ISEE Upper Math

Question 1

The spinner shown is divided into $4$ equal sections. What is the probability of spinning $Y$?

Accepted Answer

$\frac{1}{4}$

Answer

$\frac{1}{2}$

Answer

$\frac{1}{3}$

Answer

$\frac{3}{4}$

Question 2

For $f(t)=2t+17$, what input $t$ produces output 33?

Accepted Answer

$8$

Answer

$7$

Answer

$9$

Answer

$33$

Question 3

Two adjacent angles form a straight line. One angle measures $115^\circ$, and the other angle measures $x^\circ$. What is the value of $x$?

Accepted Answer

$65^\circ$

Answer

$55^\circ$

Answer

$115^\circ$

Answer

$180^\circ$

Question 4

Which expression is equivalent to $\sqrt{128}$?

Accepted Answer

$8\sqrt2$

Answer

$16\sqrt2$

Answer

$64\sqrt2$

Answer

$4\sqrt2$

Question 5

Which of the following is an integer?

Accepted Answer

$-6$

Answer

$\dfrac{2}{3}$

Answer

$\sqrt{5}$

Answer

$\pi$

Question 6

The bar graph shows how many students in a science class earned each score on the unit test. How many students earned a score of $3$?

Accepted Answer

$11$

Answer

$4$

Answer

$6$

Answer

$9$

Question 7

Which inequality represents the solution to $5-2x<-7$?

Accepted Answer

$x>6$

Answer

$x<-6$

Answer

$x<6$

Answer

$x>12$

Question 8

What is the slope of the line that passes through the points $(-2,-1)$ and $(4,11)$?

Accepted Answer

$2$

Answer

$1$

Answer

$4$

Answer

$8$

Question 9

What is the simple interest on $200$ dollars at $5\%$ per year for $3$ years?

Accepted Answer

$30$

Answer

$10$

Answer

$15$

Answer

$60$

Question 10

A bag contains $5$ red marbles, $3$ blue marbles, and $4$ green marbles. If one marble is chosen at random, what is the probability that it is not blue?

Accepted Answer

$\frac{3}{4}$

Answer

$\frac{1}{4}$

Answer

$\frac{1}{3}$

Answer

$\frac{2}{3}$

Question 11

Which expression is equivalent to $2(x^2-4x)+3x^2+4x$?

Accepted Answer

$5x^2-4x$

Answer

$5x^2-12x$

Answer

$5x^2-8x$

Answer

$6x^2-4x$

Question 12

A cylinder has radius $3$ cm and height $5$ cm. Its volume is $k\pi$ cubic cm. What is $k$?

Accepted Answer

$45$

Answer

$9$

Answer

$15$

Answer

$30$

Question 13

A sequence starts with $3$. Each term after the first is found by multiplying the previous term by the same positive number. If the fourth term is $81$, what is the multiplier?

Accepted Answer

$3$

Answer

$2$

Answer

$4$

Answer

$6$

Question 14

The two triangles shown are similar, with corresponding sides in the same position. What is the length of the side marked $x$?

Accepted Answer

$20$

Answer

$17$

Answer

$18$

Answer

$24$

Question 15

Four quiz scores have a mean of $12$. A fifth score of $22$ is added. What is the new mean?

Accepted Answer

$14$

Answer

$12$

Answer

$16$

Answer

$28$

Question 16

What is the distance between points $A$ and $B$?

Accepted Answer

$10$

Answer

$8$

Answer

$12$

Answer

$14$

Question 17

A cable is 6 yards 4 feet long. What is its total length in inches?

Accepted Answer

$264$

Answer

$76$

Answer

$220$

Answer

$276$

Question 18

The sum of three consecutive even integers is $84$. What is the least of the three integers?

Accepted Answer

$26$

Answer

$24$

Answer

$28$

Answer

$30$

Question 19

A fitness app recorded one person's daily steps (in thousands) for seven days. What is the interquartile range, in thousands, of the daily step counts?

Accepted Answer

$4$

Answer

$5$

Answer

$7$

Answer

$9$

Question 20

What is the value of $(4.8	imes10^3)\div(6	imes10^{-2})$?

Accepted Answer

$80{,}000$

Answer

$80$

Answer

$800$

Answer

$8{,}000$

Question 21

The dark squares form one fabric piece, and each grid segment is $2$ centimeters long. A seam follows the entire boundary, including the indentation at the top. How long is the seam?

