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Student Directions

This assessment will help us find the best place for you to start your math learning.

Read each question carefully and do your best.
You may use scratch paper to work out problems if needed.
If you are not sure of an answer, make your best guess and move on.
Take your time, but try to work independently without help from a parent or calculator.
The questions may get more challenging as you move through the assessment. That’s okay! Just keep trying your best.

Remember, this is not a graded test. There is no passing or failing. The goal is simply to learn what you already know and what you are ready to learn next.

Let's get started!

Grade 1

1

Count the number of objects:

7

6

8

9

1

Which number is one hundred eighteen?

81

108

180

118

1

$3+5$ =

$9$

$4$

$3$

$8$

1

$13+6$ =

$16$

$19$

$7$

$73$

1

$24+33$ =

$27$

$65$

$67$

$57$

1

$5-2$ =

$9$

$3$

$4$

$7$

1

$10-6$ =

$4$

$6$

$7$

$3$

1

Which fraction is one half?

$\frac{1}{2}$

$1\frac{1}{3}$

$\frac{1}{4}$

$1\frac{1}{2}$

1

Which number in $472$ is in the hundreds’ place?

$2$

$1$

$4$

$7$

1

$3+5-2$ =

$6$

$8$

$4$

$10$

1

How many inches are in a foot?

12

5

10

17

1

Which one of these is a triangle?

Triangle

Rectangle

Circle

Square

1

What time does the clock show?

3:12

12:15

12:03

3:00

1

If Tom had 11 apples and gave 4 to his sister, Jill, how many apples does he have now?

13

8

15

7

1

What are the first three numbers when counting by twos?

2, 3, 4

2, 4, 6

1, 2, 3

1, 3, 5

Grade 2

1

$53+108$ =

$155$

$151$

$165$

$161$

1

$25+12+81$ =

$74$

$118$

$107$

$138$

1

$452+226$ =

$678$

$774$

$588$

$494$

1

$796-92$ =

$692$

$704$

$694$

$888$

1

$489-224$ =

$265$

$244$

$163$

$275$

1

What are the first three numbers in counting by $5$s?

1, 5, 10

5, 6, 7

3, 4, 5

5, 10, 15

1

Jacob has 3 nickels, 2 pennies, and 1 dime. How many cents does he have altogether?

6

22

27

37

1

How many minutes are in an hour?

12

25

10

60

1

How many ounces are in a pound?

16

60

12

10

1

What is $189$ cents in dollars?

$18,900

$1.89

$0.189

$189

1

$54+47$ =

$101$

$91$

$113$

$83$

1

$167+263$ =

$320$

$430$

$1310$

$330$

1

$62-47$ =

$15$

$17$

$25$

$5$

1

What time does the clock show?

5:09

5:45

4:45

9:05

1

Alfred had 84 cents, then he spent 37 cents on a carrot. How many cents does he have left?

41

47

57

53

Grade 3

1

$22-18+37$ =

$49$

$31$

$41$

$53$

1

$263-88$ =

$181$

$113$

$285$

$175$

1

$3\times 4$ =

$12$

$1$

$9$

$7$

1

$6\times 8$ =

$48$

$24$

$14$

$45$

Grade 4

1

What number is eight million, sixty-five thousand, seven?

8,065,007

8,000,657

8,657

1,800,065,007

1

What time does the clock show?

1:05

1:25

5:05

5:01

1

What is the value of the Roman numeral CXXXIV?

84

134

86

136

1

How many meters are in $5$ kilometers?

$500$

$5{,}000$

$1{,}000$

$15$

1

$600-346$ =

$266$

$264$

$254$

$356$

1

$34\div 6$ =

$5$

$5\ \text{R}\ 4$

$6$

$5\ \text{R}\ 6$

1

$1{,}982+3{,}092+5{,}863$ =

$9{,}837$

$10{,}937$

$9{,}747$

$11{,}147$

1

What is $\frac{8}{16}$ in lowest terms?

$\frac{2}{4}$

$\frac{0}{8}$

$\frac{1}{16}$

$\frac{1}{2}$

1

Ben spent $12.85 for a dictionary and $0.69 for a bookmark. What was his change from $20.00?

