $$(- \ 1, 4)$$ and C $$(7, 9)$$.
Triangle ABC is reflected over $$x$$ axes to create triangle A’B’C’.
Which order pair represents the coordinate of C’?
(A) $$(7, 9)$$
(B) $$(7, - \ 9)$$
(C) $$(- \ 7, - \ 9)$$
(D) $$(- \ 7, 9)$$
38- $$7$$ days $$21$$ hours $$21$$ minutes $$– \ 4$$ days $$14$$ hours $$14$$ minutes $$=$$?
(A) $$3$$ days $$7$$ hours $$7$$ minutes
(B) $$3$$ days $$7$$ hours $$14$$ minutes
(C) $$2$$ days $$6$$ hours $$21$$ minutes
(D) $$2$$ days $$7$$ hours $$19$$ minutes
39- A square measures $$6$$ inches on one side. By how much will the area be decreased if its length is increased by $$5$$ inches and its width decreased by $$3$$ inches.
(A) $$2$$ sq decreased
(B) $$1$$ sq decreased
(C) $$4$$ sq decreased
(D) $$3$$ sq decreased
40- A circle is inscribed in a square, as shown below.
The area of the circle is $$24 \ π$$ cm$$^2$$. What is the area of the square? (A) $$100$$ cm$$^2$$
(B) $$80$$ cm$$^2$$
(C) $$50$$ cm$$^2$$
(D) $$150$$ cm$$^2$$
41- $$6 \ x^2 \ y^3 \ + \ 2 \ x^3 \ y^5 \ – \ (8 \ x^2 \ y^3 \ – \ 3 \ x^3 \ y^5) =$$ ___
(A) $$2 \ x^2 \ y^3 \ - \ 5 \ x^3 \ y^5$$
(B) $$3 \ x^2 \ y^3 \ - \ 7 \ x^3 \ y^5$$
(C) $$- \ 2 \ x^2 \ y^3 \ + \ 5 \ x^3 \ y^5$$
(D) $$- \ 5 \ x^2 \ y^3 \ - \ 2 \ x^3 \ y^5$$
42- Increased by $$45\%$$, the numbers $$91$$ becomes:
(A) $$122.31$$
(B) $$110.87$$
(C) $$131.95$$
(D) $$140.12$$
43- How many $$3 \ × \ 3$$ squares can fit inside a rectangle with a height of $$35$$ and width of $$18$$?
(A) $$70$$
(B) $$73$$
(C) $$62$$
(D) $$52$$
44- The radius of circle A is three times the radius of circle B. If the circumference of circle A is $$12 \ π$$, what is the area of circle B?
(A) $$8 \ 𝜋$$
(B) $$4 \ 𝜋$$
(C) $$12 \ 𝜋$$
(D) $$10 \ 𝜋$$
45- Which set of ordered pairs represents $$y$$ as a function of $$x$$?
(A) $$\left\{(3, - \ 2), (3, 7), (9, - \ 8), (4, - \ 7)\right\}$$
(B) $$\left\{(4, 2), (3, - \ 9), (5, 8), (4, 7)\right\}$$
(C) $$\left\{(9, 12), (5, 7), (6, 11), (5, 18)\right\}$$
(D) $$\left\{(6, 1), (3, 1), (0, 5), (4, 5)\right\}$$
46- David makes a weekly salary of $$350$$ plus $$10\%$$ commission on his sales. What will his income be for a week in which he makes sales totaling $$1,500$$?
(A) $$500$$
(B) $$540$$
(C) $$480$$
(D) $$620$$
47- If a box contains red and blue balls in ratio of $$4 : 5$$ red to blue, how many red balls are there if $$50$$ blue balls are in the box?
