 ## 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 4

• 47 questions
• Total time for this section: 40 Minutes
• Calculators are not allowed at the test.
1- Ella (E) is $$6$$ years older than her friend Ava (A) who is $$4$$ years younger than her sister Sofia (S). If E, A and S denote their ages, which one of the following represents the given information?
(A) $$\begin{cases}E = 6 \ - \ A\\A = S \ + \ 4\end{cases}$$
(B) $$\begin{cases}E = 4 \ - \ A\\A = S \ - \ 2\end{cases}$$
(C) $$\begin{cases}A = 4 \ - \ E\\S = A \ - \ 2\end{cases}$$
(D) $$\begin{cases}E = 6 \ + \ A\\A = S \ – \ 4\end{cases}$$
2- An angle is equal to one fourth of its supplement. What is the measure of that angle?
(A) $$36^\circ$$
(B) $$30^\circ$$
(C) $$25^\circ$$
(D) $$39^\circ$$
3- $$3$$ less than twice a positive integer is $$91$$. What is the integer?
(A) $$44$$
(B) $$45$$
(C) $$47$$
(D) $$49$$
4- The cost, in thousands of dollars, of producing $$x$$ thousands of textbooks is:
$$C(x)=x^2 \ - \ 4 \ x$$.
The revenue, also in thousands of dollars, is $$R(x)=30 \ x$$.
find the profit or loss if $$30$$ textbooks are produced. (profit $$=$$ revenue $$–$$ cost)
(A) $$120$$ profit
(B) $$240$$ profit
(C) $$130$$ loss
(D) $$180$$ loss
5- $$\frac{1}{4 \ b^2} \ + \ \frac{1}{4 \ b} = \frac{1}{b^2}$$, then $$b =$$?
(A) $$3$$
(B) $$\frac{2}{7}$$
(C) $$- \ \frac{15}{17}$$
(D) $$- \ 3$$
6- Simplify $$4 \ x^2 \ y^3 \ (3 \ x^2 \ y)^3=$$
(A) $$100 \ x^6 \ y^6$$
(B) $$108 \ x^8 \ y^6$$
(C) $$54 \ x^5 \ y^3$$
(D) $$68 \ x^8 \ y^2$$
7- $$\frac{|6 \ + \ x|}{2} \ ≤ \ 8$$, then $$x =$$?
(A) $$– \ 28 \ ≤ \ x \ ≤ \ 12$$
(B) $$– \ 22 \ ≤ \ x \ ≤ \ 10$$
(C) $$– \ 24 \ ≤ \ x \ ≤ \ 15$$
(D) $$– \ 18\ ≤ \ x \ ≤ \ 18$$
8- Which of the following points lies on the line $$2 \ x \ + \ 5 \ y=12$$?
(A) $$(2, 1)$$
(B) $$(– \ 1, 3)$$
(C) $$(– \ 2, 2)$$
(D) $$(2, 2)$$
9- $$1.3$$ is what percent of $$13$$?
(A) $$4$$
(B) $$10$$
(C) $$5$$
(D) $$12$$
10- Write $$674$$ in expanded form, using exponents.
(A) $$(6 \ × \ 10^3) \ + \ (7 \ × \ 10^2) \ + \ (4 \ × \ 10)$$
(B) $$(6 \ × \ 10^2) \ + \ (7 \ × \ 10^1) \ – \ 4$$
(C) $$(6 \ × \ 10^2) \ + \ (7 \ × \ 10^1) \ + \ 4$$
(D)  $$(6 \ × \ 10^1) \ + \ (7 \ × \ 10^1) \ + \ 4$$
11- What is the area of an isosceles right triangle that has one leg that measures $$4$$ cm?
(A) $$4$$ cm$$^2$$
(B) $$8$$ cm$$^2$$
(C) $$12$$ cm$$^2$$
(D) $$16$$ cm$$^2$$
12- Right triangle ABC has two legs of lengths $$5$$ cm (AB) and $$12$$ cm (AC). What is the length of the third side (BC)?
(A) $$12$$ cm
(B) $$11$$ cm
(C) $$13$$ cm
(D) $$15$$ cm
13- A circle has a diameter of $$12$$ inches. What is its approximate circumference?
(A) $$44.24$$
(B) $$64.91$$
(C) $$34.28$$
(D) $$37.68$$
14- A company pays its writer $$5$$ for every $$200$$ words written. How much will a writer earn for an article with $$1,100$$ words?