$6.46

$8.66

$7.56

$7.46

1

Which number is a factor of $12$?

$5$

$8$

$11$

$4$

1

According to the graph, how many more books did Daniel read than Abigail?

$3$

$1$

$4$

$7$

1

$\frac{2}{3}+\frac{5}{12}$ =

$1\frac{1}{12}$

$1\frac{3}{12}$

$\frac{7}{15}$

$\frac{7}{12}$

1

$5{,}130\div 6$ =

$848\ \text{R}\ 5$

$855$

$954\ \text{R}\ 2$

$866$

1

What is the average of $16$, $12$, $20$, $24$, and $18$?

$18$

$17$

$12$

$24$

1

$2{,}450\times 7$ =

14,835

16,100

17,150

16,850

Grade 5

1

How many minutes are in $7$ hours?

420 minutes

540 minutes

350 minutes

700 minutes

1

What is $4$ gal. and $3$ qt. plus $6$ gal. and $2$ qt. plus $3$ gal. and $3$ qt.?

14 gallons

14 gallons and 3 quarts

15 gallons

14 gallons and 2 quarts

1

What is the greatest common factor of $12$ and $32$?

$2$

$12$

$4$

$64$

1

Which number is a prime number?

$6$

$13$

$9$

$4$

1

$786\times 213$ =

167,218

147,218

167,418

4,716

1

Which number in $4.837$ is in the hundredths’ place?

$4$

$8$

$3$

$7$

1

$6.37+3.045+0.802$ =

$9.884$

$9.1217$

$10.184$

$10.217$

1

$6.490\times 58$ =

$78.67$

$352.72$

$84.37$

$376.42$

1

The fraction $\frac{3}{20}$ is equal to what percent?

$33%$

$15%$

$20%$

$3%$

1

$\frac{2}{3}\times 4$ =

$\frac{8}{12}$

$\frac{6}{3}$

$\frac{8}{7}$

$\frac{8}{3}$

1

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

$\frac{1}{5}$

$\frac{3}{5}$

$\frac{1}{2}$

$\frac{5}{7}$

1

What is the freezing point of water on the Fahrenheit scale?

$-40^\circ!\text{F}$

$100^\circ!\text{F}$

$0^\circ!\text{F}$

$32^\circ!\text{F}$

1

What type of angle is this?

Straight

Acute

Right

Obtuse

1

Which pair of shapes are congruent?

A

B

C

D

1

What is the perimeter of the rectangle?

2 ft.

24 ft.

18 ft.

36 ft.

Grade 6

1

If Henry travels $442$ miles at $52$ m.p.h., how long will it take him to reach his destination?

$9.1$ hours

$6.6$ hours

$8.5$ hours

$7$ hours

1

What are the prime factors of $84$?

2, 2, 3, 7

3, 7, 11

2, 2, 2, 3, 3

2, 2, 2, 5

1

What is the least common multiple of $16$ and $36$?

$84$

$36$

$144$

$178$

1

$3\frac{3}{8}\div 2\frac{7}{10}$ =

$1\frac{1}{4}$

$6\frac{21}{80}$

$1\frac{1}{9}$

$9\frac{1}{9}$

1

What number is MCXLVII?

1,642

647

1,147

967

1

What is $12.905786$ rounded to the nearest thousandth?

$12.905$

$12.9057$

$12.9058$

$12.906$

1

How many centiliters are in $13$ hectoliters?

130

13,000

130,000

1,300

1

How many pounds are in a kilogram?

1.15

5.0

2.2

0.87

1

$56%$ of $125$ =

$70$

$137.5$

$56$

$108$

1

$18$ is what percent of $30$?

$54%$

$60%$

$16.6%$

$6%$

1

If James buys a book for $4.67, sells it for $9.95, and pays a shipping cost of $1.37, how much is his profit?

$4.08

$3.91

$5.28

$9.95

1

What is the area of the triangle?

$60$ ft.$^2$

$30$ ft.$^2$

$216$ ft.$^2$

$108$ ft.$^2$

1

What is the circumference of a circle with a radius of $2.5$ inches, to the nearest tenth?