(A) $$60$$
(B) $$40$$
(C) $$50$$
(D) $$70$$
 1- Choice C is correct Solve for $$x$$.$$3 \ \leq \ 2 \ x \ - \ 3 \ < \ 13⇒$$ (add $$3$$ all sides) $$3 \ + \ 3 \ \leq \ 2 \ x \ - \ 3 \ + \ 3 \ < \ 13 \ + \ 3⇒$$$$6 \ \leq \ 2 \ x \ < \ 16⇒$$ ⇒ (divide all sides by $$2$$)$$3 \ ≤ \ x \ < \ 8$$$$x$$ is between $$3$$ and $$8$$. Choice C represent this inequality. 2- Choice D is correct A linear equation is a relationship between two variables, $$x$$ and $$y$$, and can be written in the form of $$y= m \ x \ + \ 𝑏$$.A non-proportional linear relationship takes on the form $$y= m \ x \ + \ 𝑏$$, where $$b ≠ 0$$ and its graph is a line that does not cross through the origin. 3- Choice C is correct The correct answer is $$576$$ cmWrite the proportion and solve for missing side.$$\frac{Smaller \ triangle \ height}{Smaller \ triangle \ base }= \frac{Bigger \ triangle \ height}{Bigger \ triangle \ base}⇒$$$$\frac{100 \ cm}{162 \ cm} = \frac{100 \ + \ 250 \ cm}{x }⇒ x=576$$ cm 4- Choice C is correct The correct answer is $$- \ 7, - \ \frac{1}{2}$$$$x{1,2} = \frac{− \ b \ ± \ \sqrt{b^2 \ − \ 4 \ a \ c}}{ 2a}$$$$a \ x^2 \ + \ b \ x + \ c = 0$$$$2 \ x^2 \ + \ 15 \ x \ + \ 7 = 0 ⇒$$ then:$$a = 2, b = 15$$ and $$c = 7$$$$x = \frac{− \ 15 \ + \ \sqrt{15^2 \ − \ 4 \ . \ 2 \ . \ 7}}{ 2 \ . \ 2 }== \frac{− \ 15 \ + \ 13}{ 4 }= \frac{− \ 2}{4}= - \ \frac{1}{2}$$$$x =\frac{ − \ 15 \ − \ \sqrt{15^2 \ − \ 4 \ . \ 2 \ . \ 7}}{ 2 \ . \ 2}=\frac{ − \ 15 \ − \ 13}{4}=\frac{ − \ 28}{4}= – \ 7$$ 5- Choice A is correct The correct answer is $$2$$$$|1 \ – \ (12 \ ÷ \ | 1 \ - \ 5 |) | =|1 \ – \ (12 \ ÷ \ | - \ 4 |) | =|1 \ – \ (12 \ ÷ \ 4) | = |1 \ – \ 3 | = | – \ 2 | = 2$$ 6- Choice A is correct The correct answer is $$350$$The ratio of boy to girls is $$7:4$$.Therefore, there are $$7$$ boys out of $$4$$ students.To find the answer, first divide the total number of students by $$11$$, then multiply the result by $$7$$.$$550 \ ÷ \ 11 = 50 ⇒ 50 \ × \ 7 = 350$$ 7- Choice B is correct Translated $$5$$ units down and $$4$$ units to the left means: $$(x.y) ⇒ (x \ − \ 4, y \ − \ 5)$$ 8- Choice A is correct The correct answer is $$7.685 \ × \ 10^{–7}$$$$0.0000007685 = \frac{7.685}{10000000 }⇒7.685 \ × \ 10^{–7}$$ 9- Choice D is correct The correct answer is $$x^2 \ - \ 6 \ x \ - \ 27$$Use FOIL (First, Out, In, Last) method.