(A) $$22.5$$
(B) $$21.7$$
(C) $$27.5$$
(D) $$30.6$$
15- Which is the longest time?
(A) $$23$$ hours
(B) $$1610$$ minutes
(C) $$1$$ days
(D) $$3,900$$
16- The equation of a line is given as : $$y = 6 \ , x \ – \ 2$$. Which of the following points lie on the line?
17- $$85.23 \ ÷ \ 0.03 =$$?
(A) $$1,931$$
(B) $$2,969$$
(C) $$2,841$$
(D) $$2,691$$
18- The drivers at G & G trucking must report the mileage on their trucks each week. The mileage reading of Ed’s vehicle was $$42,687$$ at the beginning of one week, and $$47,353$$ at the end of the same week. What was the total number of miles driven by Ed that week?
(A) $$489$$ Miles
(B) $$723$$ Miles
(C) $$692$$ Miles
(D) $$666$$ Miles
19- A circular logo is enlarged to fit the lid of a jar. The new diameter is $$25\%$$ larger than the original. By what percentage has the area of the logo increased?
(A) $$69\%$$
(B) $$54\%$$
(C) $$76\%$$
(D) $$39\%$$
20- What is the area of an isosceles right triangle that has one leg that measures $$8$$ cm?
(A) $$32$$ cm$$^2$$
(B) $$64$$ cm$$^2$$
(C) $$53$$ cm$$^2$$
(D) $$24$$ cm$$^2$$
21- If $$x \ + \ y = 24$$, what is the value of $$4 \ x \ + \ 4 \ y$$?
(A) $$76$$
(B) $$80$$
(C) $$100$$
(D) $$96$$
22- What’s the area of the non-shaded part of the following figure? (A) $$104$$
(B) $$78$$
(C) $$120$$
(D) $$112$$
23- What’s the reciprocal of $$\frac{x^3}{16}$$?
(A) $$\frac{16}{x^3}$$
(B) $$\frac{16}{x^3} \ - \ 1$$
(C) $$\frac{x^3}{16} \ - \ 1$$
(D) $$\frac{x^3}{16} \ + \ 1$$
24- Given that $$x = 0.5$$ and $$y = 3$$, what is the value of $$2 \ x^2 \ (y \ + \ 8)$$?
(A) $$5.5$$
(B) $$7.2$$
(C) $$11.4$$
(D) $$8.9$$
25- Mario loaned Jett $$2,500$$ at a yearly interest rate of $$4\%$$. After two year what is the interest owned on this loan?
(A) $$245$$
(B) $$195$$
(C) $$185$$
(D) $$200$$
26- Which equation represents the statement Two plus the sum of the squares of $$w$$ and $$x$$ is $$25$$.
(A) $$2 \ (w^2 \ - \ x) = 25$$
(B) $$2 \ (w^2 \ + \ x) = 25$$
(C) $$25 \ (w^2 \ + \ x) = 2$$
(D) $$2 \ (w \ + \ x) = 25$$

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27- $$29$$ hr. $$21$$ min
$$23$$ hr. $$44$$ min
_________________

(A) $$5$$ hr. $$37$$ min
(B) $$6$$ hr. $$37$$ min
(C) $$6$$ hr. $$13$$ min
(D) $$5$$ hr. $$13$$ min
28- A bread recipe calls for $$4 \ \frac{1}{2}$$ cups of flour. If you only have $$5 \frac{4}{3}$$ cups, how much more flour is needed?
(A) $$\frac{ 5}{4}$$
(B) $$- \ \frac{ 5}{4}$$
(C) $$- \ \frac{ 1}{2}$$
(D) $$1$$
29- Which of the following is a factor of both $$x^2 \ - \ 2 \ x \ - \ 8$$ and $$x^2 \ - \ 6 \ x \ + \ 8$$?
(A) $$(x \ – \ 2)$$
(B) $$(x \ + \ 2)$$
(C) $$(x \ + \ 4)$$
(D) $$(x \ - \ 4)$$
30- What is the solution of the following system of equations?
$$\begin{cases}- \ 2 \ x \ - \ 3 \ y =\ - \ 12\\4 \ x\ + \ y= 25\end{cases}$$
(A) $$(4, 2)$$
(B) $$(7, 2)$$
(C) $$(6, 1)$$
(D) $$(5, 3)$$
31- Ellis just got hired for on-the-road sales and will travel about $$1,200$$ miles a week during an $$60-$$hour work week. If the time spent traveling is $$\frac{2}{3}$$ of his week, how many hours a week will he be on the road?