Accepted Answer

$36$ centimeters

Answer

$18$ centimeters

Answer

$32$ centimeters

Answer

$44$ centimeters

Question 22

The spinner shown is divided into $8$ equal sections numbered $1$ through $8$. What is the probability of landing on a number that is a multiple of $3$ or an even number?

Accepted Answer

$\dfrac{5}{8}$

Answer

$\dfrac{1}{4}$

Answer

$\dfrac{1}{2}$

Answer

$\dfrac{3}{4}$

Question 23

The right triangle has legs 56 and 192. What is the hypotenuse length?

Accepted Answer

$200$

Answer

$199$

Answer

$201$

Answer

$248$

Question 24

At a coding club, student tickets cost $\$3$ less than adult tickets. One student ticket and one adult ticket together cost $\$17$. What is the cost of a student ticket?

Accepted Answer

$7$

Answer

$8$

Answer

$10$

Answer

$14$

Question 25

Which expression has a value that is a whole number?

Accepted Answer

$\dfrac{\sqrt{72}}{\sqrt{2}}$

Answer

$\sqrt{3}+\sqrt{3}$

Answer

$\dfrac{\sqrt{25}}{2}$

Answer

$\sqrt{49}-8$

Question 26

A science club measured average plant height (in centimeters) under grow lights after several weeks. The bar graph they posted is shown.

Plant Height Under Grow Lights

Which feature of the display could mislead a reader about how the plants grew over time?

Accepted Answer

The horizontal axis gives equal spacing to unequal time intervals.

Answer

The vertical axis starts above zero.

Answer

The vertical axis uses unequal numerical intervals.

Answer

The horizontal axis places weeks out of chronological order.

Question 27

The positive number $s$ satisfies $s^2=242$. What is the value of $2s$?

Accepted Answer

$22\sqrt{2}$

Answer

$11\sqrt{2}$

Answer

$22$

Answer

$484$

Question 28

A circular park has radius $6$ meters. At its center is a circular pond of radius $2$ meters, as indicated in the figure. What is the area, in square meters, of the park that is not covered by the pond?

Accepted Answer

$32\pi$

Answer

$8\pi$

Answer

$16\pi$

Answer

$36\pi$

Question 29

A fair coin is flipped $3$ times. What is the probability of getting at least two heads?

Accepted Answer

$\dfrac{1}{2}$

Answer

$\dfrac{1}{8}$

Answer

$\dfrac{3}{8}$

Answer

$\dfrac{5}{8}$

Question 30

The variable $z$ satisfies $|2z-5|=9$. Which choice gives all possible values of $z$?

Accepted Answer

$z=-2$ and $z=7$

Answer

$z=7$ only

Answer

$z=-2$ only

Answer

$z=-7$ and $z=2$

Question 31

Point $P(-4,2)$ is rotated $90^\circ$ clockwise about the origin and then translated $3$ units up. What are its final coordinates?

Accepted Answer

$(2,7)$

Answer

$(-2,7)$

Answer

$(2,1)$

Answer

$(4,5)$

Question 32

If $f(x-1)=4x+5$ for all $x$, what is the value of $f(2)$?

Accepted Answer

$17$

Answer

$9$

Answer

$13$

Answer

$21$

Question 33

The fair spinner shown is divided into $8$ equal sections. What is the probability that one spin lands on a number that is prime or greater than $5$, but not both?

Accepted Answer

$\dfrac{5}{8}$

Answer

$\dfrac{1}{4}$

Answer

$\dfrac{3}{8}$

Answer

$\dfrac{1}{2}$

Question 34

A garden hose fills a wading pool with water at a rate of $900$ cups per minute. ($2$ cups $=1$ pint, $2$ pints $=1$ quart, $4$ quarts $=1$ gallon.) Which expression can be used to find the rate at which the pool is being filled, in gallons per hour?

Accepted Answer

$\dfrac{900	imes60}{2	imes2	imes4}$

Answer

$900	imes2	imes2	imes4	imes60$

Answer

$\dfrac{900}{2	imes2	imes4	imes60}$

Answer

$\dfrac{900	imes2	imes2	imes4}{60}$

Question 35

Maya cycles $44$ kilometers in $2$ hours. There are $1{,}000$ meters in a kilometer. Which numerical expression represents Maya's average speed in meters per second?