$$(x \ - \ 9) \ (x \ + \ 3) = x^2 \ + \ 3 \ x \ - \ 9 \ x \ - \ 27 =x^2 \ - \ 6 \ x \ - \ 27$$ 10- Choice B is correct The correct answer is $$\frac{7}{48}$$$$\frac{2}{25} = 0.08$$ and $$25\% = 0.25$$ therefore $$x$$ should be between $$0.08$$ and $$0.25$$Choice B, $$\frac{7}{48} = 0.145$$ is between $$0.08$$ and $$0.25$$ 11- Choice C is correct The correct answr is $$s \ \sqrt{15}$$Use Pythagorean theorem: $$a^2 \ + \ b^2 = c^2→$$$$s^2 \ + \ ℎ^2=(4 \ s)^2→$$$$s^2 \ + \ ℎ^2=16 \ s^2$$Subtracting $$s^2$$ from both sides gives: $$ℎ^2=15 \ s^2$$Square roots of both sides:$$ℎ=\sqrt{15 \ s^2}=\sqrt{s^2} \times \sqrt{15} =s \ \sqrt{15}$$ 12- Choice A is correct The area of the trapezoid is $$40 \ + \ 4 \ \sqrt{ 10 }$$Area $$=\frac{1}{2} \ ℎ \ (𝑏1 \ + \ 𝑏2)=\frac{1}{2} \ (x) \ (16 \ + \ 12)=168 →$$$$14 \ x=168→x=12$$$$y=\sqrt{4^2 \ + \ 12^2}=\sqrt{16 \ + \ 144}=\sqrt{160}=\sqrt{16 \times 10 } =4 \ \sqrt{ 10 }$$The perimeter of the trapezoid is:$$12 \ + \ 16 \ + \ 12 \ + \ 4 \ \sqrt{ 10 } =40 \ + \ 4 \ \sqrt{ 10 }$$ 13- Choice C is correct The correct answer is $$9,860$$ sq. ft.Area $$=$$ w $$×$$ hArea $$= 145 \ × \ 68 = 9,860$$ sq. ft. 14- Choice A is correct The correct answer is $$6$$Emily $$=$$ DanielEmily $$= 3$$ ClaireDaniel $$= 12 \ +$$ ClaireEmily $$=$$ Daniel $$→$$ Emily $$= 12 \ +$$ ClaireEmily $$= 3$$ Claire $$→ 3$$ Claire $$= 12 \ +$$ Claire $$→$$$$3$$ Claire $$–$$ Claire $$= 12$$$$2$$ Claire $$= 12$$Claire $$= 6$$ 15- Choice D is correct The correct answer is $$465$$$$93 \ ÷ \ \frac{1}{5} = \frac{\frac{93}{1}}{\frac{1}{5}} = 93 \ × \ 5=465$$ 16- Choice D is correct The correct answer is $$- \ 3$$$$3 \ – \ 12 \ ÷ \ (5^2 \ ÷ \ 5) =$$$$3 \ – \ 12 \ ÷ \ (25 \ ÷ \ 5) =$$$$3 \ – \ 12 \ ÷ \ (3) = - \ 9 \ ÷ \ 3= - \ 3$$ 17- Choice B is correct The correct answer is $$2 \ \frac{1}{10}$$ Miles$$\frac{1}{2}$$ of the distance is $$4 \ \frac{1}{5}$$ miles.Then: $$\frac{1}{2} \ × \ 4 \ \frac{1}{5}=\frac{1}{2} \ × \ \frac{21}{5}=\frac{21}{10}$$Converting $$\frac{21}{10}$$ to a mixed number gives: $$\frac{21}{10}=2 \ \frac{1}{10}$$ 18- Choice A is correct The correct answer is $$0.25$$$$\frac{5}{32}=0.25$$ 19- Choice D is correct The correct answer is $$\frac{7}{15}$$Let $$x$$ be the number of purple marbles.Let’s review the choices provided:A. $$\frac{1}{10}$$if the probability of choosing a purple marble is one out of ten, then:Probability $$=\frac{number \ of \ desired \ outcomes}{number \ of \ total \ outcomes}=\frac{x}{30 \ + \ 20 \ + \ 40 \ + \ x}=\frac{1}{10}$$Use cross multiplication and solve for $$x$$.