(A) Ellis spends about $$48$$ hours of his $$60-$$hour work week on the road.
(B) Ellis spends about $$40$$ hours of his $$60-$$hour work week on the road.
(C) Ellis spends about $$44$$ hours of his $$60-$$hour work week on the road.
(D) Ellis spends about $$42$$ hours of his $$60-$$hour work week on the road.
32- $$\frac{12}{27}$$ is equal to:
(A) $$0.444$$...
(B) $$0.25$$
(C) $$0.40$$
(D) $$0.38$$
33- Find the perimeter of a rectangle with the dimensions $$49 \ × \ 28$$.
(A) $$132$$
(B) $$281$$
(C) $$154$$
(D) $$164$$
34- In a school, the ratio of number of boys to girls is $$5:9$$. If the number of boys is $$235$$, what is the total number of students in the school?
(A) $$780$$
(B) $$658$$
(C) $$568$$
(D) $$865$$
35- A car uses $$12$$ gallons of gas to travel $$240$$ miles. How many miles per gallon does the car get?
(A) $$20$$
(B) $$12$$
(C) $$30$$
(D) $$25$$
36- How many square feet of tile is needed for a $$12$$ foot $$x \ 12$$ foot room?
(A) $$256$$ square feet
(B) $$144$$ square feet
(C) $$169$$ square feet
(D) $$218$$ square feet
37- If $$x$$ is $$38\%$$ percent of $$740$$, what is $$x$$?
(A) $$270.5$$
(B) $$240.1$$
(C) $$281.2$$
(D) $$269.7$$
38- Karen is $$6$$ years older than her sister Michelle, and Michelle is $$4$$ years younger than her brother David. If the sum of their ages is $$67$$, how old is Michelle?
(A) $$21$$
(B) $$19$$
(C) $$25$$
(D) $$17$$
39- A tree $$24$$ feet tall casts a shadow $$8$$ feet long. Jack is $$6$$ feet tall. How long is Jack’s shadow?
(A) $$3$$ ft.
(B) $$5$$ ft.
(C) $$2$$ ft.
(D) $$\frac{1}{2}$$ ft.
40- Calculate the area of a parallelogram with a base of $$3$$ feet and height of $$4.2$$ feet.
(A) $$10.2$$ square feet
(B) $$15.5$$ square feet
(C) $$18.6$$ square feet
(D) $$12.6$$ square feet
41- What is the result of the expression?
$$\begin{bmatrix}2 & 6 \\- \ 1 & - \ 2\\- \ 5 & - \ 4 \end{bmatrix} \ + \ \begin{bmatrix}0 & - \ 6 \\1 & 0\\2 & 7 \end{bmatrix}=$$
(A) $$\ \begin{bmatrix}2 & 0\\0 & - \ 2\\- \ 3 & 3 \end{bmatrix}$$
(B) $$\ \begin{bmatrix}0 & 2\\0 & - \ 2\\3 & - \ 3 \end{bmatrix}$$
(C) $$\ \begin{bmatrix}1 & 3\\0 & - \ 3\\2 & - \ 2 \end{bmatrix}$$
(D) $$\ \begin{bmatrix}- \ 1 & 0\\2 & - \ 3\\2 & 0 \end{bmatrix}$$
42- If $$x∎y=\sqrt{x^2 \ + \ y}$$, what is the value of $$7∎15$$?
(A) $$\sqrt{63}$$
(B) $$8$$
(C) $$6$$
(D) $$9$$
43- A shirt costing $$150$$ is discounted $$15\%$$. After a month, the shirt is discounted another $$15\%$$. Which of the following expressions can be used to find the selling price of the shirt?
(A) $$(150) \ (0.85)$$
(B) $$(150) \ (0.85) \ - \ (0.70)$$
(C) $$(150) \ (0.85) \ - \ (150) \ (0.70)$$
(D) $$(150) \ (0.85) \ (0.70)$$
44- The average weight of $$21$$ girls in a class is $$65$$ kg and the average weight of $$30$$ boys in the same class is $$72$$ kg. What is the average weight of all the $$51$$ students in that class?