Accepted Answer

$\dfrac{44 	imes 1{,}000}{2 	imes 60 	imes 60}$

Answer

$\dfrac{44 	imes 1{,}000}{2 	imes 60}$

Answer

$\dfrac{44 	imes 60 	imes 60}{2 	imes 1{,}000}$

Answer

$\dfrac{2 	imes 60 	imes 60}{44 	imes 1{,}000}$

Question 36

A cube’s edge length is increased by $50\%$. What is the percent increase in the cube’s surface area?

Accepted Answer

$125\%$

Answer

$50\%$

Answer

$100\%$

Answer

$225\%$

Question 37

Which describes all values of $u$ for which $\lvert 5u+5\rvert < 15$?

Accepted Answer

$-4 < u < 2$

Answer

$u > -4$

Answer

$u < 2$

Answer

$-4 < u < 4$

Question 38

The spinner shown is divided into $5$ equal sections, $2$ of which are shaded. If the spinner is spun twice, what is the probability that it lands on a shaded section exactly once?

Accepted Answer

$\dfrac{12}{25}$

Answer

$\dfrac{4}{25}$

Answer

$\dfrac{6}{25}$

Answer

$\dfrac{16}{25}$

Question 39

What are the solutions of $2x^2-5x-3=0$?

Accepted Answer

$-\dfrac{1}{2}$ and $3$

Answer

$-3$ and $\dfrac{1}{2}$

Answer

$\dfrac{1}{2}$ and $3$

Answer

$-\dfrac{3}{2}$ and $1$

Question 40

For the system of equations $2x+ky=11$ and $3x-2y=4$, the solution satisfies $x=3y$. What is the value of $k$?

Accepted Answer

$\frac{53}{4}$

Answer

$\frac{47}{4}$

Answer

$12$

Answer

$14$

Question 41

A cylinder with radius $3$ inches and height $8$ inches is filled to $\frac{5}{8}$ of its height with water. All of the water is poured into a rectangular tank with base dimensions $9$ inches by $4$ inches. What is the height of the water in the tank?

Accepted Answer

$\frac{5\pi}{4}	ext{ inches}$

Answer

$\frac{3\pi}{2}	ext{ inches}$

Answer

$2\pi	ext{ inches}$

Answer

$\frac{15\pi}{4}	ext{ inches}$

Question 42

A bag contains $5$ red beads, $4$ blue beads, and $3$ green beads. Two beads are chosen without replacement. What is the probability that both beads are the same color?

Accepted Answer

$\dfrac{19}{66}$

Answer

$\dfrac{5}{22}$

Answer

$\dfrac13$

Answer

$\dfrac{7}{18}$

Question 43

Suppose $x$ and $y$ each represent a prime number larger than $3$. What is the least common multiple of the three expressions $5x$, $10xy$, and $15x^2y$?

Accepted Answer

$30x^2y$

Answer

$15x^2y$

Answer

$30xy$

Answer

$30x^2y^2$

Question 44

If $2^a\cdot4^b=2^{10}$ and $a+b=7$, what is the value of $b$?

Accepted Answer

$3$

Answer

$2$

Answer

$4$

Answer

$5$

Question 45

A square has side length $m$ centimeters, as shown. If each side of the square is increased by $3$ centimeters, by how many square centimeters does the area increase?

Accepted Answer

$(6m+9)	ext{ cm}^{2}$

Answer

$(3m+9)	ext{ cm}^{2}$

Answer

$(6m+3)	ext{ cm}^{2}$

Answer

$(9m)	ext{ cm}^{2}$

Question 46

The line $y=2x-1$ intersects the graph of $y=x^2-6x+11$ at two points. What is the sum of the $x$-coordinates of those two points?

Accepted Answer

$8$

Answer

$4$

Answer

$6$

Answer

$12$

Question 47

A survey asked $32$ students at Lincoln Middle School how many pets they own. The frequency bar graph shows the results. Which statement about the data is correct?

Accepted Answer

The median number of pets owned is $1.5$.

Answer

The range in the number of pets owned is $5$.

Answer

The mode for the number of pets owned is $11$.

Answer

The mean number of pets owned is $2$.

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