$12.5$ inches

$19.6$ inches

$7.9$ inches

$15.7$ inches

1

What type of triangle is this?

Acute

Right

Equilateral

Obtuse

1

According to the graph, which three continents combined make up less than one-quarter of the land area of the earth?

South America, Oceania, Asia

Africa, Antarctica, Europe

Antarctica, South America, Africa

Europe, Oceania, Antarctica

Grade 7

1

$165%$ of $80$ =

$197$

$132$

$52$

$157$

1

$165%$ of $80$ =

$197$

$52$

$132$

$157$

1

Phillip receives a $15%$ commission on everything he sells at work. One day, he sold a lawn mower for $53 and a set of flower boxes for $15. How much did Phillip make in commissions for those two items?

$17.87

$21.87

$10.20

$9.20

1

Phillip receives a $15%$ commission on everything he sells at work. One day, he sold a lawn mower for $53 and a set of flower boxes for $15. How much did Phillip make in commissions for those two items?

$21.87

$10.20

$9.20

$17.87

1

If an $8$ ounce block of cheese costs $3.36, how much does the cheese cost per ounce?

$0.27

$0.42

$0.67

$1.09

1

On one round trip to Central America, the beginning odometer reading on the vehicle was 72,121 miles. The oil was changed at 75,124 miles, and at the end of the trip the odometer showed 79,115 miles. At $11$ miles per gallon, how many gallons of fuel did the vehicle use on the trip?

$497$

$362\frac{9}{11}$

$273$

$635\frac{9}{11}$

1

What is the volume of the cylinder to the nearest tenth of a cubic centimeter?

$25.1$ cm$^3$

$37.7$ cm$^3$

$50.3$ cm$^3$

$16.0$ cm$^3$

1

What is $68^\circ!\text{F}$ in Celsius to the nearest degree?

$45^\circ!\text{C}$

$8^\circ!\text{C}$

$38^\circ!\text{C}$

$20^\circ!\text{C}$

1

What is $0.\overline{1}$ in fractional form?

$\frac{1}{9}$

$\frac{1}{11}$

$\frac{3}{22}$

$\frac{4}{29}$

1

$(6-3)8-4$ =

$-6$

$12$

$20$

$7$

1

What is $7$ times $5$ ft. $9$ in.?

38 ft. 9 in.

41 ft. 3 in.

44 ft. 7 in.

40 ft. 3 in.

1

$6^2$ =

$12$

$54$

$36$

$8$

1

$\sqrt{64}$ =

$8$

$4$

$16$

$32$

1

$(-9)+7-(-3)$ =

$1$

$19$

$16$

$-5$

1

$\frac{6(-4)}{-3}$ =

$\frac{10}{3}$

$8$

$-8$

$\frac{2}{-3}$

1

If $a=2$, $b=3$, and $c=4$, then $ab+c$ =

$15$

$9$

$10$

$24$

1

If $x-12=24$, then $x$ =

$12$

$40$

$16$

$36$

Grade 8

1

$2[3+3(12-3^2)]$ =

$42$

$33$

$36$

$24$

1

Find the value of $n$ in this equation: $\frac{3}{2}=\frac{n}{120}$

$130$

$180$

$80$

$160$

1

Find the median of these numbers:
1, 1, 1, 2, 5, 5, 6, 7, 8

6.3

5

4

1

What is the length of the triangle’s hypotenuse? Use the Pythagorean rule to solve.

$21$

$14.2$

$18.5$

$15$

1

$4^6\div 4^2$ =

$4^4$

$12$

$3$

$4^3$

1

$2x-4x+6x$ =

$8x+1$

$12x$

$4-4x$

$4x$

1

At a produce market, apples originally cost $1.70 per pound. The apples are now discounted by $20%$. With the discount, how much do $5$ pounds of apples cost, to the nearest cent?