$$10 \ x=90 \ + \ x→9 \ x=90→x=9$$Since, number of purple marbles can be $$9$$, then, choice be the probability of randomly selecting a purple marble from the bag.Use same method for other choices.B. $$\frac{1}{4}$$$$\frac{x}{20 \ + \ 30 \ + \ 40 \ + \ x}=\frac{1}{4}→4 \ x=90 \ + \ x→3 \ x=90→x=30$$C. $$\frac{2}{5}$$$$\frac{x}{20 \ + \ 30 \ + \ 40 \ + \ x}=\frac{2}{5}→5 \ x=180 \ + \ 2 \ x→3 \ x=180→x=60$$D. $$\frac{7}{15}$$$$\frac{x}{20 \ + \ 30 \ + \ 40 \ + \ x}=\frac{7}{15}→15 \ x=630 \ + \ 7 \ x→8 \ x=630→x=78.75$$Number of purple marbles cannot be a decimal. 20- Choice C is correct The correct answer is $$0$$$$(3.2 \ + \ 3.6 \ + \ 3.8) \ x = x$$$$10.6 \ x = x$$Then $$x = 0$$ 21- Choice B is correct The correct answer is $$\frac{1}{4}$$For sum of $$6: \ (1$$ & $$5)$$ and $$(5$$ & $$1), \ (2$$ & $$4)$$ and $$(4$$ & $$2), \ (3$$ & $$3)$$, therefore we have $$5$$ options.For sum of $$9: \ (3$$ & $$6)$$ and $$(6$$ & $$3), \ (4$$ & $$5)$$ and $$(5$$ & $$4)$$, we have $$4$$ options.To get a sum of $$6$$ or $$9$$ for two dice: $$5 \ + \ 4 = 9$$Since, we have $$6 \ × \ 6 = 36$$ total number of options, the probability of getting a sum of $$6$$ and $$9$$ is $$9$$ out of $$36$$ or $$\frac{9}{36}=\frac{1}{4}$$. 22- Choice D is correct The correct answer is $$29$$ Milesaverage $$=\frac{𝑠𝑢𝑚}{total}=\frac{25 \ + \ 40 \ + \ 22}{3}=\frac{87}{3}=29$$ Miles 23- Choice C is correct The correct answer is $$10 \ 𝜋$$The distance of A to B on the coordinate plane is: $$\sqrt{(x_{1} \ − \ x_{2})^2 \ + \ (y_{1} \ − \ y_{2} )^2}= \sqrt{(12 \ − \ 4)^2 \ + \ (8 \ − \ 2)^2}=\sqrt{8^2 \ + \ 6^2}=\sqrt{64 \ + \ 36}=\sqrt{100} = 10$$The diameter of the circle is $$10$$ and the radius of the circle is $$5$$. Then: the circumference of the circle is:$$2 \ \pi \ 𝑟=2 \ \pi (5)=10 \ 𝜋$$ 24- Choice C is correct The correct answer is $$966.4$$$$48.32 \ ÷ \ 0.05 =966.4$$ 25- Choice D is correct The correct answer is $$± \ 2$$$$4 \ x^2 \ + \ 8 = 24$$$$4 \ x^2 = 16$$$$x^2 = 4$$$$x =± \ 2$$ 26- Choice A is correct The correct answer is $$113.28$$$$25\%$$ of $$x = 28.32$$$$\frac{25}{100 } \ x =28.32$$$$x = \frac{100 \ × \ 28.32}{25} = 113.28$$ 27- Choice A is correct The correct answer is $$5$$$$\frac{x \ + \ 10 \ + \ 12 \ + \ 15 \ + \ 8}{5} = 10 →$$$$x \ + \ 45 = 50 →$$$$x = 50 \ – \ 45 = 5$$ 28- Choice A is correct The correct answer is $$254.34$$ in$$^2$$Diameter $$= 18$$then: Radius $$= 9$$Area of a circle $$= π \ r^2 ⇒$$A $$= 3.14 \ (9)^2 = 254.34$$ in$$^2$$ 29- Choice C is correct The correct answer is $$55$$$$\frac{240}{6 } \ < \ x \ < \ \frac{390}{6}$$$$40 \ < \ x \ < \ 65$$Then:Only choice C