(A) $$69.11$$ kg
(B) $$73$$ kg
(C) $$65.32$$ kg
(D) $$70$$ kg
45- There are three equal tanks of water. If $$\frac{3}{4}$$ of a tank contains $$320$$ liters of water, what is the capacity of the two tanks of water together?
(A) $$450$$ Liters
(B) $$240$$ Liters
(C) $$720$$ Liters
(D) $$480$$ Liters
46- $$(2 \ x \ + \ 6) \ (- \ x \ + \ 2) =$$
(A) $$2 \ x^2 \ + \ 2 \ x \ - \ 12$$
(B) $$x^2 \ + \ 4 \ x \ - \ 4$$
(C) $$- \ 2 \ x^2 \ - \ 2 \ x \ + \ 12$$
(D) $$- \ 2 \ x^2 \ + \ 2 \ x \ - \ 6$$
47- What is the area of the shaded region if the diameter of the bigger circle is $$18$$ inches and the diameter of the smaller circle is $$8$$ inches? (A) $$49 \ π$$
(B) $$81 \ π$$
(C) $$72 \ π$$
(D) $$65 \ π$$
 1- Choice D is correct The correct answer is:$$E = 6 \ + \ A$$$$A = S \ – \ 4$$ 2- Choice A is correct The correct answer is $$36^\circ$$The sum of supplement angles is $$180$$.Let $$x$$ be that angle.Therefore, $$x \ + \ 4 \ x = 180$$$$5 \ x = 180$$, divide both sides by $$5: \ x = 36$$ 3- Choice C is correct The correct answer is $$47$$Let $$x$$ be the integer. Then:$$2 \ x \ – \ 3 = 91$$Add 5 both sides: $$2x = 94$$Divide both sides by $$2: \ x = 47$$ 4- Choice A is correct The correct answer is $$120$$ profitPlug in the value of $$x=30$$ into both equations. Then:$$𝐶(x)=x^2 \ - \ 4 \ x=(30)^2 \ - 4 \ (30)=900 \ - \ 120=780$$$$𝑅(x)=30 \ x=30 \ × \ 30=900$$$$900 \ − \ 780=120$$ 5- Choice A is correct The correct answer is $$3$$Subtract $$\frac{1}{4 \ b}$$ and $$\frac{1}{𝑏^2}$$ from both sides of the equation. Then:$$\frac{1}{4 \ b^2} \ + \ \frac{1}{4 \ b} = \frac{1}{b^2}→\frac{1}{4 \ b^2} \ − \ \frac{1}{b^2}=− \ \frac{1}{4 \ 𝑏}$$Multiply both numerator and denominator of the fraction $$\frac{1}{b^2}$$ by $$4$$. Then:$$\frac{1}{4 \ b^2} \ − \ \frac{4}{4 \ b^2}=− \ \frac{1}{4 \ b}$$Simplify the first side of the equation: $$− \ \frac{3}{4 \ b^2 }=− \ \frac{1}{4 \ b}$$Use cross multiplication method: $$12 \ 𝑏=4 \ 𝑏^2→12=4 \ 𝑏→𝑏=3$$ 6- Choice B is correct The correct answer is $$108 \ x^8 \ y^6$$Simplify.$$4 \ x^2 \ y^3 \ (3 \ x^2 \ y)^3=4 \ x^2 \ y^3 \ (27 \ x^6 \ y^3) = 108 \ x^8 \ y^6$$ 7- Choice B is correct The correct answer is $$– \ 22 \ ≤ \ x \ ≤ \ 10$$First, multiply both sides of inequality by $$2$$.Then: $$\frac{|6 \ + \ x|}{2} \ ≤ \ 8→|6 \ +\ x| \ ≤ \ 16$$Since $$6 \ + \ x$$ can be positive or negative, then: $$6 \ + \ x \ ≤ \ 16$$ or $$6 \ + \ x \ ≥ \ − \ 16$$Then: $$x \ ≤ \ 10$$ or $$x \ ≥ \ − \ 22$$ 8- Choice D is correct The correct answer is $$(2, 2)$$Plug in each pair of numbers in the equation.The answer should be $$12$$.A. $$(2, 1): \ \ \ 2 \ (2) \ + \ 5 \ (1) = 9$$ No!B. $$(– \ 1, 3): \ \ \ 2 \ (–1) \ + \ 5 \ (2) = 8$$ No!C. $$(– \ 2, 2): \ \ \ 2 \ (– \ 2) \ + \ 5 \ (2) = 6$$ No!D. $$(2, 2): \ \ \ 2 \ (2) \ + \ 5 \ (2) = 12$$ Yes! 9- Choice B is correct The correct answer is $$10$$$$x\% \ 13 = 1.3$$$$\frac{x}{100} \ 13 = 1.3 →$$$$x = \frac{1.3 \ × \ 100}{13} = 10$$ 10- Choice C is correct The correct answer is $$(6 \ × \ 10^2) \ + \ (7 \ × \ 10^1) \ + \ 4$$Let’s review the choices provided:A. $$(6 \ × \ 10^3) \ + \ (7 \ × \ 10^2) \ + \ (4 \ × \ 10) = 6,000 \ + \ 700 \ + \ 40 = 6,740$$B. $$(6 \ × \ 10^2) \ + \ (7 \ × \ 10^1) \ – \ 4 = 600 \ + \ 70 \ – \ 4= 666$$C. $$(6 \ × \ 10^2) \ + \ (7 \ × \ 10^1) \ + \ 4 = 600 \ + \ 70 \ + \ 4 = 674$$D. $$(6 \ × \ 10^1) \ + \ (7 \ × \ 10^1) \ + \ 4 = 60 \ + \ 70 \ + \ 4 = 134$$Only choice C equals to $$674$$. 11- Choice A is correct The correct answer is $$4$$ cm$$^2$$First draw an isosceles triangle.Remember that two sides of the triangle are equal.Let put $$a$$ for the legs. Then:$$𝑎=4⇒$$ area of the triangle is $$=\frac{1}{2} \ (4 \ × \ 4)=\frac{16}{2}=4$$ cm$$^2$$ 12- Choice C is correct The correct answer is $$13$$ cmUse Pythagorean Theorem: $$a^2 \ + \ b^2 = c^2$$$$5^2 \ + \ 12^2 = c^2 ⇒$$$$25 \ + \ 144 = c^2 ⇒$$$$c^2 = 169 ⇒ c=13$$ 13- Choice D is correct The correct answer is $$37.68$$$$C = 2 \ π \ r$$$$C = 2 \ π \ × \ 6 = 12 \ π$$$$π = 3.14 → C = 12 \ π = 37.68$$ 14- Choice C is correct The correct answer is $$27.5$$$$\frac{5}{200} = \frac{x}{1,100}$$$$x = \frac{5 \ × \ 1,100}{200} =27.5$$ 15- Choice B is correct The correct answer is $$1610$$ minutes$$23$$ hours $$= 82,800$$ seconds$$1610$$ minutes $$= 96,600$$ seconds$$1$$ days $$= 24$$ hours $$= 86,400$$ seconds$$3,900$$ seconds 15- Choice B is correct The correct answer is $$1610$$ minutes$$23$$ hours $$= 82,800$$ seconds$$1610$$ minutes $$= 96,600$$ seconds$$1$$ days $$= 24$$ hours $$= 86,400$$ seconds$$3,900$$ seconds 17- Choice C is correct The correct answer is $$2,841$$$$85.23 \ ÷ \ 0.03 =2,841$$ 18- Choice D is correct The correct answer is $$666$$ MilesTo find total number of miles driven by Ed that week, you only need to subtract $$46,687$$ from $$47,353$$.$$47,353 \ − \ 46,687=666$$ 19- Choice A is correct The correct answer is $$69\%$$Area of a circle equals: $$𝐴=\pi \ r^2$$The new diameter is $$30\%$$ larger than the original then the new radius is also $$30\%$$ larger than the original.$$30\%$$ larger than $$𝑟$$ is $$1.3 \ r$$.Then, the area of larger circle is: $$𝐴=\pi \ r^2=\pi \ (1.3 \ 𝑟)^2=\pi \ (1.69 \ 𝑟^2)=1.69 \ 𝜋 \ r^2$$$$1.69 \ \pi \ r^2$$ is $$69\%$$ bigger than $$\pi \ r^2$$. 20- Choice A is correct The correct answer is $$32$$ cm$$^2$$First draw an isosceles triangle.Remember that two sides of the triangle are equal.Let put $$𝑎$$ for the legs. Then:$$𝑎=5⇒$$ area of the triangle is $$=\frac{1}{2} \ (8 \ × \ 8)=\frac{64}{2}=32$$ cm$$^2$$ 21- Choice D is correct The correct answer is $$96$$$$x \ + \ y = 24$$Then: $$4 \ x \ + \ 4 \ y = 24 \ × \ 4 = 96$$ 22- Choice A is correct The correct answer is $$104$$The area of the non-shaded region is equal to the area of the bigger rectangle subtracted by the area of smaller rectangle.Area of the