$7.33

$1.70

$6.80

$3.47

1

In simplified form, $\frac{x^9}{x^3}\cdot x$ =

$x^7$

$x^4$

$x^3$

$x^6$

1

$5s-4t-2s+3t+6$ =

$8st$

$2st+6$

$3s-t+6$

$3s(-t)6$

1

What is the area of this shape? (excluding any shaded portion)

$97.3$ in.$^2$

$114.1$ in.$^2$

$213.1$ in.$^2$

$128.3$ in.$^2$

1

What is the surface area of the rectangular solid?

$128$ in.$^2$

$236$ in.$^2$

$240$ in.$^2$

$256$ in.$^2$

1

What is the simple interest on $525 at $4%$ for $5$ years?

$262.50

$105.00

$73.20

$4.20

1

What is the square root of $17{,}424$?

268

132

418

148

1

Marlene is three times older than Darren. The sum of their ages is $36$. How old is Darren?

9

5

12

27

1

Which shape is an irregular heptagon?

A

B

C

D

Math Diagnostic Test Grades 1 - 8

Math Diagnostic Test Grades 1 - 8

Student Directions

Count the number of objects:

Which number is one hundred eighteen?

$3+5$ =

$13+6$ =

$24+33$ =

$5-2$ =

$10-6$ =

Which fraction is one half?

Which number in $472$ is in the hundreds’ place?

$3+5-2$ =

How many inches are in a foot?

Which one of these is a triangle?

What time does the clock show?

If Tom had 11 apples and gave 4 to his sister, Jill, how many apples does he have now?

What are the first three numbers when counting by twos?

$53+108$ =

$25+12+81$ =

$452+226$ =

$796-92$ =

$489-224$ =

What are the first three numbers in counting by $5$s?

Jacob has 3 nickels, 2 pennies, and 1 dime. How many cents does he have altogether?

How many minutes are in an hour?

How many ounces are in a pound?

What is $189$ cents in dollars?

$54+47$ =

$167+263$ =

$62-47$ =

What time does the clock show?

Alfred had 84 cents, then he spent 37 cents on a carrot. How many cents does he have left?

$22-18+37$ =

$263-88$ =

$3\times 4$ =

$6\times 8$ =

What number is eight million, sixty-five thousand, seven?

What time does the clock show?

What is the value of the Roman numeral CXXXIV?

How many meters are in $5$ kilometers?

$600-346$ =

$34\div 6$ =

$1{,}982+3{,}092+5{,}863$ =

What is $\frac{8}{16}$ in lowest terms?

Ben spent $12.85 for a dictionary and $0.69 for a bookmark. What was his change from $20.00?

Which number is a factor of $12$?

According to the graph, how many more books did Daniel read than Abigail?

$\frac{2}{3}+\frac{5}{12}$ =

$5{,}130\div 6$ =

What is the average of $16$, $12$, $20$, $24$, and $18$?

$2{,}450\times 7$ =

How many minutes are in $7$ hours?

What is $4$ gal. and $3$ qt. plus $6$ gal. and $2$ qt. plus $3$ gal. and $3$ qt.?

What is the greatest common factor of $12$ and $32$?

Which number is a prime number?

$786\times 213$ =

Which number in $4.837$ is in the hundredths’ place?

$6.37+3.045+0.802$ =

$6.490\times 58$ =

The fraction $\frac{3}{20}$ is equal to what percent?

$\frac{2}{3}\times 4$ =

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

What is the freezing point of water on the Fahrenheit scale?

What type of angle is this?

Which pair of shapes are congruent?

What is the perimeter of the rectangle?

If Henry travels $442$ miles at $52$ m.p.h., how long will it take him to reach his destination?

What are the prime factors of $84$?

What is the least common multiple of $16$ and $36$?

$3\frac{3}{8}\div 2\frac{7}{10}$ =

What number is MCXLVII?

What is $12.905786$ rounded to the nearest thousandth?

How many centiliters are in $13$ hectoliters?

How many pounds are in a kilogram?

$56%$ of $125$ =

$18$ is what percent of $30$?

If James buys a book for $4.67, sells it for $9.95, and pays a shipping cost of $1.37, how much is his profit?

What is the area of the triangle?

What is the circumference of a circle with a radius of $2.5$ inches, to the nearest tenth?

Find the median of these numbers:
1, 1, 1, 2, 5, 5, 6, 7, 8