is correct 30- Choice A is correct The correct answer is $$\frac{ - \ 6 \ x \ - \ 20}{6 \ x^2 \ - \ 9}$$Simplify:$$\frac{\frac{1}{3} \ - \ \frac{x \ + \ 4}{2}}{\frac{x^2}{2} \ - \ \frac{3}{4}} = \frac{\frac{1}{3} \ - \ \frac{x \ + \ 4}{2}}{\frac{2 \ x^2 \ - \ 3}{4}} = \frac{4 \ (\frac{1}{3} \ - \ \frac{x \ + \ 4}{2})}{2 \ x^2 \ - \ 3}⇒$$Simplify: $$\frac{1}{3} \ - \ \frac{x \ + \ 4}{2}= \frac{2 \ - \ 3 \ (x \ + \ 4)}{6}= \frac{2 \ - \ 3 \ x \ - \ 12}{6}= \frac{ - \ 3 \ x \ - \ 10}{6}$$Then:$$\frac{4 \ (\frac{- \ 3 \ x \ - \ 10}{6})}{2 \ x^2 \ - \ 3} =\frac{2 \ (\frac{- \ 3 \ x \ - \ 10}{3})}{2 \ x^2 \ - \ 3} =\frac{ \frac{- \ 6 \ x \ - \ 20}{3}}{2 \ x^2 \ - \ 3} =\frac{- \ 6 \ x \ - \ 20}{3\ (2 \ x^2 \ - \ 3)}=\frac{ - \ 6 \ x \ - \ 20}{6 \ x^2 \ - \ 9}$$ 31- Choice B is correct The correct answer is $$8$$ square feetFormula of triangle area $$= \frac{1}{2}$$ (base $$×$$ height)Since the angles are $$45-45-90$$, then this is an isosceles triangle, meaning that the base and height of the triangle are equal.Triangle area $$= \frac{1}{2}$$ (base $$×$$ height) $$= \frac{1}{2} \ (4 × 4) = 8$$ 32- Choice B is correct The correct answer is $$40$$$$\frac{5}{25}= \frac{x}{200} → x = \frac{5 \ × \ 200}{25} = 40$$ 33- Choice C is correct The correct answer is $$2 \ (4 \ H \ - \ 2) = 25$$ 34- Choice D is correct The correct answer is $$952,691$$The difference of the file added, and the file deleted is:$$552,129 \ – \ 439,566 = 112,563$$$$840,128 \ + \ 112,563 = 952,691$$ 35- Choice B is correct The correct answer is $$3,840$$$$x^{\frac{1}{2}}$$ equals to the root of $$x$$. Then: $$5 \ + \ x^{\frac{1}{2}}=20→4 \ + \ \sqrt{x}=20→\sqrt{x}=16→x=256$$$$x=256$$ and $$15 \ × \ x$$ equals: $$15 \ × \ 256=3,840$$ 36- Choice A is correct The correct answer is $$1,728$$ cm$$^3$$If the length of the box is $$36$$, then the width of the box is one third of it, $$12$$, and the height of the box is $$4$$ (one third of the width).The volume of the box is:$$𝑉 = 𝑙𝑤ℎ = (36) \ (12) \ (4) = 1,728$$ 37- Choice B is correct The correct answer is $$(7, − \ 9)$$When a point is reflected over $$x$$ axes, the $$(y)$$ coordinate of that point changes to $$(− \ y)$$ while its $$x$$ coordinate remains the same.C $$(7, 9)$$ → C’ $$(7, − \ 9)$$ 38- Choice A is correct The correct answer is $$3$$ days $$7$$ hours $$7$$ minutes$$7$$ days $$21$$ hours $$21$$ minutes $$– \ 4$$ days $$14$$ hours $$14$$ minutes $$= 3$$ days $$7$$ hours $$7$$ minutes 39- Choice D is correct The correct answer is $$3$$ sq decreasedThe area of the square is $$36$$ square inches. Area of square $$=$$ side $$×$$ side $$=6 \ × \ 6=36$$The length of the square is increased by $$5$$ inches and its width decreased by $$3$$ inches. Then, its area equals:Area of rectangle $$=$$ width $$×$$ length $$=11 \ × \ 3=33$$The area of the square will be decreased by $$3$$ square inches.