bigger rectangle $$= 12 \ × \ 10 = 120$$Area of the smaller rectangle $$= 8 \ × \ 2 = 16$$Area of the non-shaded region $$= 120 \ – \ 16 = 104$$ 23- Choice A is correct The correct answer is $$\frac{16}{x^3}$$$$\frac{x^3}{16} ⇒$$ reciprocal is : $$\frac{16}{x^3}$$ 24- Choice A is correct The correct answer is $$5.5$$$$2 \ x^2 \ (y \ + \ 8) = 2 \ (0.5)^2 \ (3 \ + \ 8) = 2 \ (0.25) \ (11) = 5.5$$ 25- Choice D is correct The correct answer is $$200$$Use interest rate formula:Interet $$=$$ principal $$×$$ rate $$×$$ time $$=2,500 \ × \ 0.04 \ × \ 2=200$$ 26- Choice B is correct The correct answer is $$2 \ (w^2 \ + \ x) = 25$$ 27- Choice A is correct The correct answer is $$5$$ hr. $$37$$ min$$29$$ hr. $$21$$ min$$23$$ hr. $$44$$ min_________________$$5$$ hr. $$37$$ min 28- Choice B is correct The correct answer is $$- \ \frac{ 5}{4}$$$$4 \ \frac{1}{2} - 5 \frac{3}{4}=$$$$4 \ \frac{2}{4} \ - \ 5 \frac{3}{4} =$$$$\frac{18}{4} \ - \ \frac{23}{4} =$$$$\frac{- \ 5}{4} =- \ \frac{ 5}{4}$$ 29- Choice D is correct The correct answer is $$(x \ – \ 4)$$Factor each trinomial $$x^2 \ – \ 2 \ x \ – 8$$ and $$x^2 \ – \ 6 \ x \ + \ 8$$$$x^2 \ – \ 2 \ x \ – 8 ⇒ (x \ – \ 4) \ (x \ + \ 2)$$$$x^2 \ – \ 6 \ x \ + \ 8 ⇒ (x \ – \ 2) \ (x \ – \ 4)$$ 30- Choice C is correct The correct answer is $$(6, 1)$$$$\begin{cases}- \ 2 \ x \ - \ 3 \ y =\ - \ 15\\4 \ x\ + \ y= 25\end{cases}⇒$$ Multiplication $$(3)$$ in first equation$$⇒\begin{cases}- \ 2 \ x \ - \ 3 \ y =\ - \ 15\\12 \ x\ + \ 3 y= 75\end{cases}$$ Add two equations together $$⇒ 10 \ x =60 ⇒ x=6$$ then; $$y=1$$ 31- Choice B is correct The correct answer is Ellis spends about $$40$$ hours of his $$60-$$hour work week on the road.Ellis travels $$\frac{2}{3}$$ of $$60$$ hours. $$\frac{2}{3} \ × \ 60=40$$Ellis will be on the road for $$40$$ hours. 32- Choice A is correct The correct answer is $$0.444$$... $$\frac{12}{27} =0.444$$... 33- Choice C is correct The correct answer is $$154$$Perimeter of a rectangle $$=2$$ (width $$+$$ length) $$=2 \ (49 \ + \ 28)=154$$ 34- Choice B is correct The correct answer is $$658$$The ratio of boys to girls is $$5:9$$.Therefore, there are $$5$$ boys out of $$14$$ students. To find the answer, first divide the number of boys by $$5$$, then multiply the result by $$14$$.$$235 \ ÷ \ 5 = 47 ⇒ 47 \ × \ 10 = 658$$ 35- Choice A is correct The correct answer is $$20$$$$\frac{240}{12} = 20$$ 36- Choice B is correct The correct answer is $$144$$ square feetThe area of a $$12$$ feet $$x \ 12$$ feet room is $$144$$ square feet.$$12 \ × \ 12 = 144$$ 37- Choice C is correct The correct answer is $$281.2$$$$\frac{38}{100} \ × \ 740 =x$$$$x=281.2$$ 38- Choice B is correct The correct answer is $$19$$Michelle $$=$$ Karen $$– \ 6$$Michelle $$=$$ David $$– \ 4$$Karen $$+$$ Michelle $$+$$ David $$= 67$$Karen $$+ \ 6 =$$ Michelle $$⇒$$ Karen $$=$$ Michelle $$– \ 6$$Karen $$+$$ Michelle $$+$$ David $$= 67$$Now, replace the ages of Karen and David by Michelle. Then:Michelle $$+ \ 6 \ +$$ Michelle $$+$$ Michelle $$+ \ 4 =67$$$$3$$ Michelle $$+ \ 10 = 67 ⇒ 3$$ Michelle $$= 67 \ – \ 10$$$$3$$ Michelle $$= 57$$Michelle $$= 19$$ 39- Choice C is correct The correct answer is $$2$$ ft.Write a proportion and solve for the missing number.