$$36 \ − \ 33=3$$ 40- Choice A is correct The correct answer is $$100$$ cm$$^2$$The area of the circle is $$25 \ π$$ cm$$^2$$, then, its diameter is $$10$$ cm.Area of circle $$=\pi \ r^2=12 \ π→𝑟^2=25→r=5$$Radius of the circle is $$5$$ and diameter is twice of it, $$10$$.One side of the square equals to the diameter of the circle. Then:Area of square $$=$$ side $$×$$ side $$=10 \ × \ 10=100$$ 41- Choice C is correct The correct answer is $$- \ 2 \ x^2 \ y^3 \ + \ 5 \ x^3 \ y^5$$$$6 \ x^2 \ y^3 \ + \ 2 \ x^3 \ y^5 \ – \ (8 \ x^2 \ y^3 \ – \ 3 \ x^3 \ y^5) =$$$$6 \ x^2 \ y^3 \ + \ 2 \ x^3 \ y^5 \ – \ 8 \ x^2 \ y^3 \ + \ 3 \ x^3 \ y^5 =$$$$- \ 2 \ x^2 \ y^3 \ + \ 5 \ x^3 \ y^5$$ 42- Choice C is correct The correct answer is $$131.95$$$$45\%$$ of $$91 = 40.95$$$$91 \ + \ 40.95= 131.95$$ 43- Choice A is correct The correct answer is $$70$$Number of squares equal to: $$\frac{35 \ ×\ 18}{3 \ × \ 3}=35 \ × \ 2=70$$ 44- Choice B is correct The correct answer is $$4 \ 𝜋$$Let P be circumference of circle A, then; $$2 \ \pi \ r_{A} = 12 \ 𝜋→r_{𝐴}=6$$$$r_{𝐴}=3 \ r_{B}→r_{B}=\frac{6}{3}=2→$$Area of circle B is; $$𝜋 \ r_{B}^2=4 \ 𝜋$$ 45- Choice D is correct The correct answer is $$\left\{(6, 1), (3, 1), (0, 5), (4, 5)\right\}$$A set of ordered pairs represents $$y$$ as a function of $$x$$ if: $$x_{1}=x_{2}→y_{1}=y_{2}$$In choice A: $$(3, - \ 2)$$ and $$(3, 7)$$ are ordered pairs with same $$x$$ and different $$y$$, therefore $$y$$ isn’t a function of $$x$$.In choice B: $$(4, 2)$$ and $$(4, 7)$$ are ordered pairs with same $$x$$ and different $$y$$, therefore $$y$$ isn’t a function of $$x$$.In choice C: $$(5, 7)$$ and $$(5, 18)$$ are ordered pairs with same $$x$$ and different $$y$$, therefore $$y$$ isn’t a function of $$x$$. 46- Choice A is correct The correct answer is $$500$$David’s weekly salary is $$350$$ plus $$10\%$$ of $$1500$$.Then: $$10\%$$ of $$1,500=0.1 \ × \ 1,500=150$$$$350 \ + \ 150=500$$ 47- Choice B is correct The correct answer is $$40$$Write a proportion and solve. $$\frac{4}{5}=\frac{x}{50}$$Use cross multiplication: $$5 \ x=200→x=40$$

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