$$\frac{24}{8} =\frac{ 6}{x}→ 24 \ x=6 \ × \ 8=48$$$$24 \ x=48→x=\frac{48}{24}=2$$ 40- Choice D is correct The correct answer is $$12.6$$ square feet$$A = b \ h$$$$A = 3 \ × \ 4.2 = 12.6$$ 41- Choice A is correct The correct answer is $$\ \begin{bmatrix}2 & 0\\0 & - \ 2\\- \ 3 & 3 \end{bmatrix}$$$$\begin{bmatrix}2 & 6 \\- \ 1 & - \ 2\\- \ 5 & - \ 4 \end{bmatrix} \ + \ \begin{bmatrix}0 & - \ 6 \\1 & 0\\2 & 7 \end{bmatrix} = \ \begin{bmatrix}2 & 0\\0 & - \ 2\\- \ 3 & 3 \end{bmatrix}$$ 42- Choice B is correct The correct answer is $$8$$$$7∎13=\sqrt{7^2 \ + \ 15}=\sqrt{49 \ + \ 15} =\sqrt{64} = 8$$ 43- Choice D is correct The correct answer is $$(150) \ (0.85) \ (0.70)$$To find the discount, multiply the number by $$(100\% \ –$$ rate of discount).Therefore, for the first discount we get: $$(150) \ (100\% \ – \ 15\%) = (150) \ (0.85)$$For the next $$15\%$$ discount: $$(150) \ (0.85) \ (0.70)$$ 44- Choice A is correct The correct answer is $$69.11$$ kgAverage $$=\frac{ sum \ of \ terms}{ number \ of \ terms}$$The sum of the weight of all girls is: $$21 \ × \ 65 = 1,365$$ kgThe sum of the weight of all boys is: $$30 \ × \ 72 = 2,160$$ kgThe sum of the weight of all students is: $$1,365 \ + \ 2,160 = 3,525$$ kgAverage $$= \frac{3,525 }{51} = 69.11$$ 45- Choice D is correct The correct answer is $$480$$ LitersLet $$x$$ be the capacity of one tank. Then, $$\frac{3}{4} \ x=320→x=320 \ × \ \frac{3}{4}=240$$ LitersThe amount of water in two tanks is equal to: $$2 \ × \ 240=480$$ Liters 46- Choice C is correct The correct answer is $$- \ 2 \ x^2 \ - \ 2 \ x \ + \ 12$$Use FOIL (First, Out, In, Last)$$(2 \ x \ + \ 6) \ (- \ x \ + \ 2) = - \ 2 \ x^2 \ + 4 \ x \ - \ 6 \ x \ + \ 12 =- \ 2 \ x^2 \ - \ 2 \ x \ + \ 12$$ 47- Choice D is correct The correct answer is $$65 \ π$$To find the area of the shaded region subtract smaller circle from bigger circle.$$S_{bigger} \ – \ S_{smaller} = π \ (r_{bigger} )^2 \ – \ π \ (r_{smaller} )^2 ⇒ S_{bigger} \ – \ S_{smaller }= π \ (9)^2 \ – \ π \ (4)^2$$$$⇒ 81 \ π \ – \ 16 \ π = 65 \ π$$

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Includes ISEE Upper Level Math Prep Books, Workbooks, and Practice Tests

### Practice Test 1

Simulate test day with an official practice test. Then, score your test. The answers come with explanations so you can learn from your mistakes.

### Practice Test 2

Simulate test day with an official practice test. Then, score your test. The answers come with explanations so you can learn from your mistakes.

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